Noesis

Study checklist

Every topic across all 8 subjects — 3,512 in total. Tick topics off as you master them; progress lives in this browser.

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3,512 topics

Physics

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1.1Measurement, Vectors & Kinematics0 / 22
  1. 1.1.1Physical quantities — fundamental and derived
  2. 1.1.2SI units — seven base units and all derived units
  3. 1.1.3Dimensional analysis — checking equations, deriving relations
  4. 1.1.4Significant figures — rules for operations
  5. 1.1.5Errors — absolute, relative, percentage; systematic vs random
  6. 1.1.6Scalars vs vectors — definition, examples
  7. 1.1.7Vector representation — magnitude, direction, components
  8. 1.1.8Vector addition — triangle law, parallelogram law
  9. 1.1.9Resolution of vectors — into components (any axes)
  10. 1.1.10Unit vectors — î, ĵ, k̂; constructing unit vector
  11. 1.1.11Dot product — formula, geometric meaning, work calculation
  12. 1.1.12Cross product — formula, direction (right-hand rule), torque - area calculation
  13. 1.1.13Position vector, displacement, distance
  14. 1.1.14Average velocity vs instantaneous velocity
  15. 1.1.15Average acceleration vs instantaneous acceleration
  16. 1.1.16Equations of motion (SUVAT) — derivations from calculus
  17. 1.1.17Free fall — g = 9.8 m - s², sign conventions
  18. 1.1.18Graphs — x-t, v-t, a-t; areas and slopes meaning
  19. 1.1.19Projectile motion — horizontal - vertical independence, full derivation
  20. 1.1.20Range, max height, time of flight — all derived
  21. 1.1.21Relative motion — 1D and 2D; river-boat problems
  22. 1.1.22Reference frames — Galilean transformations
1.2Newton's Laws & Dynamics0 / 25
  1. 1.2.1Newton's first law — inertia, operational definition of force
  2. 1.2.2Newton's second law — F = ma (net force), impulse-momentum form
  3. 1.2.3Newton's third law — action-reaction, common misconceptions
  4. 1.2.4Free body diagrams — systematic drawing technique
  5. 1.2.5Normal force — reaction force, not always = mg
  6. 1.2.6Friction — static (maximum), kinetic, rolling
  7. 1.2.7Coefficients of friction — measurement, material dependence
  8. 1.2.8Angle of friction, angle of repose — derivation
  9. 1.2.9Tension in inextensible strings
  10. 1.2.10Atwood machine — derivation
  11. 1.2.11Inclined planes — with and without friction
  12. 1.2.12Pulley systems — mechanical advantage
  13. 1.2.13Non-inertial reference frames — pseudo forces
  14. 1.2.14Rotating frames — centrifugal force, Coriolis force
  15. 1.2.15Circular motion — centripetal acceleration derivation
  16. 1.2.16Centripetal force — what provides it in various situations
  17. 1.2.17Banking of roads — derivation
  18. 1.2.18Vertical circular motion — minimum speed conditions
  19. 1.2.19Newton's law of gravitation — universal, action at distance
  20. 1.2.20Gravitational field intensity g = GM - r²
  21. 1.2.21Variation of g — with altitude, latitude, depth
  22. 1.2.22Gravitational potential energy — U = −GMm - r (not mgh)
  23. 1.2.23Escape velocity — derivation
  24. 1.2.24Orbital velocity for circular orbit — derivation
  25. 1.2.25Weightlessness — true (free fall) vs apparent
1.3Work, Energy & Power0 / 13
  1. 1.3.1Work — definition, dot product F·d, sign convention
  2. 1.3.2Work done by variable force — integration
  3. 1.3.3Work-energy theorem — derivation from Newton's second law
  4. 1.3.4Kinetic energy — derivation
  5. 1.3.5Potential energy — definition, gravitational (mgh and −GMm - r), elastic (½kx²)
  6. 1.3.6Conservative forces — path-independent work, potential energy defined
  7. 1.3.7Non-conservative forces — friction, air drag
  8. 1.3.8Conservation of mechanical energy — derivation
  9. 1.3.9Power — average and instantaneous, units
  10. 1.3.10Efficiency
  11. 1.3.11Hooke's law — spring force F = −kx
  12. 1.3.12Spring potential energy — derivation
  13. 1.3.13Spring-mass systems — collision problems
1.4Momentum & Collisions0 / 12
  1. 1.4.1Linear momentum p = mv
  2. 1.4.2Impulse-momentum theorem — derivation
  3. 1.4.3Conservation of linear momentum — derivation from Newton's third law
  4. 1.4.4System with external forces — conditions for conservation
  5. 1.4.5Elastic collisions — 1D - solve for final velocities
  6. 1.4.6Elastic collisions — 2D - angle relationship
  7. 1.4.7Perfectly inelastic collisions — maximum KE loss
  8. 1.4.8Coefficient of restitution e = (v₂ − v₁) - (u₁ − u₂)
  9. 1.4.9Centre of mass — definition for system of particles
  10. 1.4.10Centre of mass — derivation for common shapes (rod, triangle, semicircle, hemisphere)
  11. 1.4.11Motion of centre of mass — external force determines a_CM
  12. 1.4.12Systems with variable mass — rocket equation derivation preview
1.5Rotational Mechanics0 / 18
  1. 1.5.1Rigid body — definition, degrees of freedom
  2. 1.5.2Angular displacement θ, angular velocity ω, angular acceleration α
  3. 1.5.3Relation to linear quantities - v = rω, a_t = rα, a_c = rω²
  4. 1.5.4Torque τ = r × F — definition, physical meaning
  5. 1.5.5Moment of inertia I = Σmᵢrᵢ² — concept
  6. 1.5.6Parallel axis theorem — I = I_CM + Md² — proof
  7. 1.5.7Perpendicular axis theorem — I_z = I_x + I_y — proof, restrictions
  8. 1.5.8Moment of inertia of - rod (about end, centre), disk, ring, sphere (solid, hollow), cylinder
  9. 1.5.9Rotational kinetic energy = ½Iω²
  10. 1.5.10Angular momentum L = Iω (fixed axis), L = r × p (general)
  11. 1.5.11Torque = dL - dt
  12. 1.5.12Conservation of angular momentum — conditions
  13. 1.5.13Rolling without slipping — v = Rω condition
  14. 1.5.14Rolling KE = ½mv² + ½Iω²
  15. 1.5.15Acceleration of rolling objects on inclines — comparison
  16. 1.5.16Gyroscopic effect — precession of spinning top
  17. 1.5.17Gyroscope in spacecraft attitude control — preview
  18. 1.5.18Equilibrium of rigid bodies — translational + rotational
1.6Oscillations & Waves0 / 23
  1. 1.6.1Simple harmonic motion — definition, restoring force F = −kx
  2. 1.6.2SHM differential equation — solution - x = A cos(ωt + φ)
  3. 1.6.3ω, T, f relationships
  4. 1.6.4Velocity and acceleration in SHM — v = ω√(A² − x²)
  5. 1.6.5Energy in SHM — KE + PE = ½kA² (constant)
  6. 1.6.6Simple pendulum — small angle approximation, T = 2π√(L - g) derivation
  7. 1.6.7Physical pendulum — compound pendulum
  8. 1.6.8Spring-mass system — horizontal, vertical
  9. 1.6.9Damped oscillations — underdamped, critically damped, overdamped
  10. 1.6.10Q factor — quality of oscillator
  11. 1.6.11Forced oscillations — driving frequency
  12. 1.6.12Resonance — physical consequences, design implications
  13. 1.6.13Mechanical waves — transverse and longitudinal
  14. 1.6.14Wave parameters — amplitude, wavelength, frequency, period, wave speed
  15. 1.6.15Wave equation — derivation for string
  16. 1.6.16Superposition principle
  17. 1.6.17Interference — constructive, destructive conditions
  18. 1.6.18Standing waves — formation, nodes, antinodes
  19. 1.6.19Harmonics and overtones — on strings and in pipes
  20. 1.6.20Beats — derivation, applications
  21. 1.6.21Doppler effect — all cases - source moving, observer moving, both
  22. 1.6.22Shock waves — Mach number, Mach cone — - CRITICAL for rockets -
  23. 1.6.23Sound intensity — decibels (logarithmic scale)
1.7Thermodynamics0 / 26
  1. 1.7.1Temperature — thermal equilibrium, thermometers, scales
  2. 1.7.2Zeroth law — transitivity of thermal equilibrium
  3. 1.7.3Heat and internal energy — microscopic vs macroscopic
  4. 1.7.4Specific heat capacity — calorimetry
  5. 1.7.5Latent heat — phase transitions
  6. 1.7.6Heat transfer — conduction (Fourier's law k), convection, radiation (Stefan-Boltzmann σT⁴)
  7. 1.7.7Thermal expansion — linear, area, volumetric
  8. 1.7.8Ideal gas law PV = nRT — derivation from kinetic theory
  9. 1.7.9Kinetic theory — pressure derivation, temperature as mean KE
  10. 1.7.10Internal energy of ideal gas U = (f - 2)nRT
  11. 1.7.11Mean free path, mean speed, RMS speed — derivations
  12. 1.7.12Maxwell-Boltzmann speed distribution — derivation (key for propulsion)
  13. 1.7.13First law of thermodynamics — dU = dQ − dW, sign conventions
  14. 1.7.14Thermodynamic processes — isothermal (T const), isochoric (V const), isobaric (P const), adiabatic (Q = 0)
  15. 1.7.15Work done in each process — derivation
  16. 1.7.16Adiabatic relations — PV^γ = const, TV^(γ−1) = const (derivation)
  17. 1.7.17γ = Cp - Cv — for monatomic, diatomic, polyatomic
  18. 1.7.18Second law — Kelvin-Planck statement, Clausius statement
  19. 1.7.19Heat engines — efficiency η = 1 − Q_C - Q_H
  20. 1.7.20Refrigerators and heat pumps — COP
  21. 1.7.21Carnot cycle — full derivation, efficiency = 1 − T_C - T_H
  22. 1.7.22Entropy — Clausius definition dS = dQ_rev - T
  23. 1.7.23Entropy change in irreversible processes — always - 0
  24. 1.7.24Entropy and disorder — Boltzmann S = k·ln(W)
  25. 1.7.25Third law of thermodynamics — S → 0 as T → 0
  26. 1.7.26Thermodynamic potentials — U, H, F, G (preview)
1.8Electromagnetism0 / 36
  1. 1.8.1Electric charge — properties, quantization, conservation
  2. 1.8.2Coulomb's law — force, comparison with gravity
  3. 1.8.3Superposition principle for forces
  4. 1.8.4Electric field — definition, field lines, superposition
  5. 1.8.5Electric field of point charge, dipole, ring, disk, line charge (Gauss's law)
  6. 1.8.6Gauss's law — integral form, choosing Gaussian surfaces
  7. 1.8.7Applications — sphere, cylinder, infinite plane
  8. 1.8.8Electric potential — definition V = −∫E·dl
  9. 1.8.9Potential of point charge, potential from field and vice versa
  10. 1.8.10Equipotential surfaces — perpendicular to field
  11. 1.8.11Capacitance — parallel plate derivation, cylindrical, spherical
  12. 1.8.12Series and parallel capacitors — derivations
  13. 1.8.13Energy stored in capacitor U = ½CV²
  14. 1.8.14Dielectrics — polarization, dielectric constant, effect on capacitance
  15. 1.8.15Drift velocity, mobility, conductivity
  16. 1.8.16Ohm's law — microscopic origin, resistivity
  17. 1.8.17Series and parallel resistance
  18. 1.8.18Kirchhoff's current law (KCL), Kirchhoff's voltage law (KVL)
  19. 1.8.19RC circuits — charging, discharging, time constant τ = RC
  20. 1.8.20Magnetic force on charge — F = qv × B
  21. 1.8.21Magnetic force on current-carrying conductor
  22. 1.8.22Biot-Savart law — magnetic field from current element
  23. 1.8.23Ampere's circuital law — magnetostatic form
  24. 1.8.24Magnetic field of straight wire, circular loop, solenoid, toroid
  25. 1.8.25Magnetic flux Φ = ∫B·dA
  26. 1.8.26Faraday's law — EMF = −dΦ - dt
  27. 1.8.27Lenz's law — opposing induced current
  28. 1.8.28Self-inductance L, mutual inductance M
  29. 1.8.29RL circuit — growth and decay of current
  30. 1.8.30LC circuit — oscillations (electrical analog of SHM)
  31. 1.8.31Maxwell's equations — integral form, all four
  32. 1.8.32Displacement current — Maxwell's addition to Ampere's law
  33. 1.8.33Electromagnetic waves — derivation from Maxwell's equations
  34. 1.8.34Speed of light c = 1 - √(ε₀ μ₀)
  35. 1.8.35EM spectrum — all bands and applications
  36. 1.8.36Poynting vector — energy flux in EM waves
2.1Analytical Mechanics0 / 25
  1. 2.1.1Constraints — holonomic vs non-holonomic, rheonomic vs scleronomic
  2. 2.1.2Generalized coordinates — choosing them, degrees of freedom
  3. 2.1.3Kinetic energy in generalized coordinates
  4. 2.1.4Lagrangian L = T − V
  5. 2.1.5Derivation of Euler-Lagrange equations from D'Alembert's principle
  6. 2.1.6Applying E-L equations to various systems
  7. 2.1.7Generalized momenta and generalized forces
  8. 2.1.8Cyclic coordinates — corresponding conservation law
  9. 2.1.9Noether's theorem — symmetry ↔ conservation law
  10. 2.1.10Constraints using Lagrange multipliers
  11. 2.1.11Hamiltonian — definition H = Σpᵢq̇ᵢ − L
  12. 2.1.12Hamilton's equations of motion
  13. 2.1.13Phase space — trajectories, phase portraits
  14. 2.1.14Liouville's theorem — phase space volume conservation
  15. 2.1.15Poisson brackets — definition, properties, connection to commutators
  16. 2.1.16Canonical transformations — generating functions
  17. 2.1.17Hamilton-Jacobi equation
  18. 2.1.18Action-angle variables — integrable systems
  19. 2.1.19Principle of least action — Hamilton's principle derivation
  20. 2.1.20Normal modes — coupled oscillators, normal coordinates
  21. 2.1.21Rigid body dynamics — Euler angles, Euler's equations of motion
  22. 2.1.22Inertia tensor — principal axes, principal moments
  23. 2.1.23Torque-free rotation — Euler's equations, asymmetric top
  24. 2.1.24Gyroscope — steady precession derivation
  25. 2.1.25Chaotic systems — sensitivity to initial conditions, Lyapunov exponents
2.2Fluid Mechanics0 / 30
  1. 2.2.1Fluid definition — shear stress, no fixed shape
  2. 2.2.2Density, specific gravity
  3. 2.2.3Viscosity — dynamic μ, kinematic ν = μ - ρ; Newtonian vs non-Newtonian
  4. 2.2.4Surface tension — origin, Young-Laplace equation
  5. 2.2.5Hydrostatics — pressure = ρgh, derivation
  6. 2.2.6Pascal's law — pressure transmits equally
  7. 2.2.7Buoyancy — Archimedes' principle, derivation from pressure difference
  8. 2.2.8Manometers, barometers
  9. 2.2.9Fluid kinematics — Eulerian vs Lagrangian description
  10. 2.2.10Streamlines, pathlines, streaklines
  11. 2.2.11Stream function, velocity potential
  12. 2.2.12Continuity equation — derivation (conservation of mass), ρAv = const
  13. 2.2.13Reynolds transport theorem
  14. 2.2.14Bernoulli's equation — derivation from F = ma along streamline
  15. 2.2.15Assumptions in Bernoulli — steady, inviscid, incompressible, along streamline
  16. 2.2.16Applications — Pitot tube, Venturi meter, orifice flow
  17. 2.2.17Viscous flow — Poiseuille flow, velocity profile in pipe
  18. 2.2.18Navier-Stokes equations — derivation from Newton's second law for fluid
  19. 2.2.19Reynolds number Re = ρvL - μ — laminar vs turbulent criterion
  20. 2.2.20Boundary layer — Prandtl's concept, growth along flat plate
  21. 2.2.21Boundary layer thickness, displacement thickness, momentum thickness
  22. 2.2.22Blasius solution — exact laminar boundary layer solution
  23. 2.2.23Boundary layer separation — adverse pressure gradient
  24. 2.2.24Drag — pressure (form) drag, skin friction drag
  25. 2.2.25Lift — Kutta-Joukowski theorem L = ρV∞Γ
  26. 2.2.26Dimensional analysis — Buckingham π theorem
  27. 2.2.27Similarity — geometric, kinematic, dynamic; Reynolds similarity
  28. 2.2.28Potential flow — irrotational, inviscid; superposition of basic flows
  29. 2.2.29Vorticity — ω = ∇ × v, circulation Γ
  30. 2.2.30Kelvin's circulation theorem
2.3Modern Physics0 / 33
  1. 2.3.1Blackbody radiation — Planck's quantum hypothesis
  2. 2.3.2Photoelectric effect — Einstein's explanation, work function
  3. 2.3.3Photon properties — E = hf, p = h - λ
  4. 2.3.4Compton scattering — wavelength shift derivation
  5. 2.3.5De Broglie hypothesis — matter waves λ = h - p
  6. 2.3.6Davisson-Germer experiment — electron diffraction
  7. 2.3.7Heisenberg uncertainty principle — Δx Δp ≥ ℏ - 2, ΔE Δt ≥ ℏ - 2
  8. 2.3.8Wave function ψ — probability density - ψ - ²
  9. 2.3.9Schrödinger equation — time-dependent, time-independent
  10. 2.3.10Particle in a box — solving TISE, energy levels, wavefunctions
  11. 2.3.11Quantum tunneling — concept, transmission coefficient
  12. 2.3.12Hydrogen atom — solving in spherical coordinates
  13. 2.3.13Quantum numbers n, l, mₗ, mₛ
  14. 2.3.14Hydrogen energy levels Eₙ = −13.6 - n² eV
  15. 2.3.15Spectral series — Lyman, Balmer, Paschen
  16. 2.3.16Pauli exclusion principle
  17. 2.3.17Spin — intrinsic angular momentum
  18. 2.3.18Nuclear structure — protons, neutrons, nuclear forces
  19. 2.3.19Binding energy — mass defect, BE per nucleon curve
  20. 2.3.20Nuclear reactions — Q-value calculation
  21. 2.3.21Radioactive decay — alpha, beta, gamma — mechanisms
  22. 2.3.22Decay law — N = N₀ e^(−λt), half-life, activity
  23. 2.3.23Fission — chain reaction, critical mass
  24. 2.3.24Fusion — solar fusion, tokamak (concept)
  25. 2.3.25Special relativity — Michelson-Morley experiment
  26. 2.3.26Postulates of SR
  27. 2.3.27Simultaneity — relativity of simultaneity
  28. 2.3.28Lorentz transformation — derivation
  29. 2.3.29Time dilation — derivation, twin paradox
  30. 2.3.30Length contraction — derivation
  31. 2.3.31Relativistic momentum p = γmv
  32. 2.3.32Mass-energy equivalence E² = (pc)² + (mc²)²
  33. 2.3.33General relativity — equivalence principle, curved spacetime (overview)
2.4Thermodynamics & Statistical Mechanics (Advanced)0 / 19
  1. 2.4.1Thermodynamic potentials — U (internal), H (enthalpy), F (Helmholtz), G (Gibbs)
  2. 2.4.2Legendre transforms connecting them
  3. 2.4.3Maxwell relations — derivation from each potential
  4. 2.4.4Gibbs-Helmholtz equation
  5. 2.4.5Chemical potential μ = (∂G - ∂N)_{T,P}
  6. 2.4.6Phase equilibrium — Clausius-Clapeyron equation
  7. 2.4.7Phase rule — Gibbs phase rule
  8. 2.4.8Statistical mechanics — microstate, macrostate
  9. 2.4.9Boltzmann's entropy S = k_B ln(Ω)
  10. 2.4.10Canonical ensemble — partition function Z
  11. 2.4.11Average energy from partition function
  12. 2.4.12Free energy from partition function
  13. 2.4.13Maxwell-Boltzmann distribution — full derivation
  14. 2.4.14Equipartition theorem — ½k_BT per quadratic degree of freedom
  15. 2.4.15Quantum statistics — distinguishable vs indistinguishable particles
  16. 2.4.16Bose-Einstein statistics — bosons
  17. 2.4.17Fermi-Dirac statistics — fermions, Fermi energy
  18. 2.4.18Bose-Einstein condensation — concept
  19. 2.4.19Blackbody radiation from statistical mechanics — Planck distribution
2.5Optics0 / 18
  1. 2.5.1Geometric optics — rectilinear propagation, reflection, refraction
  2. 2.5.2Mirrors — plane, concave, convex; mirror equation 1 - v + 1 - u = 1 - f
  3. 2.5.3Sign convention for mirrors and lenses
  4. 2.5.4Snell's law — derivation from Fermat's principle
  5. 2.5.5Total internal reflection — critical angle derivation
  6. 2.5.6Thin lenses — lens equation, lens maker's equation
  7. 2.5.7Power of a lens, combination of lenses
  8. 2.5.8Optical instruments — human eye, simple microscope, compound microscope, telescope
  9. 2.5.9Aberrations — chromatic, spherical (concepts)
  10. 2.5.10Huygens' principle — wavefront propagation
  11. 2.5.11Young's double slit — fringe width derivation
  12. 2.5.12Thin film interference — reflected and transmitted
  13. 2.5.13Newton's rings — derivation
  14. 2.5.14Diffraction — single slit intensity pattern derivation
  15. 2.5.15Diffraction grating — condition for maxima
  16. 2.5.16Resolving power — Rayleigh criterion
  17. 2.5.17Polarization — Malus's law, Brewster's angle derivation
  18. 2.5.18Birefringence — ordinary and extraordinary rays
3.1Compressible Flow & Aerodynamics0 / 30
  1. 3.1.1Review of thermodynamics applied to flow — first law for open systems
  2. 3.1.2Stagnation (total) quantities — T₀, P₀, ρ₀ — derivations
  3. 3.1.3Speed of sound — a = √(γRT) — derivation
  4. 3.1.4Mach number M = V - a — subsonic ( - 1), transonic (~1), supersonic ( - 1), hypersonic ( - 5)
  5. 3.1.5Area-velocity relation — dA - A = (M² − 1)(dV - V) — derivation (explains de Laval nozzle)
  6. 3.1.6Area-Mach number relation A - A - = f(M) — isentropic flow
  7. 3.1.7Isentropic flow tables — P - P₀, T - T₀, ρ - ρ₀ as functions of M
  8. 3.1.8Choked flow — condition M = 1 at throat, maximum mass flow
  9. 3.1.9Converging nozzle — subsonic flow, Mach 1 at exit
  10. 3.1.10Converging-diverging (de Laval) nozzle — subsonic, supersonic flow
  11. 3.1.11Normal shock waves — Rankine-Hugoniot relations (all 5) — derivations
  12. 3.1.12Normal shock properties — M₂, P₂ - P₁, T₂ - T₁, ρ₂ - ρ₁, P₀₂ - P₀₁
  13. 3.1.13Oblique shock waves — θ-β-M relation
  14. 3.1.14Shock wave angle, deflection angle
  15. 3.1.15Detached bow shock
  16. 3.1.16Prandtl-Meyer expansion waves — isentropic, supersonic turning
  17. 3.1.17Prandtl-Meyer function ν(M)
  18. 3.1.18Over - under expanded nozzle flows
  19. 3.1.19Airfoil aerodynamics — camber, chord, thickness
  20. 3.1.20Angle of attack, lift coefficient, drag coefficient
  21. 3.1.21Thin airfoil theory — lift per unit span = πρV²(α + 2β - π c)
  22. 3.1.22Finite wing theory — induced drag, Prandtl's lifting line
  23. 3.1.23Aspect ratio — effect on induced drag
  24. 3.1.24Critical Mach number — onset of local supersonic flow
  25. 3.1.25Wave drag — transonic and supersonic
  26. 3.1.26Area rule — Whitcomb's rule for transonic drag reduction
  27. 3.1.27Hypersonic flow — Mach 5+, high temperature effects
  28. 3.1.28Aerodynamic heating — recovery temperature, heat flux
  29. 3.1.29Aerodynamic coefficients — CN, CA, CL, CD, Cm as functions of angle of attack, Mach
  30. 3.1.30Computational aerodynamics — panel method (intro), CFD overview
3.2Orbital Mechanics & Astrodynamics0 / 40
  1. 3.2.1Two-body problem — equations of motion, reduction to one-body
  2. 3.2.2Conservation of energy and angular momentum in gravitational field
  3. 3.2.3Orbit equation r = p - (1 + e·cos θ) — derivation from equations of motion
  4. 3.2.4Orbit shape from eccentricity — circle (e=0), ellipse (0 - e - 1), parabola (e=1), hyperbola (e - 1)
  5. 3.2.5Kepler's first law — orbits are conic sections
  6. 3.2.6Kepler's second law — equal areas in equal times, from angular momentum conservation
  7. 3.2.7Kepler's third law — T² ∝ a³ — derivation
  8. 3.2.8Orbital elements (Keplerian) — semi-major axis a, eccentricity e, inclination i, RAAN Ω, argument of perigee ω, true ano
  9. 3.2.9Physical meaning of each orbital element
  10. 3.2.10Vis-viva equation v² = GM(2 - r − 1 - a) — derivation
  11. 3.2.11Specific orbital energy ε = −GM - 2a
  12. 3.2.12Specific angular momentum h = √(GMp)
  13. 3.2.13Circular orbit — velocity, period, energy
  14. 3.2.14Kepler's equation M = E − e·sin E — derivation, eccentric anomaly
  15. 3.2.15Solving Kepler's equation — Newton-Raphson iteration
  16. 3.2.16True anomaly from eccentric anomaly
  17. 3.2.17Converting between orbital elements and state vectors (r, v)
  18. 3.2.18Orbit determination — Gauss's method, Gibbs method
  19. 3.2.19Hohmann transfer — derivation, minimum energy transfer
  20. 3.2.20Hohmann Δv calculation — both maneuvers
  21. 3.2.21Bi-elliptic transfer — when it wins over Hohmann
  22. 3.2.22Plane change maneuvers — Δv = 2v·sin(Δi - 2)
  23. 3.2.23Combined maneuvers — optimal split between plane change and velocity change
  24. 3.2.24Gravity assist (slingshot) — patched conic, v-infinity vectors
  25. 3.2.25Sphere of influence — radius derivation
  26. 3.2.26Patched conic method — interplanetary trajectory design
  27. 3.2.27Pork chop plots — Δv vs launch - arrival date
  28. 3.2.28Lambert's problem — connecting two positions in given time
  29. 3.2.29Gauss's method for Lambert's problem
  30. 3.2.30Lagrange points L1–L5 — derivation, stability
  31. 3.2.31Halo orbits — linearized motion near Lagrange points
  32. 3.2.32Three-body problem — restricted (CR3BP), characteristic equation
  33. 3.2.33Orbital perturbations — J2 effect (oblateness), derivation of nodal precession
  34. 3.2.34Atmospheric drag — exponential atmosphere model, orbit decay
  35. 3.2.35Solar radiation pressure
  36. 3.2.36Third-body perturbations
  37. 3.2.37Orbit types — LEO, MEO, GEO, HEO, SSO, Molniya
  38. 3.2.38Groundtrack analysis — swath, revisit
  39. 3.2.39Launch window — phasing with target orbit
  40. 3.2.40Rendezvous and proximity operations — Clohessy-Wiltshire equations
3.3Rocket Propulsion0 / 50
  1. 3.3.1Tsiolkovsky rocket equation — full first-principles derivation from momentum
  2. 3.3.2Δv = v_e · ln(m₀ - m_f) — understanding each term
  3. 3.3.3Mass ratio m₀ - m_f — why it's so critical
  4. 3.3.4Specific impulse Isp = v_e - g₀ — definition, physical meaning, units
  5. 3.3.5Typical Isp values — solid (~260s), LOX - RP1 (~311s), LOX - LH2 (~450s), ion engines (~3000s)
  6. 3.3.6Thrust equation F = ṁv_e + (P_e − P_a)A_e — derivation
  7. 3.3.7Mass flow rate ṁ and its relation to throat area
  8. 3.3.8Effective exhaust velocity c = v_e + (P_e − P_a)A_e - ṁ
  9. 3.3.9Thrust coefficient C_F = F - (P_c A - ) — derivation
  10. 3.3.10Characteristic velocity c - = P_c A - ṁ — derivation, combustion efficiency measure
  11. 3.3.11Nozzle thermodynamics — isentropic expansion from chamber to exit
  12. 3.3.12Chamber-to-exit relation - all quantities as f(M_e, γ)
  13. 3.3.13Optimum expansion — P_e = P_a for maximum thrust
  14. 3.3.14Over-expanded nozzle — oblique shocks in plume, efficiency loss
  15. 3.3.15Under-expanded nozzle — Prandtl-Meyer expansion, efficiency loss
  16. 3.3.16Altitude compensation methods — nozzle extension, aerospike
  17. 3.3.17De Laval nozzle geometry — conical, bell (Rao contour), 80% bell
  18. 3.3.18Nozzle area ratio ε = A_e - A - — choosing for optimal performance
  19. 3.3.19Combustion thermodynamics — stoichiometry, adiabatic flame temperature
  20. 3.3.20Real gas effects — dissociation, recombination
  21. 3.3.21Characteristic velocity c - and its relation to flame temperature, MW
  22. 3.3.22Staged combustion cycle — full flow, fuel-rich, oxidizer-rich preburners
  23. 3.3.23Gas generator cycle — performance penalty vs simplicity
  24. 3.3.24Expander cycle — hydrogen-cooled nozzle drives turbine
  25. 3.3.25Pressure-fed cycle — simplest, used in upper stages
  26. 3.3.26Electric pump-fed cycle — modern innovation
  27. 3.3.27Turbopump design — centrifugal pump, axial turbine stages, NPSH
  28. 3.3.28Regenerative cooling — heat flux, coolant flow, pressure drop
  29. 3.3.29Film cooling — effectiveness, coverage fraction
  30. 3.3.30Ablative cooling — charring, blowing
  31. 3.3.31Transpiration cooling
  32. 3.3.32Combustion instability — low-frequency (chugging), high-frequency (screaming)
  33. 3.3.33Acoustic modes in combustion chamber — cause of instability
  34. 3.3.34Injector design — impinging, coaxial, swirl injectors
  35. 3.3.35Solid propellants — fuel + oxidizer in polymer matrix
  36. 3.3.36Burn rate r = a·P^n — Vieille's law
  37. 3.3.37Grain geometry — BATES, star, wagon wheel; neutral - progressive - regressive burn
  38. 3.3.38Solid rocket Isp derivation from grain properties
  39. 3.3.39Hybrid engines — advantages, disadvantages
  40. 3.3.40Electric propulsion — thrust, power, Isp trade-off
  41. 3.3.41Ion engine — ionization, acceleration grid, neutralizer
  42. 3.3.42Hall-effect thruster — cross-field discharge, annular channel
  43. 3.3.43FEEP, MEMS thrusters — micro-propulsion
  44. 3.3.44Nuclear thermal propulsion — NTR Isp ~900 s concept
  45. 3.3.45Rocket staging — series staging, parallel staging
  46. 3.3.46Optimal staging — equal mass ratios (for same Isp)
  47. 3.3.47Payload fraction as function of Δv and Isp
  48. 3.3.48Propellant properties — density, freezing point, toxicity, storability
  49. 3.3.49Cryogenic propellants — handling, insulation, boil-off
  50. 3.3.50Hypergolic propellants — N2O4 - UDMH, MMH
3.4Rocket Flight Mechanics0 / 26
  1. 3.4.1Coordinate systems — Earth-Centered Inertial (ECI), Earth-Centered Earth-Fixed (ECEF), North-East-Down (NED), launch, bo
  2. 3.4.2Transformation between frames — direction cosine matrices
  3. 3.4.3Forces on a rocket in flight — thrust, aerodynamic (normal, axial), gravity
  4. 3.4.4Equations of motion — 3DOF point mass (trajectory analysis)
  5. 3.4.56DOF equations — translational (Newton), rotational (Euler's equations)
  6. 3.4.6Mass properties — CG location, inertia tensor changing with propellant depletion
  7. 3.4.7Aerodynamic coefficients — CA (axial force), CN (normal force), Cm (pitching moment)
  8. 3.4.8Barrowman equations — centre of pressure calculation for finned rockets
  9. 3.4.9Static margin = (XCP − XCG) - d — must be positive (at least 1 caliber)
  10. 3.4.10Static stability — weather-cocking tendency
  11. 3.4.11Dynamic stability — pitch - yaw damping derivatives
  12. 3.4.12Propulsive forces — thrust misalignment, gimbal angle
  13. 3.4.13Gravity turn trajectory — pitch rate from aerodynamic angle of attack = 0
  14. 3.4.14Pitch program — open-loop pitch-over
  15. 3.4.15Trajectory optimization — minimum gravity loss, minimum drag loss
  16. 3.4.16Max-Q — maximum dynamic pressure q = ½ρv²; structural limit
  17. 3.4.17Staging events — separation dynamics, thrust tail-off
  18. 3.4.18Fairing separation — altitude, dynamic pressure requirements
  19. 3.4.19Reentry mechanics — ballistic coefficient β = m - (C_D A)
  20. 3.4.20Reentry corridor — angle of attack constraints
  21. 3.4.21Aerodynamic heating during reentry — stagnation point heat flux Chapman equation
  22. 3.4.22Thermal protection systems — ablators (PICA, SLA), metallic tiles, RCC
  23. 3.4.23Plasma sheath — communications blackout
  24. 3.4.24Aerocapture — using atmosphere to decelerate into orbit
  25. 3.4.25Aerobraking — gradual orbit lowering using atmospheric drag
  26. 3.4.26Terminal landing — propulsive descent, suicide burn
3.5Guidance, Navigation & Control (GNC)0 / 55
  1. 3.5.1Reference frames — body frame, inertial frame; rotation between them
  2. 3.5.2Euler angles — roll φ, pitch θ, yaw ψ; rotation sequence (3-2-1 convention)
  3. 3.5.3Direction cosine matrix (DCM) — construction from Euler angles
  4. 3.5.4DCM kinematics — Ċ = −[ω×]C
  5. 3.5.5Gimbal lock — problem with Euler angles at θ = ±90°
  6. 3.5.6Quaternions — definition q = (q₀, q₁, q₂, q₃), unit quaternion constraint
  7. 3.5.7Quaternion product — Hamilton product
  8. 3.5.8Quaternion rotation formula — rotating vector v by quaternion q
  9. 3.5.9Quaternion kinematics — q̇ = ½ Ξ(q) ω
  10. 3.5.10Converting between DCM, quaternions, Euler angles
  11. 3.5.11Modified Rodrigues parameters — singularity-free, compact
  12. 3.5.12Attitude estimation — triad method (two vector measurements)
  13. 3.5.13Inertial navigation — accelerometer measures non-gravitational specific force
  14. 3.5.14Gyroscope — angular velocity measurement, bias, noise
  15. 3.5.15IMU — integrated accelerometer + gyroscope
  16. 3.5.16Mechanization equations — integrating IMU to get position, velocity, attitude
  17. 3.5.17INS error propagation — error state equations
  18. 3.5.18GPS — pseudorange, trilateration, dilution of precision
  19. 3.5.19GNSS — GPS, GLONASS, Galileo, BeiDou
  20. 3.5.20Sensor fusion — complementary filter (simple), Kalman filter (optimal)
  21. 3.5.21Kalman filter derivation — predict step, update step
  22. 3.5.22Kalman gain — minimizes trace of covariance
  23. 3.5.23Observability — when KF can estimate state
  24. 3.5.24Extended Kalman Filter (EKF) — linearization, Jacobians
  25. 3.5.25Unscented Kalman Filter (UKF) — sigma points, better for nonlinear
  26. 3.5.26Control system fundamentals — plant, actuator, sensor, controller
  27. 3.5.27Transfer function — Laplace domain, poles and zeros
  28. 3.5.28Block diagram algebra
  29. 3.5.29State-space representation — x' = Ax + Bu, y = Cx + Du
  30. 3.5.30Eigenvalues of A — system modes, stability
  31. 3.5.31Lyapunov stability — Lyapunov function, positive definiteness
  32. 3.5.32Controllability matrix — rank test
  33. 3.5.33Observability matrix — rank test
  34. 3.5.34Pole placement — Ackermann's formula
  35. 3.5.35Linear Quadratic Regulator (LQR) — Riccati equation, optimal gains
  36. 3.5.36LQG — LQR + Kalman filter, separation principle
  37. 3.5.37H∞ control — robust to uncertainty (intro)
  38. 3.5.38PID control — proportional, integral, derivative terms
  39. 3.5.39PID tuning — Ziegler-Nichols, loop shaping
  40. 3.5.40Root locus — Evans' method, rules for sketching
  41. 3.5.41Bode plot — magnitude and phase vs frequency
  42. 3.5.42Gain margin, phase margin — stability margins
  43. 3.5.43Nyquist stability criterion — encirclements of −1
  44. 3.5.44Thrust vector control — single-gimbal, dual-gimbal; TVC angles
  45. 3.5.45TVC dynamics — gimbal servo bandwidth, time delay
  46. 3.5.46Reaction control system — thruster selection, plume impingement limits
  47. 3.5.47Attitude control modes — spin stabilization, 3-axis active
  48. 3.5.48Reaction wheels — momentum management, zero-crossing
  49. 3.5.49Control moment gyroscopes (CMG) — high torque, singularity
  50. 3.5.50Proportional navigation guidance — N·V_c·λ̇, derivation
  51. 3.5.51Augmented proportional navigation — gravity compensation
  52. 3.5.52Optimal guidance — ZEM - ZEV formulation
  53. 3.5.53Powered descent guidance — G-FOLD algorithm (convex optimization)
  54. 3.5.54Terminal descent — velocity vector alignment, touchdown constraints
  55. 3.5.55Autonomous GNC for reusable rockets — SpaceX approach overview
3.6Spacecraft Structures & Systems Engineering0 / 35
  1. 3.6.1Structural loads — axial (thrust), bending (wind shear), dynamic (vibration, acoustics, shock)
  2. 3.6.2Structural design process — load cases, FOS (factor of safety)
  3. 3.6.3Stress and strain — σ = F - A, ε = ΔL - L, Young's modulus E
  4. 3.6.4Hooke's law in 3D — generalized stress-strain (tensor)
  5. 3.6.5Yield stress, ultimate stress — material behavior
  6. 3.6.6Buckling — Euler column buckling load derivation
  7. 3.6.7Shell buckling — thin-walled cylinder under axial load
  8. 3.6.8Fatigue — S-N curves, Miner's rule
  9. 3.6.9Fracture mechanics — stress intensity factor K, toughness K_IC
  10. 3.6.10Modal analysis — natural frequencies, mode shapes
  11. 3.6.11Random vibration — PSD, RMS acceleration
  12. 3.6.12Acoustic loads — SPL, octave band analysis
  13. 3.6.13Shock response spectrum (SRS)
  14. 3.6.14Thermal analysis — conduction in structures, thermal stress
  15. 3.6.15Composite materials — fiber-matrix, ply properties, laminate theory
  16. 3.6.16Classical laminate theory — ABD matrix
  17. 3.6.17Sandwich structures — face sheets, core
  18. 3.6.18Finite element method — nodes, elements, stiffness matrix
  19. 3.6.19FEM for structures — assembling global stiffness
  20. 3.6.20FEM software — NASTRAN, ABAQUS (concepts and use)
  21. 3.6.21Spacecraft bus — structure, power, thermal, ADCS, C&DH, comms, propulsion
  22. 3.6.22Power systems — solar arrays (I-V curve, power tracking), batteries (DoD, cycles), RTG
  23. 3.6.23Thermal control — multi-layer insulation (MLI), heaters, heat pipes, radiators
  24. 3.6.24Mass budgets — dry mass, wet mass, margin
  25. 3.6.25Link budget — path loss, EIRP, G - T, Eb - N0
  26. 3.6.26Systems engineering — V-model, requirements traceability
  27. 3.6.27Requirements — SMART (Specific, Measurable, Achievable, Relevant, Testable)
  28. 3.6.28Verification methods — analysis, test, inspection, demonstration
  29. 3.6.29FMEA — failure mode, effect, severity, detection, RPN
  30. 3.6.30Fault tree analysis (FTA) — top-down, AND - OR gates
  31. 3.6.31Reliability — MTTF, MTBF, exponential failure model
  32. 3.6.32Redundancy — cold standby, hot standby, active redundancy
  33. 3.6.33Environmental testing — thermal vacuum (TVAC), vibration, acoustic, EMC - EMI
  34. 3.6.34Space environment — LEO radiation (SAA, Van Allen), atomic oxygen, MMOD debris
  35. 3.6.35Radiation effects — TID, SEE, displacement damage

Chemistry

0 / 304 · 0%
1.1Matter, Measurement & the Mole0 / 16
  1. 1.1.1States of matter — solid, liquid, gas, plasma; macroscopic vs particulate view
  2. 1.1.2Pure substances vs mixtures — elements, compounds, homogeneous - heterogeneous
  3. 1.1.3Separation techniques — filtration, distillation, chromatography, centrifugation, sublimation
  4. 1.1.4Physical vs chemical change
  5. 1.1.5SI units in chemistry — kg, mol, K, Pa; derived units (J, L)
  6. 1.1.6Significant figures and rounding rules
  7. 1.1.7Density, molar mass, molar volume
  8. 1.1.8Law of conservation of mass (Lavoisier) — proof, examples
  9. 1.1.9Law of definite proportions (Proust)
  10. 1.1.10Law of multiple proportions (Dalton)
  11. 1.1.11Avogadro's law and Avogadro's number N_A = 6.022 × 10²³
  12. 1.1.12The mole concept — counting by weighing
  13. 1.1.13Molar mass calculations
  14. 1.1.14Empirical formula vs molecular formula — determination from % composition
  15. 1.1.15Concentration units — mass %, volume %, ppm, ppb, molarity (M), molality (m), mole fraction
  16. 1.1.16Dilution formula M₁V₁ = M₂V₂
1.2Atomic Structure (Classical)0 / 11
  1. 1.2.1Dalton's atomic theory — postulates and limitations
  2. 1.2.2Discovery of electron (Thomson, cathode rays), proton (Goldstein), neutron (Chadwick)
  3. 1.2.3Thomson's plum-pudding model
  4. 1.2.4Rutherford's gold-foil experiment — nuclear model
  5. 1.2.5Atomic number Z, mass number A, isotopes, isobars, isotones
  6. 1.2.6Calculation of atomic mass from isotopic abundance
  7. 1.2.7Bohr model of hydrogen — postulates, radius rₙ = 0.529 n² - Z Å, energy Eₙ = −13.6 Z² - n² eV
  8. 1.2.8Derivation of Bohr's radii and energies from electrostatics + quantization
  9. 1.2.9Hydrogen emission spectrum — Lyman, Balmer, Paschen, Brackett, Pfund
  10. 1.2.10Rydberg formula 1 - λ = R(1 - n₁² − 1 - n₂²)
  11. 1.2.11Limitations of Bohr — fails for multi-electron atoms, fine structure
1.3Chemical Reactions & Stoichiometry0 / 9
  1. 1.3.1Writing and balancing chemical equations
  2. 1.3.2Types of reactions — combination, decomposition, displacement, double displacement, redox
  3. 1.3.3Limiting reagent problems
  4. 1.3.4Percent yield, theoretical yield, actual yield
  5. 1.3.5Solution stoichiometry — titrations, dilutions
  6. 1.3.6Oxidation number rules — assigning, change
  7. 1.3.7Balancing redox equations — ion-electron (half-reaction) method, oxidation-number method
  8. 1.3.8Acid-base reactions — neutralization, salt formation
  9. 1.3.9Combustion stoichiometry — fuel + O₂ → CO₂ + H₂O
1.4Periodic Table — First Look0 / 5
  1. 1.4.1Mendeleev's periodic table — based on atomic mass
  2. 1.4.2Modern periodic law — based on atomic number
  3. 1.4.3Groups (1–18), periods (1–7), s - p - d - f blocks
  4. 1.4.4Metals, non-metals, metalloids — properties
  5. 1.4.5Common elements and their symbols (first 30)
2.1Quantum Atomic Structure0 / 11
  1. 2.1.1Black-body radiation and Planck's quantum hypothesis E = hν
  2. 2.1.2Photoelectric effect — Einstein's photon model
  3. 2.1.3Dual nature of matter — de Broglie λ = h - p
  4. 2.1.4Heisenberg uncertainty principle — Δx Δp ≥ ℏ - 2
  5. 2.1.5Quantum numbers — n (principal), l (azimuthal), mₗ (magnetic), mₛ (spin)
  6. 2.1.6Orbital shapes — s (spherical), p (dumbbell), d (cloverleaf), f
  7. 2.1.7Aufbau principle — order of filling (Madelung rule, n + l)
  8. 2.1.8Pauli exclusion principle
  9. 2.1.9Hund's rule of maximum multiplicity
  10. 2.1.10Electronic configuration of elements (Z = 1 to 30) — exceptions Cr, Cu
  11. 2.1.11Stability of half-filled and fully-filled subshells
2.2Periodic Trends0 / 9
  1. 2.2.1Effective nuclear charge Z_eff — Slater's rules
  2. 2.2.2Atomic radius — covalent, metallic, van der Waals; trends across period and group
  3. 2.2.3Ionic radius — cation - parent atom, anion - parent atom; isoelectronic series
  4. 2.2.4Ionization energy — first, second, …; trends and anomalies (e.g. B - Be)
  5. 2.2.5Electron gain enthalpy - electron affinity — trends, anomalies (e.g. Cl - F)
  6. 2.2.6Electronegativity — Pauling, Mulliken, Allred-Rochow scales
  7. 2.2.7Diagonal relationship — Li - Mg, Be - Al, B - Si
  8. 2.2.8Metallic - non-metallic character trends
  9. 2.2.9Variation of oxidation state across the table
2.3Chemical Bonding0 / 18
  1. 2.3.1Octet rule — Lewis structures, exceptions (incomplete octet, expanded octet, odd-electron species)
  2. 2.3.2Formal charge calculation — best resonance structure
  3. 2.3.3Ionic bonding — Born-Haber cycle, lattice energy (Kapustinskii equation)
  4. 2.3.4Fajan's rules — covalent character in ionic compounds
  5. 2.3.5Covalent bonding — bond length, bond energy, bond order
  6. 2.3.6Polarity of bonds — dipole moment μ = q·d
  7. 2.3.7Polarity of molecules — vector sum of bond dipoles
  8. 2.3.8VSEPR theory — geometry from electron pairs (linear, trigonal planar, tetrahedral, trigonal bipyramidal, octahedral, etc
  9. 2.3.9Effect of lone pairs on geometry (e.g. H₂O bent, NH₃ pyramidal)
  10. 2.3.10Valence Bond Theory (VBT) — hybridization (sp, sp², sp³, sp³d, sp³d²)
  11. 2.3.11σ vs π bonds — overlap, strength
  12. 2.3.12Molecular Orbital Theory (MOT) — LCAO, bonding - antibonding orbitals
  13. 2.3.13MO diagrams of H₂, He₂, N₂, O₂, F₂, NO, CO — bond order, magnetism
  14. 2.3.14Why O₂ is paramagnetic (MOT prediction)
  15. 2.3.15Resonance — delocalization, resonance energy (benzene, ozone, carbonate)
  16. 2.3.16Hydrogen bonding — intermolecular, intramolecular; consequences (boiling points, water density)
  17. 2.3.17van der Waals forces — London dispersion, dipole-dipole, dipole-induced dipole
  18. 2.3.18Metallic bonding — electron sea, band theory (intro)
2.4States of Matter (Quantitative)0 / 17
  1. 2.4.1Gas laws — Boyle (PV const at T), Charles (V - T const at P), Gay-Lussac (P - T const at V)
  2. 2.4.2Combined gas law and ideal gas equation PV = nRT
  3. 2.4.3Dalton's law of partial pressures
  4. 2.4.4Graham's law of effusion - diffusion (rate ∝ 1 - √M)
  5. 2.4.5Kinetic molecular theory — derivation of P = (1 - 3)ρv²_rms
  6. 2.4.6Maxwell-Boltzmann distribution of speeds — most probable, mean, rms
  7. 2.4.7Real gases — deviations from ideality, compressibility factor Z
  8. 2.4.8van der Waals equation (P + a - V²)(V − b) = RT — physical meaning of a, b
  9. 2.4.9Critical constants Tc, Pc, Vc; law of corresponding states
  10. 2.4.10Liquefaction of gases — Linde, Claude processes (concept)
  11. 2.4.11Liquid state — vapour pressure, viscosity, surface tension
  12. 2.4.12Solid state — crystalline vs amorphous; unit cell, Bravais lattices
  13. 2.4.13Cubic systems — SCC, BCC, FCC; packing fraction calculations
  14. 2.4.14Coordination number, voids (tetrahedral, octahedral)
  15. 2.4.15Ionic crystals — NaCl, CsCl, ZnS, fluorite, antifluorite structures
  16. 2.4.16Defects — Schottky, Frenkel; non-stoichiometric defects
  17. 2.4.17Electrical properties — conductors, semiconductors, insulators; doping (n-type, p-type)
2.5Thermodynamics (Chemical)0 / 16
  1. 2.5.1System vs surroundings; open, closed, isolated
  2. 2.5.2State functions vs path functions
  3. 2.5.3First law - ΔU = q + w (chemist sign convention)
  4. 2.5.4Work in expansion - reversible isothermal w = −nRT ln(V₂ - V₁), irreversible w = −P_ext ΔV
  5. 2.5.5Enthalpy H = U + PV; ΔH for reactions at constant P
  6. 2.5.6Heat capacities Cp, Cv; relationship Cp − Cv = nR (ideal gas)
  7. 2.5.7Standard enthalpy of formation ΔH°f
  8. 2.5.8Hess's law — enthalpy is a state function; enthalpy cycles
  9. 2.5.9Bond enthalpies — estimating ΔH_rxn from bond energies
  10. 2.5.10Born-Haber cycle revisited — calculating lattice energy
  11. 2.5.11Enthalpy of combustion, neutralization, hydration, solution
  12. 2.5.12Spontaneity — second law; entropy ΔS
  13. 2.5.13Standard entropy S° and ΔS_rxn = Σ S°(products) − Σ S°(reactants)
  14. 2.5.14Gibbs free energy ΔG = ΔH − TΔS; spontaneity criteria
  15. 2.5.15ΔG° and equilibrium constant - ΔG° = −RT ln K
  16. 2.5.16Coupling reactions — driving unfavorable reactions
2.6Equilibrium0 / 16
  1. 2.6.1Reversible reactions and dynamic equilibrium
  2. 2.6.2Law of mass action and Kc, Kp
  3. 2.6.3Relationship Kp = Kc(RT)^Δn
  4. 2.6.4Reaction quotient Q vs K — direction of shift
  5. 2.6.5Le Chatelier's principle — pressure, temperature, concentration, catalyst effects
  6. 2.6.6Heterogeneous equilibria — pure solids - liquids excluded
  7. 2.6.7Acids and bases — Arrhenius, Brønsted-Lowry, Lewis definitions
  8. 2.6.8Conjugate acid-base pairs
  9. 2.6.9Ionic product of water Kw = 10⁻¹⁴ at 25 °C
  10. 2.6.10pH, pOH, pKa, pKb scales
  11. 2.6.11Strong vs weak acids - bases; degree of dissociation α
  12. 2.6.12Ostwald's dilution law (weak acid) - α = √(Ka - C)
  13. 2.6.13Common ion effect
  14. 2.6.14Buffer solutions — Henderson-Hasselbalch equation
  15. 2.6.15Solubility product Ksp — common-ion suppression, selective precipitation
  16. 2.6.16Salt hydrolysis — pH of salt solutions (4 cases - SA - SB, SA - WB, WA - SB, WA - WB)
2.7Redox & Electrochemistry (Intro)0 / 11
  1. 2.7.1Galvanic (voltaic) cells — anode (oxidation), cathode (reduction)
  2. 2.7.2Standard electrode potentials — SHE reference, electrochemical series
  3. 2.7.3Cell EMF E°_cell = E°_cathode − E°_anode
  4. 2.7.4Nernst equation E = E° − (RT - nF) ln Q
  5. 2.7.5Spontaneity from E°_cell and ΔG = −nFE
  6. 2.7.6Equilibrium constant from E° - ln K = nFE° - RT
  7. 2.7.7Concentration cells
  8. 2.7.8Batteries — primary (dry cell), secondary (lead-acid, Li-ion)
  9. 2.7.9Fuel cells — H₂ - O₂ fuel cell (spacecraft relevance)
  10. 2.7.10Electrolysis — Faraday's laws (m = ZIt), industrial electrolysis (NaCl, Al)
  11. 2.7.11Corrosion — electrochemical mechanism; cathodic protection, galvanization
2.8Chemical Kinetics0 / 12
  1. 2.8.1Rate of reaction — average vs instantaneous
  2. 2.8.2Rate law — order vs molecularity
  3. 2.8.3Differential rate equations for 0, 1st, 2nd order — derivations
  4. 2.8.4Integrated rate laws — half-life t₁ - ₂ for each order
  5. 2.8.5Pseudo-first-order kinetics
  6. 2.8.6Methods to determine order — initial rates, integrated method, half-life method
  7. 2.8.7Temperature dependence — Arrhenius equation k = A·e^(−Ea - RT)
  8. 2.8.8Activation energy from Arrhenius plot; effect of catalyst
  9. 2.8.9Collision theory — frequency factor, steric factor
  10. 2.8.10Transition state theory — activated complex (intro)
  11. 2.8.11Reaction mechanisms — elementary steps, rate-determining step
  12. 2.8.12Catalysis — homogeneous, heterogeneous, enzyme catalysis
3.1Hydrogen and s-Block0 / 10
  1. 3.1.1Position of hydrogen in the periodic table (anomalous)
  2. 3.1.2Isotopes of hydrogen — protium, deuterium, tritium
  3. 3.1.3Preparation, properties, uses of dihydrogen
  4. 3.1.4Hydrides — ionic, covalent, interstitial
  5. 3.1.5Water — structure (HOH = 104.5°), anomalous expansion, hardness (temporary - permanent), softening
  6. 3.1.6Heavy water D₂O, hydrogen peroxide H₂O₂ — structure, preparation, reactions
  7. 3.1.7Alkali metals (Group 1) — physical - chemical properties, anomaly of Li, diagonal Li-Mg
  8. 3.1.8Alkaline earth metals (Group 2) — physical - chemical properties, anomaly of Be, diagonal Be-Al
  9. 3.1.9Important compounds — NaOH, NaCl, Na₂CO₃ (Solvay), NaHCO₃; CaO, CaCO₃, gypsum, plaster of Paris
  10. 3.1.10Biological importance of Na, K, Ca, Mg
3.2p-Block0 / 11
  1. 3.2.1Group 13 (Boron family) — anomaly of B, diagonal B-Si; BX₃ Lewis acidity; diborane B₂H₆ (3c-2e bond), borazine
  2. 3.2.2Aluminium — chemistry, alloys; alumina, alums
  3. 3.2.3Group 14 (Carbon family) — allotropes of C (diamond, graphite, fullerenes, graphene, CNTs)
  4. 3.2.4Silicon and silicates; silicones; zeolites
  5. 3.2.5Group 15 (Nitrogen family) — N₂ inertness; NH₃ synthesis (Haber); HNO₃ (Ostwald); oxides of N (N₂O, NO, NO₂, N₂O₄, N₂O₅)
  6. 3.2.6Phosphorus allotropes (white, red, black); P₄O₆, P₄O₁₀; oxoacids of P (H₃PO₃ vs H₃PO₄ basicity)
  7. 3.2.7Group 16 (Oxygen family) — allotropes of O (O₂, O₃); ozone chemistry, ozone layer
  8. 3.2.8Sulfur — allotropes (rhombic, monoclinic); SO₂, SO₃; H₂SO₄ (Contact process); oxoacids of S
  9. 3.2.9Group 17 (Halogens) — properties, oxidizing power; HX strengths; interhalogens; pseudohalogens
  10. 3.2.10Oxoacids of halogens — HClO, HClO₂, HClO₃, HClO₄ — acidity trend
  11. 3.2.11Group 18 (Noble gases) — discovery, isolation, compounds of Xe (XeF₂, XeF₄, XeF₆, XeO₃) — structure and bonding
3.3d-Block (Transition Metals) & f-Block0 / 9
  1. 3.3.1General electronic configuration (n−1)d¹⁻¹⁰ ns⁰⁻²
  2. 3.3.2Variable oxidation states — reasons
  3. 3.3.3Atomic - ionic size trends; lanthanide contraction
  4. 3.3.4Magnetic properties — paramagnetism via spin-only formula μ = √(n(n+2)) BM
  5. 3.3.5Colour of complexes — d-d transitions
  6. 3.3.6Catalytic properties — examples (V₂O₅, Fe, Ni, Pt)
  7. 3.3.7Important compounds — KMnO₄, K₂Cr₂O₇ — preparation, oxidizing reactions
  8. 3.3.8Lanthanides — electronic configuration, lanthanide contraction, oxidation states (mostly +3)
  9. 3.3.9Actinides — electronic configuration, comparison with lanthanides; nuclear chemistry tie-in
3.4Coordination Chemistry0 / 15
  1. 3.4.1Werner's theory of coordination compounds
  2. 3.4.2Ligands — classification (mono, bi, poly, ambidentate, chelating); denticity
  3. 3.4.3Nomenclature (IUPAC) — naming complex ions and compounds
  4. 3.4.4Coordination number and geometry — 2 (linear), 4 (tetrahedral - square planar), 6 (octahedral)
  5. 3.4.5Isomerism — structural (linkage, ionization, coordination, hydrate) and stereo (geometrical, optical)
  6. 3.4.6Effective Atomic Number (EAN) rule
  7. 3.4.7VBT applied to complexes — inner vs outer orbital, hybridization, magnetism
  8. 3.4.8Crystal Field Theory (CFT) — Δ_oct, Δ_tet, splitting diagrams
  9. 3.4.9Crystal Field Stabilization Energy (CFSE) — high-spin vs low-spin; spectrochemical series
  10. 3.4.10Jahn-Teller distortion
  11. 3.4.11Colour and spectra — d-d transitions, charge transfer; selection rules
  12. 3.4.12Magnetic moments of complexes
  13. 3.4.13Ligand Field Theory (LFT) and MO description (overview)
  14. 3.4.14Stability constants of complexes — chelate effect
  15. 3.4.15Applications — biological (haemoglobin, chlorophyll, vit B₁₂), medicinal (cisplatin), industrial (catalysts)
3.5Inorganic Qualitative Analysis0 / 4
  1. 3.5.1Cation groups I–V — group reagents, separation scheme
  2. 3.5.2Common anions — Cl⁻, Br⁻, I⁻, SO₄²⁻, NO₃⁻, CO₃²⁻ — confirmatory tests
  3. 3.5.3Flame tests — characteristic colours
  4. 3.5.4Borax bead, charcoal cavity tests
4.1General Organic Chemistry (GOC)0 / 12
  1. 4.1.1Tetravalency of carbon; hybridization recap (sp, sp², sp³)
  2. 4.1.2Catenation and the diversity of organic molecules
  3. 4.1.3Functional groups and homologous series
  4. 4.1.4IUPAC nomenclature — alkanes, alkenes, alkynes, aromatics, alcohols, ethers, aldehydes, ketones, acids, esters, amines,
  5. 4.1.5Isomerism — structural (chain, position, functional, metamerism, tautomerism) and stereo (geometrical - cis-trans - E-Z,
  6. 4.1.6Chirality — chiral centres, enantiomers, diastereomers, meso compounds
  7. 4.1.7Optical activity — specific rotation, racemic mixtures, resolution
  8. 4.1.8Electronic effects — inductive (+I - −I), mesomeric - resonance (+M - −M), hyperconjugation, electromeric
  9. 4.1.9Reactive intermediates — carbocations (stability), carbanions, free radicals, carbenes, nitrenes; rearrangements (hydrid
  10. 4.1.10Reagent classification — electrophiles, nucleophiles (hard - soft)
  11. 4.1.11Types of organic reactions — addition, substitution, elimination, rearrangement
  12. 4.1.12Reaction mechanisms — curved-arrow notation, bond formation - breaking (heterolysis vs homolysis)
4.2Hydrocarbons0 / 10
  1. 4.2.1Alkanes — preparation (Wurtz, Kolbe electrolysis, hydrogenation), properties, free-radical halogenation (Cl₂ - Br₂)
  2. 4.2.2Conformations of ethane, butane — Newman projections
  3. 4.2.3Cycloalkanes — Baeyer's strain theory; cyclohexane chair - boat, axial vs equatorial
  4. 4.2.4Alkenes — preparation (dehydration, dehydrohalogenation, Zaitsev's rule), addition reactions
  5. 4.2.5Markovnikov vs anti-Markovnikov (peroxide effect, Kharasch)
  6. 4.2.6Hydroboration-oxidation, ozonolysis (reductive - oxidative), syn vs anti dihydroxylation, halohydrin formation
  7. 4.2.7Alkynes — preparation, acidity of terminal alkynes, addition reactions, hydration to ketones
  8. 4.2.8Aromaticity — Hückel's rule (4n + 2 π electrons); examples (benzene, naphthalene, pyridine, furan, cyclopentadienyl anio
  9. 4.2.9Electrophilic aromatic substitution (EAS) — nitration, halogenation, sulfonation, Friedel-Crafts alkylation - acylation;
  10. 4.2.10Activating vs deactivating groups; ortho - para vs meta directors; reactivity order
4.3Halides and Oxygenated Derivatives0 / 9
  1. 4.3.1Alkyl halides — preparation, SN1 vs SN2 (mechanism, kinetics, stereochemistry), E1 vs E2 (mechanism, Zaitsev - Hofmann)
  2. 4.3.2Effect of substrate, nucleophile - base, solvent, leaving group
  3. 4.3.3Aryl halides — low reactivity, addition-elimination (benzyne mechanism), nucleophilic aromatic substitution
  4. 4.3.4Alcohols — preparation, acidity (pKa ~16), oxidation (PCC, Jones, K₂Cr₂O₇), Lucas test
  5. 4.3.5Phenols — acidity (resonance stabilization), Kolbe-Schmidt, Reimer-Tiemann, Fries rearrangement
  6. 4.3.6Ethers — Williamson synthesis, cleavage by HI
  7. 4.3.7Aldehydes and ketones — preparation; nucleophilic addition; aldol, Cannizzaro, Wittig, Claisen-Schmidt, Mannich, Reforma
  8. 4.3.8Carboxylic acids — acidity, derivatives (acid chlorides, anhydrides, esters, amides), Hell-Volhard-Zelinsky, esterificat
  9. 4.3.9α,β-Unsaturated carbonyls — Michael addition, 1,2 vs 1,4 addition
4.4Nitrogen-Containing Compounds0 / 4
  1. 4.4.1Amines — basicity (alkyl - NH₃ - aryl in water; reverse in gas phase), Hofmann elimination, carbylamine, Hinsberg te
  2. 4.4.2Diazonium salts — preparation, Sandmeyer, Gattermann, coupling reactions (azo dyes)
  3. 4.4.3Nitro compounds — preparation, reduction to amines (Sn - HCl, Fe - HCl, H₂ - Pt)
  4. 4.4.4Cyanides and isocyanides
4.5Biomolecules0 / 8
  1. 4.5.1Carbohydrates — classification (mono - di - polysaccharides), Fischer - Haworth projections, mutarotation, glycosidic bo
  2. 4.5.2Amino acids — zwitterion, isoelectric point pI, classification (essential, non-essential)
  3. 4.5.3Peptide bond; primary, secondary, tertiary, quaternary protein structure
  4. 4.5.4Enzymes — lock-and-key vs induced fit; Michaelis-Menten kinetics
  5. 4.5.5Nucleic acids — DNA, RNA; base pairing, double helix, replication, transcription, translation (overview)
  6. 4.5.6Lipids — fatty acids, triglycerides, phospholipids; saponification
  7. 4.5.7Vitamins — fat-soluble (A, D, E, K) vs water-soluble (B-complex, C)
  8. 4.5.8Hormones — peptide vs steroid (overview)
4.6Polymers0 / 7
  1. 4.6.1Classification — natural vs synthetic; addition vs condensation; thermoplastic vs thermosetting
  2. 4.6.2Addition polymers — polyethene, PVC, PTFE (Teflon), polypropylene, polystyrene, PMMA, polyacrylonitrile
  3. 4.6.3Condensation polymers — nylon-6,6, nylon-6, terylene (PET), bakelite, melamine, Kevlar
  4. 4.6.4Polymerization mechanisms — free-radical, cationic, anionic, coordination (Ziegler-Natta), step-growth
  5. 4.6.5Number-average vs weight-average molecular weight; polydispersity index
  6. 4.6.6Biodegradable polymers — PHBV, nylon-2-nylon-6
  7. 4.6.7- Aerospace polymers - — Kevlar (body armour, parachutes), Nomex (fire-resistant), PBO, epoxy resins (composite matrix)
4.7Chemistry in Everyday Life (compressed)0 / 3
  1. 4.7.1Drugs — analgesics, antibiotics, antiseptics, antacids (mechanism overview)
  2. 4.7.2Food chemistry — preservatives, artificial sweeteners, antioxidants
  3. 4.7.3Cleansing agents — soaps (saponification), detergents (anionic, cationic, non-ionic)
4.8Spectroscopy & Analysis (Intro)0 / 7
  1. 4.8.1Electromagnetic spectrum recap — UV, visible, IR, NMR, microwave, X-ray
  2. 4.8.2UV-Vis spectroscopy — Beer-Lambert law, conjugation and λ_max
  3. 4.8.3IR spectroscopy — characteristic group frequencies (O-H, N-H, C=O, C≡N, C=C, etc.); fingerprint region
  4. 4.8.4¹H NMR — chemical shift, multiplicity (n + 1 rule), integration; common ranges
  5. 4.8.5¹³C NMR (overview); DEPT
  6. 4.8.6Mass spectrometry — molecular ion, fragmentation patterns, m - z
  7. 4.8.7Chromatography — TLC, column, GC, HPLC (principles)
5.1Physical Chemistry (Advanced)0 / 10
  1. 5.1.1Quantum chemistry — particle in a box revisited; H-atom solutions
  2. 5.1.2Variational principle and perturbation theory (intro)
  3. 5.1.3Hartree-Fock method (concept); DFT (concept)
  4. 5.1.4Molecular spectroscopy — rotational (rigid rotor), vibrational (harmonic oscillator, Morse potential), rotational-vibrat
  5. 5.1.5Statistical thermodynamics — partition functions, Q_trans, Q_rot, Q_vib, Q_elec; computing thermodynamic properties
  6. 5.1.6Surface chemistry — adsorption isotherms (Langmuir, Freundlich, BET), catalysis on surfaces
  7. 5.1.7Colloids and surfactants — micelles, CMC, emulsions
  8. 5.1.8Electrochemistry (advanced) — Butler-Volmer equation, Tafel plot, overpotential
  9. 5.1.9Photochemistry — Stark-Einstein law, quantum yield, Jablonski diagram, fluorescence vs phosphorescence
  10. 5.1.10Solid-state chemistry — band theory, semiconductors, superconductivity, magnetism in solids
5.2Nuclear & Radiochemistry0 / 9
  1. 5.2.1Nuclear stability — N - Z ratio, magic numbers, binding energy per nucleon
  2. 5.2.2Radioactive decay modes — α, β⁻, β⁺, electron capture, γ, spontaneous fission
  3. 5.2.3Decay kinetics — first-order; half-life, mean life, activity
  4. 5.2.4Radioactive series — uranium, thorium, actinium
  5. 5.2.5Nuclear reactions — Q-value, cross-section
  6. 5.2.6Fission — chain reaction, critical mass, reactors (thermal vs fast)
  7. 5.2.7Fusion — D-T reaction, solar fusion (p-p chain), tokamak - ICF
  8. 5.2.8Applications — radiocarbon dating, medical (Tc-99m, I-131), RTG (Pu-238 in spacecraft)
  9. 5.2.9Radiation safety — units (Bq, Gy, Sv), shielding
5.3Combustion Chemistry (Propulsion Bridge)0 / 10
  1. 5.3.1Stoichiometric vs fuel-rich vs fuel-lean combustion
  2. 5.3.2Adiabatic flame temperature — calculation with enthalpies of formation
  3. 5.3.3Equilibrium products at high T — dissociation (H₂O ⇌ OH + H; CO₂ ⇌ CO + ½O₂)
  4. 5.3.4Chapman-Jouguet detonation; deflagration vs detonation
  5. 5.3.5Premixed vs diffusion flames
  6. 5.3.6Combustion of hydrocarbons (RP-1 - kerosene, methane) and hydrogen
  7. 5.3.7Combustion of hypergolics — N₂O₄ + UDMH - MMH; ignition delay
  8. 5.3.8Solid propellants — AP - HTPB - Al composition; burn rate dependence on pressure (Vieille's law)
  9. 5.3.9Pollutants — NOₓ, soot, unburned hydrocarbons
  10. 5.3.10CEA (Chemical Equilibrium with Applications) — using NASA-CEA tool to compute Isp, Tc, products
5.4Materials Chemistry (Aerospace)0 / 10
  1. 5.4.1Metals & alloys — Al alloys (2024, 7075), Ti alloys (Ti-6Al-4V), Ni superalloys (Inconel, Hastelloy), stainless steels
  2. 5.4.2Refractory metals — W, Mo, Ta, Re for rocket nozzles
  3. 5.4.3Heat treatment — annealing, normalising, quenching, tempering; precipitation hardening
  4. 5.4.4Ceramics — alumina, zirconia, silicon carbide, silicon nitride; properties at high T
  5. 5.4.5Carbon-carbon composites (RCC for nose cone - leading edges)
  6. 5.4.6Polymer-matrix composites — CFRP, GFRP; ply lay-up, laminate theory
  7. 5.4.7Ablative materials — phenolic-impregnated carbon ablator (PICA), AVCOAT, SLA
  8. 5.4.8Thermal protection — silica tiles (Shuttle), UHTCs (ZrB₂, HfB₂)
  9. 5.4.9Corrosion in aerospace environments — stress corrosion cracking, hydrogen embrittlement
  10. 5.4.10Surface treatments — anodising, plasma spraying, vapour deposition
5.5Green Chemistry & Sustainability0 / 5
  1. 5.5.112 principles of green chemistry
  2. 5.5.2Atom economy
  3. 5.5.3Solvent selection — water, supercritical CO₂, ionic liquids
  4. 5.5.4Green propellants — LMP-103S, AF-M315E (vs hydrazine)
  5. 5.5.5Carbon capture, hydrogen economy (electrolysis, fuel cells)

Biology

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1.1What Is Biology & Characteristics of Life0 / 18
  1. 1.1.1Define biology and its major sub-disciplines
  2. 1.1.2List the seven characteristics of living things
  3. 1.1.3Distinguish living vs non-living vs once-living
  4. 1.1.4Explain metabolism as anabolism vs catabolism
  5. 1.1.5Describe homeostasis with examples (temperature, pH, glucose)
  6. 1.1.6Explain growth and development in organisms
  7. 1.1.7Describe reproduction (sexual vs asexual) at basic level
  8. 1.1.8Explain responsiveness - irritability to stimuli
  9. 1.1.9Describe adaptation over time
  10. 1.1.10Outline the levels of biological organization (atom → biosphere)
  11. 1.1.11Define emergent properties at each organizational level
  12. 1.1.12Explain the cell as the basic unit of life
  13. 1.1.13Describe the scientific method steps
  14. 1.1.14Differentiate hypothesis, theory, and law
  15. 1.1.15Identify independent, dependent, and controlled variables
  16. 1.1.16Explain the role of controls in experiments
  17. 1.1.17Use SI units and metric prefixes in biology
  18. 1.1.18Interpret simple data tables and line graphs
1.2Chemistry of Life Basics0 / 16
  1. 1.2.1Describe atomic structure (protons, neutrons, electrons)
  2. 1.2.2Explain atomic number and mass number
  3. 1.2.3Define isotopes and their biological uses
  4. 1.2.4Distinguish ionic, covalent, and hydrogen bonds
  5. 1.2.5Explain polar vs nonpolar covalent bonds
  6. 1.2.6List the major elements in living organisms (CHNOPS)
  7. 1.2.7Explain why carbon is central to life
  8. 1.2.8Describe properties of water (cohesion, adhesion)
  9. 1.2.9Explain water's high specific heat and biological role
  10. 1.2.10Describe water as the universal solvent
  11. 1.2.11Explain surface tension and capillary action
  12. 1.2.12Define pH and the pH scale
  13. 1.2.13Distinguish acids, bases, and neutral solutions
  14. 1.2.14Explain buffers and their role in homeostasis
  15. 1.2.15Define molecule, compound, and mixture
  16. 1.2.16Explain chemical reactions and reactants - products
1.3Biomolecules — Carbohydrates & Lipids0 / 15
  1. 1.3.1Define monomers and polymers
  2. 1.3.2Explain dehydration synthesis and hydrolysis
  3. 1.3.3Identify carbohydrate elements and functions
  4. 1.3.4Distinguish monosaccharides, disaccharides, polysaccharides
  5. 1.3.5Name common monosaccharides (glucose, fructose, galactose)
  6. 1.3.6Describe glycosidic bond formation
  7. 1.3.7Compare starch, glycogen, and cellulose structure - function
  8. 1.3.8Explain chitin in fungi and arthropods
  9. 1.3.9Identify lipid elements and general properties
  10. 1.3.10Describe triglyceride structure (glycerol + fatty acids)
  11. 1.3.11Distinguish saturated vs unsaturated fatty acids
  12. 1.3.12Explain phospholipid structure and amphipathic nature
  13. 1.3.13Describe steroid structure and examples (cholesterol)
  14. 1.3.14Explain functions of lipids (energy, insulation, signaling)
  15. 1.3.15Describe waxes and their biological roles
1.4Biomolecules — Proteins & Nucleic Acids0 / 15
  1. 1.4.1Identify protein elements and functions
  2. 1.4.2Draw the general structure of an amino acid
  3. 1.4.3Explain peptide bond formation
  4. 1.4.4Describe primary protein structure
  5. 1.4.5Describe secondary structure (alpha helix, beta sheet)
  6. 1.4.6Describe tertiary and quaternary structures
  7. 1.4.7Explain protein denaturation and causes
  8. 1.4.8List protein functions (structural, enzymatic, transport, defense)
  9. 1.4.9Identify nucleic acid elements
  10. 1.4.10Describe nucleotide structure (sugar, phosphate, base)
  11. 1.4.11Distinguish purines and pyrimidines
  12. 1.4.12Compare DNA and RNA structure
  13. 1.4.13Explain complementary base pairing
  14. 1.4.14Describe ATP structure and role as energy currency
  15. 1.4.15Use biochemical food tests (Benedict's, iodine, Biuret, Sudan)
2.1Cell Theory & Microscopy0 / 8
  1. 2.1.1State the three tenets of cell theory
  2. 2.1.2Identify contributions of Hooke, Leeuwenhoek, Schleiden, Schwann, Virchow
  3. 2.1.3Distinguish magnification and resolution
  4. 2.1.4Compare light and electron microscopes (TEM, SEM)
  5. 2.1.5Calculate magnification and actual size from scale bars
  6. 2.1.6Explain staining techniques and their purpose
  7. 2.1.7Prepare a wet mount slide
  8. 2.1.8Convert between micrometers, nanometers, millimeters
2.2Prokaryotic vs Eukaryotic Cells0 / 7
  1. 2.2.1Compare prokaryotic and eukaryotic cells
  2. 2.2.2Describe bacterial cell structure (nucleoid, plasmid, capsule)
  3. 2.2.3Describe the bacterial cell wall and flagella
  4. 2.2.4Compare plant and animal cells
  5. 2.2.5Explain the endosymbiotic theory
  6. 2.2.6Describe the surface-area-to-volume ratio constraint
  7. 2.2.7Explain why cells remain microscopic
2.3Organelles & Their Functions0 / 15
  1. 2.3.1Describe nucleus structure and function
  2. 2.3.2Explain the nucleolus and ribosome assembly
  3. 2.3.3Describe rough vs smooth endoplasmic reticulum
  4. 2.3.4Explain Golgi apparatus function
  5. 2.3.5Describe ribosome structure and role
  6. 2.3.6Explain mitochondria structure and function
  7. 2.3.7Describe chloroplast structure and function
  8. 2.3.8Explain lysosome function and autophagy
  9. 2.3.9Describe peroxisomes and their role
  10. 2.3.10Explain vacuoles in plant and animal cells
  11. 2.3.11Describe the cytoskeleton (microfilaments, microtubules, intermediate filaments)
  12. 2.3.12Explain centrioles and the centrosome
  13. 2.3.13Describe cilia and flagella structure (9+2 arrangement)
  14. 2.3.14Explain the cell wall composition in plants
  15. 2.3.15Trace the endomembrane system protein pathway
2.4Cell Membrane & Transport0 / 17
  1. 2.4.1Describe the fluid mosaic model
  2. 2.4.2Explain phospholipid bilayer arrangement
  3. 2.4.3Identify membrane proteins (integral, peripheral)
  4. 2.4.4Explain the role of cholesterol in membranes
  5. 2.4.5Describe selective permeability
  6. 2.4.6Distinguish passive and active transport
  7. 2.4.7Explain simple diffusion
  8. 2.4.8Explain facilitated diffusion and channel - carrier proteins
  9. 2.4.9Describe osmosis and water potential
  10. 2.4.10Define hypertonic, hypotonic, and isotonic solutions
  11. 2.4.11Explain plasmolysis and turgor in plant cells
  12. 2.4.12Explain crenation and lysis in animal cells
  13. 2.4.13Describe primary active transport (sodium-potassium pump)
  14. 2.4.14Explain secondary active transport (co-transport)
  15. 2.4.15Describe endocytosis (phagocytosis, pinocytosis)
  16. 2.4.16Describe receptor-mediated endocytosis
  17. 2.4.17Explain exocytosis
2.5Enzymes & Bioenergetics Basics0 / 14
  1. 2.5.1Define metabolism, energy, and ATP
  2. 2.5.2Explain the laws of thermodynamics in biology
  3. 2.5.3Distinguish exergonic and endergonic reactions
  4. 2.5.4Define activation energy
  5. 2.5.5Explain enzymes as biological catalysts
  6. 2.5.6Describe the active site and lock-and-key model
  7. 2.5.7Explain the induced-fit model
  8. 2.5.8Describe effect of temperature on enzyme activity
  9. 2.5.9Describe effect of pH on enzyme activity
  10. 2.5.10Explain substrate concentration effects
  11. 2.5.11Distinguish competitive and non-competitive inhibition
  12. 2.5.12Explain allosteric regulation
  13. 2.5.13Describe feedback inhibition
  14. 2.5.14Define cofactors and coenzymes
2.6Cellular Respiration0 / 11
  1. 2.6.1Write the overall equation for aerobic respiration
  2. 2.6.2Describe glycolysis inputs and outputs
  3. 2.6.3Explain pyruvate oxidation (link reaction)
  4. 2.6.4Describe the Krebs cycle inputs and outputs
  5. 2.6.5Explain the electron transport chain
  6. 2.6.6Describe chemiosmosis and ATP synthase
  7. 2.6.7Calculate ATP yield from one glucose
  8. 2.6.8Distinguish aerobic and anaerobic respiration
  9. 2.6.9Describe lactic acid fermentation
  10. 2.6.10Describe alcoholic fermentation
  11. 2.6.11Explain the role of NAD+ and FAD as electron carriers
2.7Photosynthesis0 / 12
  1. 2.7.1Write the overall equation for photosynthesis
  2. 2.7.2Describe chloroplast structure relevant to photosynthesis
  3. 2.7.3Explain photosynthetic pigments and absorption spectra
  4. 2.7.4Describe the light-dependent reactions
  5. 2.7.5Explain photolysis of water
  6. 2.7.6Describe photophosphorylation (cyclic and non-cyclic)
  7. 2.7.7Explain the Calvin cycle (carbon fixation)
  8. 2.7.8Describe the role of RuBisCO
  9. 2.7.9Distinguish C3, C4, and CAM plants
  10. 2.7.10Explain photorespiration
  11. 2.7.11List limiting factors of photosynthesis
  12. 2.7.12Compare photosynthesis and respiration
2.8Cell Division0 / 17
  1. 2.8.1Describe the cell cycle phases (G1, S, G2, M)
  2. 2.8.2Explain interphase events
  3. 2.8.3Describe chromosome structure (chromatid, centromere)
  4. 2.8.4Explain the stages of mitosis (PMAT)
  5. 2.8.5Describe cytokinesis in plant and animal cells
  6. 2.8.6Explain the function of mitosis
  7. 2.8.7Describe cell cycle checkpoints
  8. 2.8.8Explain the role of cyclins and CDKs
  9. 2.8.9Relate uncontrolled division to cancer
  10. 2.8.10Distinguish diploid and haploid cells
  11. 2.8.11Explain homologous chromosomes
  12. 2.8.12Describe the stages of meiosis I and II
  13. 2.8.13Explain crossing over and chiasmata
  14. 2.8.14Describe independent assortment
  15. 2.8.15Compare mitosis and meiosis
  16. 2.8.16Explain how meiosis generates genetic variation
  17. 2.8.17Describe nondisjunction and its consequences
3.1Mendelian Genetics0 / 11
  1. 3.1.1Define key terms (gene, allele, genotype, phenotype)
  2. 3.1.2Distinguish dominant and recessive alleles
  3. 3.1.3Distinguish homozygous and heterozygous
  4. 3.1.4State Mendel's law of segregation
  5. 3.1.5State Mendel's law of independent assortment
  6. 3.1.6Solve monohybrid crosses with Punnett squares
  7. 3.1.7Solve dihybrid crosses
  8. 3.1.8Use the test cross to determine genotype
  9. 3.1.9Calculate probability ratios in offspring
  10. 3.1.10Apply the product and sum rules
  11. 3.1.11Construct and interpret pedigree charts
3.2Extensions of Mendelian Genetics0 / 12
  1. 3.2.1Explain incomplete dominance
  2. 3.2.2Explain codominance (e.g., ABO blood groups)
  3. 3.2.3Describe multiple alleles
  4. 3.2.4Explain polygenic inheritance
  5. 3.2.5Describe pleiotropy
  6. 3.2.6Explain epistasis
  7. 3.2.7Describe sex-linked inheritance
  8. 3.2.8Explain X-linked recessive disorders (hemophilia, colorblindness)
  9. 3.2.9Describe sex determination systems
  10. 3.2.10Explain linkage and recombination frequency
  11. 3.2.11Construct simple genetic linkage maps
  12. 3.2.12Describe environmental effects on phenotype
3.3DNA Structure & Replication0 / 12
  1. 3.3.1Summarize evidence that DNA is the genetic material (Griffith, Avery, Hershey-Chase)
  2. 3.3.2Describe the Watson-Crick double helix model
  3. 3.3.3Explain antiparallel strands and the 5'-3' directions
  4. 3.3.4Explain Chargaff's rules
  5. 3.3.5Describe semi-conservative replication (Meselson-Stahl)
  6. 3.3.6Explain the role of DNA helicase
  7. 3.3.7Describe the function of DNA polymerase
  8. 3.3.8Distinguish leading and lagging strands
  9. 3.3.9Explain Okazaki fragments and DNA ligase
  10. 3.3.10Describe primers and primase
  11. 3.3.11Explain telomeres and telomerase
  12. 3.3.12Describe DNA proofreading and repair mechanisms
3.4Transcription, Translation & Gene Expression0 / 13
  1. 3.4.1Describe the central dogma of molecular biology
  2. 3.4.2Distinguish mRNA, tRNA, and rRNA
  3. 3.4.3Describe transcription initiation, elongation, termination
  4. 3.4.4Explain the role of RNA polymerase and promoters
  5. 3.4.5Describe RNA processing (5' cap, poly-A tail, splicing)
  6. 3.4.6Explain introns and exons
  7. 3.4.7Describe alternative splicing
  8. 3.4.8Read the genetic code from a codon table
  9. 3.4.9Explain degeneracy of the genetic code
  10. 3.4.10Describe the ribosome's A, P, E sites
  11. 3.4.11Explain translation initiation, elongation, termination
  12. 3.4.12Describe the role of tRNA and anticodons
  13. 3.4.13Explain post-translational modification
3.5Mutations & Gene Regulation0 / 13
  1. 3.5.1Define mutation and mutagen
  2. 3.5.2Distinguish point mutations (substitution, insertion, deletion)
  3. 3.5.3Explain silent, missense, and nonsense mutations
  4. 3.5.4Describe frameshift mutations
  5. 3.5.5Distinguish chromosomal mutations (deletion, duplication, inversion, translocation)
  6. 3.5.6Relate mutations to genetic disorders (sickle cell, CF)
  7. 3.5.7Explain germline vs somatic mutations
  8. 3.5.8Describe the lac operon (inducible system)
  9. 3.5.9Describe the trp operon (repressible system)
  10. 3.5.10Explain transcription factors and enhancers
  11. 3.5.11Describe epigenetics (DNA methylation, histone modification)
  12. 3.5.12Explain the role of microRNA and RNA interference
  13. 3.5.13Describe gene regulation in development
4.1Digestive System0 / 11
  1. 4.1.1Describe the function of the digestive system
  2. 4.1.2Trace the path of food through the alimentary canal
  3. 4.1.3Distinguish mechanical and chemical digestion
  4. 4.1.4Describe the role of teeth and saliva
  5. 4.1.5Explain stomach function and gastric juices
  6. 4.1.6Describe small intestine structure (villi, microvilli)
  7. 4.1.7Explain the role of the pancreas and bile
  8. 4.1.8List digestive enzymes and their substrates
  9. 4.1.9Describe nutrient absorption mechanisms
  10. 4.1.10Explain large intestine and water reabsorption
  11. 4.1.11Describe peristalsis
4.2Circulatory System0 / 12
  1. 4.2.1Describe blood components (plasma, RBCs, WBCs, platelets)
  2. 4.2.2Explain the function of hemoglobin
  3. 4.2.3Describe heart structure and chambers
  4. 4.2.4Trace pulmonary and systemic circulation
  5. 4.2.5Explain the cardiac cycle
  6. 4.2.6Describe the conduction system (SA, AV node)
  7. 4.2.7Compare arteries, veins, and capillaries
  8. 4.2.8Explain blood pressure and its regulation
  9. 4.2.9Describe blood clotting mechanism
  10. 4.2.10Explain ABO and Rh blood group systems
  11. 4.2.11Describe the lymphatic system role
  12. 4.2.12Compare open and closed circulatory systems
4.3Respiratory System0 / 9
  1. 4.3.1Describe the pathway of air through the respiratory tract
  2. 4.3.2Explain alveolar gas exchange
  3. 4.3.3Describe the mechanics of breathing (diaphragm, intercostals)
  4. 4.3.4Explain inhalation and exhalation pressure changes
  5. 4.3.5Describe oxygen and CO2 transport in blood
  6. 4.3.6Explain the oxygen-hemoglobin dissociation curve
  7. 4.3.7Describe the Bohr effect
  8. 4.3.8Explain regulation of breathing rate
  9. 4.3.9Compare respiratory surfaces across organisms (gills, tracheae)
4.4Nervous System0 / 12
  1. 4.4.1Describe neuron structure (dendrites, axon, soma)
  2. 4.4.2Distinguish sensory, motor, and interneurons
  3. 4.4.3Explain the resting membrane potential
  4. 4.4.4Describe the action potential
  5. 4.4.5Explain saltatory conduction and myelin
  6. 4.4.6Describe synaptic transmission and neurotransmitters
  7. 4.4.7Compare the CNS and PNS
  8. 4.4.8Describe brain regions and functions
  9. 4.4.9Explain the reflex arc
  10. 4.4.10Distinguish somatic and autonomic systems
  11. 4.4.11Compare sympathetic and parasympathetic divisions
  12. 4.4.12Describe sensory receptors and the eye - ear basics
4.5Endocrine System0 / 10
  1. 4.5.1Distinguish endocrine and exocrine glands
  2. 4.5.2Describe the major endocrine glands and locations
  3. 4.5.3Explain hormone types (steroid vs peptide)
  4. 4.5.4Describe hormone mechanisms of action
  5. 4.5.5Explain the hypothalamus-pituitary axis
  6. 4.5.6Describe insulin and glucagon in glucose regulation
  7. 4.5.7Explain thyroid hormones and metabolism
  8. 4.5.8Describe adrenal hormones and stress response
  9. 4.5.9Explain negative feedback in hormone control
  10. 4.5.10Describe the menstrual cycle hormonal control
4.6Excretory System & Homeostasis0 / 8
  1. 4.6.1Describe kidney structure and the nephron
  2. 4.6.2Explain filtration, reabsorption, and secretion
  3. 4.6.3Describe urine formation
  4. 4.6.4Explain osmoregulation
  5. 4.6.5Describe the role of ADH and aldosterone
  6. 4.6.6Explain nitrogenous waste forms (ammonia, urea, uric acid)
  7. 4.6.7Describe thermoregulation mechanisms
  8. 4.6.8Explain the role of the liver in homeostasis
4.7Immune System0 / 12
  1. 4.7.1Distinguish innate and adaptive immunity
  2. 4.7.2Describe physical and chemical barriers
  3. 4.7.3Explain the inflammatory response
  4. 4.7.4Describe phagocytosis by macrophages and neutrophils
  5. 4.7.5Distinguish B cells and T cells
  6. 4.7.6Explain antibody structure and function
  7. 4.7.7Describe humoral vs cell-mediated immunity
  8. 4.7.8Explain antigen presentation and MHC
  9. 4.7.9Describe immunological memory
  10. 4.7.10Explain active vs passive immunity
  11. 4.7.11Describe vaccines and herd immunity
  12. 4.7.12Explain allergies and autoimmune disorders
4.8Reproductive System & Development0 / 9
  1. 4.8.1Describe male reproductive anatomy
  2. 4.8.2Describe female reproductive anatomy
  3. 4.8.3Explain spermatogenesis and oogenesis
  4. 4.8.4Describe fertilization
  5. 4.8.5Explain early embryonic development (cleavage, blastula, gastrula)
  6. 4.8.6Describe the role of the placenta
  7. 4.8.7Explain stages of pregnancy and birth
  8. 4.8.8Describe contraception methods overview
  9. 4.8.9Explain hormonal control of reproduction
4.9Plant Biology0 / 12
  1. 4.9.1Describe plant tissue types (dermal, vascular, ground)
  2. 4.9.2Explain xylem and phloem structure - function
  3. 4.9.3Describe root, stem, and leaf anatomy
  4. 4.9.4Explain transpiration and the cohesion-tension theory
  5. 4.9.5Describe translocation in phloem (pressure-flow)
  6. 4.9.6Explain stomatal opening and closing
  7. 4.9.7Describe plant hormones (auxin, gibberellin, cytokinin, ABA, ethylene)
  8. 4.9.8Explain tropisms (photo-, gravi-, thigmotropism)
  9. 4.9.9Describe plant reproduction (pollination, fertilization)
  10. 4.9.10Explain seed and fruit formation
  11. 4.9.11Describe the alternation of generations
  12. 4.9.12Explain photoperiodism and flowering
5.1Ecology & Ecosystems0 / 12
  1. 5.1.1Define ecology and levels of ecological organization
  2. 5.1.2Distinguish biotic and abiotic factors
  3. 5.1.3Describe habitat and ecological niche
  4. 5.1.4Explain food chains and food webs
  5. 5.1.5Describe trophic levels and energy flow
  6. 5.1.6Construct ecological pyramids (energy, biomass, numbers)
  7. 5.1.7Explain the 10% rule of energy transfer
  8. 5.1.8Describe the carbon cycle
  9. 5.1.9Describe the nitrogen cycle
  10. 5.1.10Describe the water and phosphorus cycles
  11. 5.1.11Distinguish primary and secondary succession
  12. 5.1.12Describe major biomes and their characteristics
5.2Population & Community Ecology0 / 11
  1. 5.2.1Define population density and distribution
  2. 5.2.2Explain exponential vs logistic growth
  3. 5.2.3Describe carrying capacity
  4. 5.2.4Distinguish density-dependent and density-independent factors
  5. 5.2.5Compare r-selected and K-selected species
  6. 5.2.6Interpret survivorship curves
  7. 5.2.7Describe predation and its effects
  8. 5.2.8Explain competition (interspecific, intraspecific)
  9. 5.2.9Describe symbiosis (mutualism, commensalism, parasitism)
  10. 5.2.10Explain keystone species and their role
  11. 5.2.11Describe biodiversity and its importance
5.3Conservation & Human Impact0 / 9
  1. 5.3.1Explain causes of biodiversity loss
  2. 5.3.2Describe habitat fragmentation effects
  3. 5.3.3Explain bioaccumulation and biomagnification
  4. 5.3.4Describe the greenhouse effect and climate change
  5. 5.3.5Explain eutrophication
  6. 5.3.6Describe ozone depletion
  7. 5.3.7Explain invasive species impacts
  8. 5.3.8Describe conservation strategies
  9. 5.3.9Explain sustainable resource management
5.4Evolution & Natural Selection0 / 11
  1. 5.4.1Describe evidence for evolution (fossils, anatomy, molecular)
  2. 5.4.2Distinguish homologous and analogous structures
  3. 5.4.3Explain vestigial structures
  4. 5.4.4Describe Darwin's theory of natural selection
  5. 5.4.5Explain variation, overproduction, and differential survival
  6. 5.4.6Distinguish natural and artificial selection
  7. 5.4.7Describe types of selection (directional, stabilizing, disruptive)
  8. 5.4.8Explain sexual selection
  9. 5.4.9Describe adaptive radiation
  10. 5.4.10Explain convergent and divergent evolution
  11. 5.4.11Describe coevolution
5.5Population Genetics & Speciation0 / 11
  1. 5.5.1State the Hardy-Weinberg principle and assumptions
  2. 5.5.2Calculate allele and genotype frequencies
  3. 5.5.3Explain genetic drift and the bottleneck - founder effects
  4. 5.5.4Describe gene flow and migration
  5. 5.5.5Explain the role of mutation in evolution
  6. 5.5.6Define species (biological species concept)
  7. 5.5.7Distinguish allopatric and sympatric speciation
  8. 5.5.8Describe reproductive isolation mechanisms (pre - postzygotic)
  9. 5.5.9Explain gradualism vs punctuated equilibrium
  10. 5.5.10Describe the origin of life hypotheses
  11. 5.5.11Explain phylogenetic trees and cladistics
5.6Taxonomy & Classification0 / 9
  1. 5.6.1Explain the purpose of classification
  2. 5.6.2Describe the binomial nomenclature system
  3. 5.6.3List the taxonomic hierarchy (domain to species)
  4. 5.6.4Describe the three-domain system
  5. 5.6.5Characterize the six kingdoms
  6. 5.6.6Distinguish Archaea, Bacteria, and Eukarya
  7. 5.6.7Describe the main features of each eukaryotic kingdom
  8. 5.6.8Explain dichotomous keys
  9. 5.6.9Describe molecular phylogenetics in classification
5.7Microbiology0 / 13
  1. 5.7.1Describe bacterial morphology and arrangement
  2. 5.7.2Explain Gram staining and cell wall differences
  3. 5.7.3Describe bacterial reproduction (binary fission)
  4. 5.7.4Explain bacterial genetic exchange (conjugation, transformation, transduction)
  5. 5.7.5Describe bacterial growth curves
  6. 5.7.6Explain virus structure and classification
  7. 5.7.7Compare lytic and lysogenic cycles
  8. 5.7.8Describe retroviruses and reverse transcription
  9. 5.7.9Explain prions and viroids
  10. 5.7.10Describe protists, fungi, and their roles
  11. 5.7.11Explain the role of microbes in disease and ecology
  12. 5.7.12Describe antibiotics and antibiotic resistance
  13. 5.7.13Explain aseptic technique and microbial culturing
6.1Genomics0 / 12
  1. 6.1.1Define genome, proteome, and transcriptome
  2. 6.1.2Describe the Human Genome Project
  3. 6.1.3Explain DNA sequencing (Sanger method)
  4. 6.1.4Describe next-generation sequencing (NGS)
  5. 6.1.5Explain whole-genome and exome sequencing
  6. 6.1.6Describe genome annotation
  7. 6.1.7Explain comparative genomics
  8. 6.1.8Describe single-nucleotide polymorphisms (SNPs)
  9. 6.1.9Explain genome-wide association studies (GWAS)
  10. 6.1.10Describe non-coding DNA and the ENCODE findings
  11. 6.1.11Explain pharmacogenomics
  12. 6.1.12Describe personalized - precision medicine
6.2Genetic Engineering & CRISPR0 / 15
  1. 6.2.1Describe recombinant DNA technology
  2. 6.2.2Explain restriction enzymes and their use
  3. 6.2.3Describe plasmids as cloning vectors
  4. 6.2.4Explain DNA ligation and transformation
  5. 6.2.5Describe gene cloning workflow
  6. 6.2.6Explain the polymerase chain reaction (PCR)
  7. 6.2.7Describe qPCR and RT-PCR applications
  8. 6.2.8Explain gel electrophoresis
  9. 6.2.9Describe DNA fingerprinting
  10. 6.2.10Explain the CRISPR-Cas9 mechanism
  11. 6.2.11Describe guide RNA design
  12. 6.2.12Distinguish knockouts and knock-ins
  13. 6.2.13Explain base editing and prime editing
  14. 6.2.14Describe gene therapy approaches
  15. 6.2.15Discuss ethical issues of genome editing
6.3Biotechnology Applications0 / 13
  1. 6.3.1Describe transgenic organisms and GMOs
  2. 6.3.2Explain production of insulin via bacteria
  3. 6.3.3Describe Bt crops and herbicide resistance
  4. 6.3.4Explain golden rice and biofortification
  5. 6.3.5Describe vaccine production technologies (mRNA, recombinant)
  6. 6.3.6Explain monoclonal antibody production
  7. 6.3.7Describe stem cells and regenerative medicine
  8. 6.3.8Explain induced pluripotent stem cells (iPSCs)
  9. 6.3.9Describe cloning (reproductive and therapeutic)
  10. 6.3.10Explain tissue engineering and organoids
  11. 6.3.11Describe industrial fermentation and bioreactors
  12. 6.3.12Explain biofuels and bioremediation
  13. 6.3.13Describe synthetic biology and engineered pathways
6.4Bioinformatics & Computational Biology0 / 12
  1. 6.4.1Define bioinformatics and its goals
  2. 6.4.2Describe biological databases (GenBank, UniProt, PDB)
  3. 6.4.3Explain sequence alignment (pairwise, multiple)
  4. 6.4.4Describe BLAST and homology searching
  5. 6.4.5Explain scoring matrices (BLOSUM, PAM)
  6. 6.4.6Describe phylogenetic tree construction algorithms
  7. 6.4.7Explain gene prediction methods
  8. 6.4.8Describe protein structure prediction (AlphaFold)
  9. 6.4.9Explain RNA-seq data analysis basics
  10. 6.4.10Describe variant calling pipelines
  11. 6.4.11Explain data visualization in genomics
  12. 6.4.12Introduce machine learning in biology
6.5Systems Biology & Frontiers0 / 13
  1. 6.5.1Define systems biology and holistic modeling
  2. 6.5.2Describe gene regulatory networks
  3. 6.5.3Explain metabolic network modeling
  4. 6.5.4Describe signal transduction networks
  5. 6.5.5Explain omics integration (multi-omics)
  6. 6.5.6Describe emergent behavior in biological systems
  7. 6.5.7Explain mathematical modeling of biological systems
  8. 6.5.8Describe the microbiome and its systemic effects
  9. 6.5.9Explain epigenomics at the genome scale
  10. 6.5.10Describe single-cell sequencing technologies
  11. 6.5.11Explain spatial transcriptomics
  12. 6.5.12Discuss synthetic genomes and minimal cells
  13. 6.5.13Describe current ethical and societal challenges in biology

Maths

0 / 507 · 0%
1.1Arithmetic & Number Systems0 / 22
  1. 1.1.1Natural numbers, whole numbers, integers — definitions and the number line
  2. 1.1.2Place value system — units, tens, hundreds, thousands, lakhs, crores
  3. 1.1.3Addition and subtraction — carrying, borrowing, word problems
  4. 1.1.4Multiplication — tables (1–20), long multiplication, area model
  5. 1.1.5Division — long division, remainder, dividend - divisor - quotient vocabulary
  6. 1.1.6Order of operations — BODMAS - PEMDAS with nested brackets
  7. 1.1.7Factors and multiples — all factors of a number, factor pairs
  8. 1.1.8Prime numbers — Sieve of Eratosthenes, primality testing
  9. 1.1.9Prime factorization — factor trees, ladder method
  10. 1.1.10HCF (GCD) — prime factorization method, Euclidean algorithm
  11. 1.1.11LCM — prime factorization method, relationship HCF × LCM = product
  12. 1.1.12Fractions — proper, improper, mixed numbers
  13. 1.1.13Equivalent fractions, simplifying fractions
  14. 1.1.14Addition, subtraction, multiplication, division of fractions
  15. 1.1.15Decimals — place value, reading and writing
  16. 1.1.16Converting - fractions ↔ decimals ↔ percentages
  17. 1.1.17Operations on decimals — all four operations
  18. 1.1.18Percentages — finding %, % of a quantity, % increase - decrease
  19. 1.1.19Ratio and proportion — equivalent ratios, dividing in a ratio
  20. 1.1.20Unitary method — direct and inverse proportion
  21. 1.1.21Profit, loss, discount, simple interest — basic applications
  22. 1.1.22Absolute value - modulus — definition, number line interpretation
1.2Basic Geometry0 / 17
  1. 1.2.1Points, lines, line segments, rays — notation and differences
  2. 1.2.2Types of angles — acute, right, obtuse, straight, reflex, complete
  3. 1.2.3Angle measurement — protractor use, angle relationships (complementary, supplementary)
  4. 1.2.4Parallel and perpendicular lines — properties, transversal, alternate - co-interior angles
  5. 1.2.5Triangles — scalene, isosceles, equilateral; acute, right, obtuse
  6. 1.2.6Triangle properties — angle sum = 180°, exterior angle theorem
  7. 1.2.7Quadrilaterals — square, rectangle, parallelogram, rhombus, trapezium, kite
  8. 1.2.8Properties of each quadrilateral — diagonals, angles, symmetry
  9. 1.2.9Circles — centre, radius, diameter, chord, arc, sector, segment
  10. 1.2.10Circumference and area of a circle
  11. 1.2.11Perimeter of polygons — regular and irregular
  12. 1.2.12Area — triangle, parallelogram, trapezium, composite shapes
  13. 1.2.133D shapes — cube, cuboid, cylinder, cone, sphere, prism, pyramid
  14. 1.2.14Surface area and volume of all above 3D shapes
  15. 1.2.15Nets of 3D shapes
  16. 1.2.16Symmetry — line symmetry, rotational symmetry, order of symmetry
  17. 1.2.17Transformations — translation, reflection, rotation, enlargement (basic)
1.3Basic Data & Probability0 / 7
  1. 1.3.1Data collection — primary vs secondary, tally charts, frequency tables
  2. 1.3.2Bar charts, pictograms, pie charts — drawing and reading
  3. 1.3.3Line graphs and scatter plots — basic interpretation
  4. 1.3.4Mean, median, mode — calculation for raw and grouped data
  5. 1.3.5Range — definition and calculation
  6. 1.3.6Probability basics — sample space, events, P(E) = favourable - total
  7. 1.3.7Complementary events — P(A') = 1 − P(A)
2.1Algebra — Introduction & Intermediate0 / 24
  1. 2.1.1Variables, constants, coefficients — algebraic expressions
  2. 2.1.2Like and unlike terms — simplification
  3. 2.1.3Addition and subtraction of algebraic expressions
  4. 2.1.4Multiplication of algebraic expressions — monomial × polynomial, polynomial × polynomial
  5. 2.1.5Algebraic identities — (a+b)², (a−b)², (a+b)(a−b), (a+b)³, (a−b)³, (a³+b³), (a³−b³)
  6. 2.1.6Factoring — common factor extraction, grouping, using identities
  7. 2.1.7Linear equations in one variable — solving, transposition method
  8. 2.1.8Word problems using linear equations
  9. 2.1.9Linear equations in two variables — graphical and algebraic solutions
  10. 2.1.10Simultaneous equations — substitution, elimination, cross-multiplication
  11. 2.1.11Inequalities — linear, solving, number line representation
  12. 2.1.12Compound inequalities — AND, OR
  13. 2.1.13Polynomials — degree, types (monomial, binomial, trinomial)
  14. 2.1.14Polynomial long division and synthetic division
  15. 2.1.15Remainder theorem and factor theorem — proof and applications
  16. 2.1.16Quadratic equations — factoring, completing the square
  17. 2.1.17Quadratic formula — derivation by completing the square
  18. 2.1.18Discriminant — nature of roots (real - equal - complex)
  19. 2.1.19Vieta's formulas — sum and product of roots
  20. 2.1.20Formation of quadratic with given roots
  21. 2.1.21Rational expressions — simplification, operations
  22. 2.1.22Radical (surd) expressions — simplification, rationalization
  23. 2.1.23Equations with radicals — squaring both sides, extraneous solutions
  24. 2.1.24Absolute value equations and inequalities
2.2Functions0 / 11
  1. 2.2.1Concept of a function — input, output, mapping
  2. 2.2.2Domain, codomain, range
  3. 2.2.3Function notation — f(x), g(x)
  4. 2.2.4Vertical line test for functions
  5. 2.2.5Types — constant, linear, quadratic, polynomial, rational, radical, piecewise
  6. 2.2.6Graphs of functions — plotting, reading key features
  7. 2.2.7Transformations — vertical - horizontal shifts, reflections, stretches - compressions
  8. 2.2.8Composition of functions — f(g(x)), g(f(x))
  9. 2.2.9Inverse functions — finding f⁻¹(x), horizontal line test
  10. 2.2.10Even and odd functions — graphical and algebraic tests
  11. 2.2.11Increasing and decreasing functions — intuitive definition
2.3Coordinate Geometry0 / 14
  1. 2.3.1Cartesian plane — axes, quadrants, ordered pairs
  2. 2.3.2Distance formula — derivation using Pythagoras
  3. 2.3.3Midpoint formula
  4. 2.3.4Section formula — internal and external division
  5. 2.3.5Slope (gradient) — definition, formula, interpretation
  6. 2.3.6Equations of a line — slope-intercept, point-slope, two-point, standard (ax+by+c=0)
  7. 2.3.7Intercepts — x-intercept, y-intercept
  8. 2.3.8Parallel lines — equal slopes
  9. 2.3.9Perpendicular lines — product of slopes = −1
  10. 2.3.10Distance from a point to a line
  11. 2.3.11Area of triangle using coordinate formula
  12. 2.3.12Collinearity of three points
  13. 2.3.13Circle equation — standard form (x−h)² + (y−k)² = r²
  14. 2.3.14General form of circle — converting, finding centre and radius
2.4Trigonometry — Foundation0 / 7
  1. 2.4.1Pythagorean theorem — proof (by similar triangles, rearrangement), converse
  2. 2.4.2Trigonometric ratios in right triangle — sin, cos, tan, cosec, sec, cot
  3. 2.4.3SOH-CAH-TOA mnemonic
  4. 2.4.4Trig ratios of standard angles — 0°, 30°, 45°, 60°, 90° (derive, don't memorize blindly)
  5. 2.4.5Complementary angle relationships — sin(90−θ) = cos θ etc.
  6. 2.4.6Reciprocal identities — cosec, sec, cot in terms of sin, cos, tan
  7. 2.4.7Applications — heights and distances problems
2.5Number Theory (Intermediate)0 / 11
  1. 2.5.1Divisibility rules — 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 (with proofs where possible)
  2. 2.5.2Integers — operations, number line, absolute value
  3. 2.5.3Rational numbers — definition, decimal expansion (terminating - repeating)
  4. 2.5.4Irrational numbers — √2, π, e — proof that √2 is irrational
  5. 2.5.5Real number system — ℕ ⊂ ℤ ⊂ ℚ ⊂ ℝ
  6. 2.5.6Modular arithmetic — definition, addition, multiplication, congruence
  7. 2.5.7Euclidean algorithm — GCD computation
  8. 2.5.8Extended Euclidean algorithm
  9. 2.5.9Bézout's identity
  10. 2.5.10Chinese Remainder Theorem (intro)
  11. 2.5.11Fermat's little theorem (statement)
2.6Matrices & Determinants — Introduction0 / 12
  1. 2.6.1Matrix definition — rows, columns, order, elements
  2. 2.6.2Types of matrices — row, column, square, diagonal, identity, zero, symmetric, skew-symmetric
  3. 2.6.3Matrix operations — addition, subtraction (conditions)
  4. 2.6.4Scalar multiplication
  5. 2.6.5Matrix multiplication — conditions, process, non-commutativity
  6. 2.6.6Transpose — definition, properties
  7. 2.6.7Determinant of 2×2 matrix
  8. 2.6.8Determinant of 3×3 matrix — cofactor expansion
  9. 2.6.9Properties of determinants
  10. 2.6.10Inverse of 2×2 matrix
  11. 2.6.11Solving 2×2 systems using Cramer's rule
  12. 2.6.12Solving systems using matrix inversion
2.7Statistics & Probability — Intermediate0 / 13
  1. 2.7.1Measures of central tendency — mean (grouped - ungrouped), median (grouped), mode (grouped)
  2. 2.7.2Cumulative frequency — ogive, median from graph
  3. 2.7.3Measures of dispersion — variance, standard deviation
  4. 2.7.4Box-and-whisker plots — quartiles, IQR
  5. 2.7.5Probability — classical, empirical, axiomatic (Kolmogorov axioms)
  6. 2.7.6Mutually exclusive events — addition rule
  7. 2.7.7Independent events — multiplication rule
  8. 2.7.8Conditional probability — P(A - B) = P(A∩B) - P(A)
  9. 2.7.9Bayes' theorem — derivation and applications
  10. 2.7.10Permutations — nPr, arrangements with restrictions
  11. 2.7.11Combinations — nCr, Pascal's triangle
  12. 2.7.12Binomial theorem — expansion, general term
  13. 2.7.13Binomial distribution — PMF, mean, variance
3.1Advanced Trigonometry0 / 22
  1. 3.1.1Unit circle definition of trig functions — all 6 trig functions for any angle
  2. 3.1.2Radian measure — definition, conversion formula degrees ↔ radians
  3. 3.1.3Arc length and sector area using radians
  4. 3.1.4Trig functions for angles beyond 90° — ASTC rule (All, Sin, Tan, Cos)
  5. 3.1.5Reference angles
  6. 3.1.6Graphs of sin x, cos x, tan x — key features, period, amplitude
  7. 3.1.7Graphs of cosec x, sec x, cot x
  8. 3.1.8Transformations of trig graphs — A·sin(Bx + C) + D (amplitude, period, phase, vertical shift)
  9. 3.1.9Pythagorean identities — sin² + cos² = 1, derivations of the other two
  10. 3.1.10Reciprocal identities, quotient identities
  11. 3.1.11Co-function identities
  12. 3.1.12Sum and difference formulas — sin(A±B), cos(A±B), tan(A±B) — proofs
  13. 3.1.13Double angle formulas — sin 2A, cos 2A (three forms), tan 2A
  14. 3.1.14Half angle formulas — derivations from double angle
  15. 3.1.15Product-to-sum formulas
  16. 3.1.16Sum-to-product formulas
  17. 3.1.17Inverse trig functions — arcsin, arccos, arctan — domain, range, graphs
  18. 3.1.18Solving trig equations — general solutions, solutions in given range
  19. 3.1.19Law of sines — proof and applications (ambiguous case)
  20. 3.1.20Law of cosines — proof and applications
  21. 3.1.21Area of triangle = ½ab·sin C
  22. 3.1.22Heron's formula (derivation using trig)
3.2Exponentials & Logarithms0 / 13
  1. 3.2.1Exponential functions aˣ — graphs, properties, asymptote
  2. 3.2.2Laws of exponents — review with real exponents
  3. 3.2.3The number e — definition as limit of (1+1 - n)ⁿ, natural growth context
  4. 3.2.4Natural exponential function eˣ — graph, derivative preview
  5. 3.2.5Exponential growth and decay models — half-life, doubling time
  6. 3.2.6Logarithm — definition as inverse of exponential
  7. 3.2.7Common log (log₁₀) and natural log (ln x)
  8. 3.2.8Laws of logarithms — product, quotient, power rules — proofs
  9. 3.2.9Change of base formula — proof
  10. 3.2.10Solving exponential equations using logarithms
  11. 3.2.11Solving logarithmic equations
  12. 3.2.12Graphs of logarithmic functions
  13. 3.2.13Logarithmic scale — decibels, Richter, pH
3.3Sequences & Series0 / 14
  1. 3.3.1Arithmetic progression (AP) — nth term, sum of n terms — derivations
  2. 3.3.2Geometric progression (GP) — nth term, sum of n terms — derivations
  3. 3.3.3Sum of infinite GP — when it converges, proof
  4. 3.3.4Harmonic progression — definition, HM
  5. 3.3.5AM-GM-HM inequalities — proofs
  6. 3.3.6Arithmetic-geometric progression — finding sum
  7. 3.3.7Sigma (Σ) notation — evaluating, telescoping sums
  8. 3.3.8Formulae — Σ1, Σn, Σn², Σn³ — proofs
  9. 3.3.9Mathematical induction — principle, steps, problems
  10. 3.3.10Strong induction
  11. 3.3.11Binomial theorem — statement, proof by induction
  12. 3.3.12Pascal's triangle — combinatorial interpretation
  13. 3.3.13General term of binomial expansion — finding specific terms
  14. 3.3.14Binomial theorem for rational indices (approximate values)
3.4Conic Sections0 / 12
  1. 3.4.1Definition via focus, directrix, eccentricity e
  2. 3.4.2Parabola — standard forms (4 orientations), focus, directrix, latus rectum, axis
  3. 3.4.3Reflective property of parabola (application in telescopes, antennas)
  4. 3.4.4Ellipse — standard forms, semi-major - minor axes, foci, eccentricity, latus rectum
  5. 3.4.5Sum of focal radii = 2a property
  6. 3.4.6Kepler's connection — orbits are ellipses (motivation)
  7. 3.4.7Hyperbola — standard forms, asymptotes, foci, eccentricity
  8. 3.4.8Difference of focal radii = 2a property
  9. 3.4.9Rectangular hyperbola xy = c²
  10. 3.4.10Circle as degenerate conic (e = 0)
  11. 3.4.11General second-degree equation Ax²+Bxy+Cy²+Dx+Ey+F=0 — discriminant classification
  12. 3.4.12Parametric forms of all conics
3.5Complex Numbers0 / 13
  1. 3.5.1Imaginary unit i = √(−1), i² = −1, powers of i cycle
  2. 3.5.2Complex number a+bi — real part, imaginary part
  3. 3.5.3Argand plane — geometric representation
  4. 3.5.4Modulus - z - and argument arg(z)
  5. 3.5.5Polar form — r(cos θ + i sin θ) = r·cis θ
  6. 3.5.6Euler's formula — e^(iθ) = cos θ + i sin θ (proof via Taylor series)
  7. 3.5.7Exponential form z = re^(iθ)
  8. 3.5.8Algebraic operations — add, subtract, multiply, divide (rectangular and polar)
  9. 3.5.9Complex conjugate — properties, applications in division
  10. 3.5.10De Moivre's theorem — statement, proof, applications
  11. 3.5.11nth roots of complex numbers — finding all n roots
  12. 3.5.12Roots of unity — cube roots, nth roots, geometric interpretation
  13. 3.5.13Applications — solving polynomial equations with complex roots
3.63D Geometry0 / 12
  1. 3.6.1Coordinate system in 3D — x, y, z axes, octants
  2. 3.6.2Distance formula in 3D
  3. 3.6.3Section formula in 3D
  4. 3.6.4Direction cosines and direction ratios
  5. 3.6.5Relation between direction cosines - l² + m² + n² = 1
  6. 3.6.6Equation of a line in 3D — vector, symmetric, parametric forms
  7. 3.6.7Angle between two lines
  8. 3.6.8Equation of a plane — normal form, intercept form, general form
  9. 3.6.9Angle between two planes
  10. 3.6.10Angle between line and plane
  11. 3.6.11Distance from a point to a plane
  12. 3.6.12Skew lines — shortest distance
4.1Calculus I — Limits & Derivatives0 / 33
  1. 4.1.1Intuitive concept of a limit — table of values, graphical
  2. 4.1.2Limit laws — sum, product, quotient, constant multiple
  3. 4.1.3One-sided limits — left-hand, right-hand
  4. 4.1.4Infinite limits and limits at infinity — vertical - horizontal asymptotes
  5. 4.1.5Squeeze theorem (sandwich theorem)
  6. 4.1.6Important limits — lim(sin x - x) = 1, lim((1+1 - n)ⁿ) = e
  7. 4.1.7Continuity — definition, types of discontinuity (removable, jump, infinite)
  8. 4.1.8Intermediate Value Theorem
  9. 4.1.9Epsilon-delta definition of a limit — formal proofs
  10. 4.1.10Derivative from first principles — difference quotient definition
  11. 4.1.11Interpretation — instantaneous rate of change, slope of tangent
  12. 4.1.12Power rule — proof for integer, rational exponents
  13. 4.1.13Sum, difference, constant multiple rules
  14. 4.1.14Product rule — proof
  15. 4.1.15Quotient rule — proof
  16. 4.1.16Chain rule — proof, composite function derivatives
  17. 4.1.17Derivatives of sin x, cos x — proofs from first principles
  18. 4.1.18Derivatives of all six trig functions
  19. 4.1.19Derivatives of eˣ and aˣ — proofs
  20. 4.1.20Derivatives of ln x and logₐ(x)
  21. 4.1.21Derivatives of inverse trig functions — all six
  22. 4.1.22Implicit differentiation — technique, applications
  23. 4.1.23Parametric differentiation — dy - dx, d²y - dx²
  24. 4.1.24Higher-order derivatives — notation, physical meaning
  25. 4.1.25Related rates — setting up and solving
  26. 4.1.26L'Hôpital's rule — proof using linear approximation, 0 - 0, ∞ - ∞, other indeterminate forms
  27. 4.1.27Mean Value Theorem — proof, Rolle's theorem
  28. 4.1.28Applications — increasing - decreasing, local extrema (first derivative test)
  29. 4.1.29Second derivative test — concavity, inflection points
  30. 4.1.30Curve sketching — systematic approach
  31. 4.1.31Optimization — constrained, unconstrained, real-world problems
  32. 4.1.32Linear approximation and differentials
  33. 4.1.33Newton-Raphson method for root finding
4.2Calculus II — Integration0 / 18
  1. 4.2.1Antiderivative — definition, family of solutions (+C)
  2. 4.2.2Basic integration rules — power, trig, exponential, log
  3. 4.2.3Riemann sums — left, right, midpoint; formal definition of definite integral
  4. 4.2.4Fundamental Theorem of Calculus — Part 1 and Part 2 — full proofs
  5. 4.2.5Net change theorem
  6. 4.2.6U-substitution — technique, change of limits for definite integrals
  7. 4.2.7Integration by parts — derivation from product rule, LIATE mnemonic
  8. 4.2.8Trigonometric integrals — sinᵐ·cosⁿ cases, tan and sec cases
  9. 4.2.9Trigonometric substitution — x = a sin θ, a tan θ, a sec θ cases
  10. 4.2.10Partial fractions — linear, repeated, irreducible quadratic factors
  11. 4.2.11Improper integrals — Type I (infinite limits), Type II (discontinuous integrand)
  12. 4.2.12Convergence tests for improper integrals — comparison
  13. 4.2.13Area between curves — horizontal and vertical slices
  14. 4.2.14Volume of revolution — disk method, washer method
  15. 4.2.15Volume of revolution — shell method
  16. 4.2.16Arc length formula — derivation
  17. 4.2.17Surface area of revolution
  18. 4.2.18Average value of a function
4.3Calculus III — Sequences & Series0 / 19
  1. 4.3.1Sequences — convergence, divergence, boundedness, monotonicity
  2. 4.3.2Squeeze theorem for sequences
  3. 4.3.3Series — partial sums, convergence definition
  4. 4.3.4Geometric series — convergence condition, proof
  5. 4.3.5Telescoping series
  6. 4.3.6Divergence test (necessary but not sufficient)
  7. 4.3.7Integral test — proof, p-series
  8. 4.3.8Direct comparison test
  9. 4.3.9Limit comparison test
  10. 4.3.10Alternating series test — Leibniz test, proof
  11. 4.3.11Absolute vs conditional convergence
  12. 4.3.12Ratio test — proof, limitations
  13. 4.3.13Root test
  14. 4.3.14Power series — centre, radius of convergence, interval of convergence
  15. 4.3.15Term-by-term differentiation and integration of power series
  16. 4.3.16Taylor series — derivation from power series
  17. 4.3.17Maclaurin series of eˣ, sin x, cos x, ln(1+x), (1+x)ⁿ — derive all
  18. 4.3.18Taylor's remainder theorem — error estimation
  19. 4.3.19Applications — approximation, evaluating limits
4.4Multivariable Calculus0 / 34
  1. 4.4.1Functions of several variables — graphs, level curves, level surfaces
  2. 4.4.2Limits and continuity in 2D — path-dependence issue
  3. 4.4.3Partial derivatives — notation, calculation, geometric meaning
  4. 4.4.4Clairaut's theorem — mixed partials are equal (under conditions)
  5. 4.4.5Tangent planes and linear approximations to surfaces
  6. 4.4.6Differentiability in multiple variables
  7. 4.4.7Chain rule for multivariable functions — all cases
  8. 4.4.8Directional derivative — definition, formula
  9. 4.4.9Gradient vector ∇f — definition, properties
  10. 4.4.10Gradient as direction of steepest ascent
  11. 4.4.11Gradient perpendicular to level curves - surfaces
  12. 4.4.12Critical points — finding, classifying
  13. 4.4.13Second derivative test — Hessian determinant
  14. 4.4.14Absolute extrema on closed bounded regions
  15. 4.4.15Lagrange multipliers — one and two constraints
  16. 4.4.16Double integrals over rectangles — Fubini's theorem
  17. 4.4.17Double integrals over general regions — Type I and II
  18. 4.4.18Changing order of integration
  19. 4.4.19Double integrals in polar coordinates — Jacobian r
  20. 4.4.20Triple integrals in Cartesian, cylindrical, spherical coordinates
  21. 4.4.21Change of variables — general Jacobian
  22. 4.4.22Applications — mass, centre of mass, moments of inertia
  23. 4.4.23Vector fields — definition, visualization
  24. 4.4.24Divergence — definition, physical meaning (flux density)
  25. 4.4.25Curl — definition, physical meaning (rotation)
  26. 4.4.26Conservative vector fields — potential functions
  27. 4.4.27Line integrals — scalar and vector, work done
  28. 4.4.28Fundamental theorem for line integrals
  29. 4.4.29Green's theorem — proof sketch, both forms
  30. 4.4.30Parametric surfaces — tangent planes, surface area
  31. 4.4.31Surface integrals — scalar and vector (flux)
  32. 4.4.32Stokes' theorem — statement, curl-circulation connection
  33. 4.4.33Divergence theorem (Gauss's theorem) — statement, flux-divergence connection
  34. 4.4.34Unification — all three theorems as generalized Stokes
4.5Linear Algebra (Full)0 / 44
  1. 4.5.1Vectors in ℝⁿ — operations, geometric interpretation
  2. 4.5.2Dot product — formula, cosine formula, Cauchy-Schwarz inequality proof
  3. 4.5.3Cross product — formula, geometric meaning (area), right-hand rule
  4. 4.5.4Projection of vectors
  5. 4.5.5Lines and planes in 3D — vector equations
  6. 4.5.6Matrices — review, operations, types
  7. 4.5.7Matrix multiplication — definition, associativity, non-commutativity
  8. 4.5.8Systems of linear equations — matrix form Ax = b
  9. 4.5.9Gaussian elimination — forward elimination, back substitution
  10. 4.5.10Row echelon form and reduced row echelon form
  11. 4.5.11Pivot positions, free variables
  12. 4.5.12Rank of a matrix — definition, row rank = column rank theorem
  13. 4.5.13Null space (kernel) and column space (image) — basis, dimension
  14. 4.5.14Rank-nullity theorem — proof
  15. 4.5.15Linear independence — formal definition, testing
  16. 4.5.16Span — definition
  17. 4.5.17Basis — definition, uniqueness of representation
  18. 4.5.18Dimension — basis cardinality
  19. 4.5.19Coordinate vectors — change of basis
  20. 4.5.20Change of basis matrix
  21. 4.5.21Determinants — cofactor expansion along any row - column
  22. 4.5.22Properties — row operations, multiplicativity
  23. 4.5.23Geometric interpretation — signed volume
  24. 4.5.24Cramer's rule
  25. 4.5.25Invertible matrix theorem — 12+ equivalent conditions
  26. 4.5.26LU decomposition — algorithm, applications
  27. 4.5.27Linear transformations — definition, kernel, image
  28. 4.5.28Matrix representation of linear transformations
  29. 4.5.29Eigenvalues and eigenvectors — characteristic polynomial
  30. 4.5.30Finding eigenspaces
  31. 4.5.31Diagonalization — conditions, procedure
  32. 4.5.32Complex eigenvalues — rotation-scaling interpretation
  33. 4.5.33Inner product spaces — dot product generalization
  34. 4.5.34Orthogonal sets and orthonormal basis
  35. 4.5.35Gram-Schmidt orthogonalization — algorithm
  36. 4.5.36QR decomposition
  37. 4.5.37Orthogonal matrices — properties, det = ±1
  38. 4.5.38Symmetric matrices — spectral theorem (real eigenvalues, orthogonal eigenvectors)
  39. 4.5.39Quadratic forms — positive definite, negative definite, indefinite
  40. 4.5.40Singular Value Decomposition (SVD) — full derivation
  41. 4.5.41Least squares — normal equations, QR approach
  42. 4.5.42Pseudoinverse
  43. 4.5.43Abstract vector spaces — axioms, examples beyond ℝⁿ
  44. 4.5.44Subspaces — four fundamental subspaces of a matrix
4.6Ordinary Differential Equations0 / 33
  1. 4.6.1Classification — order, degree, linear vs nonlinear, autonomous vs non-autonomous
  2. 4.6.2Direction fields and Euler's method — visual - numerical intuition first
  3. 4.6.3Separable ODEs — technique, implicit solutions
  4. 4.6.4First-order linear ODEs — integrating factor method (derivation)
  5. 4.6.5Bernoulli equations — substitution
  6. 4.6.6Exact equations — exactness condition, finding potential function
  7. 4.6.7Integrating factors for non-exact equations
  8. 4.6.8Existence and uniqueness theorem — Picard-Lindelöf (statement)
  9. 4.6.9Second-order linear ODEs — superposition principle, general theory
  10. 4.6.10Homogeneous with constant coefficients — characteristic equation
  11. 4.6.11Case 1 - two distinct real roots
  12. 4.6.12Case 2 - repeated real root — reduction of order
  13. 4.6.13Case 3 - complex conjugate roots — Euler's formula connection
  14. 4.6.14Non-homogeneous — method of undetermined coefficients (annihilator method)
  15. 4.6.15Non-homogeneous — variation of parameters
  16. 4.6.16Cauchy-Euler (Equidimensional) equation
  17. 4.6.17Power series solutions — ordinary points
  18. 4.6.18Frobenius method — regular singular points
  19. 4.6.19Bessel's equation and Bessel functions (intro, physical relevance)
  20. 4.6.20Legendre's equation and Legendre polynomials (intro)
  21. 4.6.21Systems of first-order linear ODEs — matrix method
  22. 4.6.22Phase plane analysis — trajectories, critical points
  23. 4.6.23Stability of equilibria — stable, unstable, saddle, spiral, centre
  24. 4.6.24Linearization of nonlinear systems
  25. 4.6.25Laplace transform — definition, region of convergence
  26. 4.6.26Transforms of standard functions — proofs
  27. 4.6.27Properties — linearity, first - second shift theorems, scaling
  28. 4.6.28Laplace of derivatives — key property for solving ODEs
  29. 4.6.29Inverse Laplace transform — partial fractions, tables
  30. 4.6.30Solving ODEs with Laplace (including discontinuous forcing)
  31. 4.6.31Heaviside step function and Dirac delta function
  32. 4.6.32Convolution theorem — proof, applications
  33. 4.6.33Impulse response and transfer function (GNC connection)
4.7Partial Differential Equations0 / 21
  1. 4.7.1Classification — elliptic, parabolic, hyperbolic (discriminant test)
  2. 4.7.2Initial value problems (IVP) vs boundary value problems (BVP)
  3. 4.7.3Fourier series — motivation from periodic functions
  4. 4.7.4Dirichlet conditions for convergence
  5. 4.7.5Full Fourier series — coefficients derivation
  6. 4.7.6Half-range sine and cosine series
  7. 4.7.7Parseval's theorem
  8. 4.7.8Heat equation (parabolic) 1D — derivation from Fourier's law
  9. 4.7.9Solving heat equation — separation of variables
  10. 4.7.10Wave equation (hyperbolic) 1D — derivation
  11. 4.7.11Solving wave equation — D'Alembert's solution
  12. 4.7.12Solving wave equation — separation of variables
  13. 4.7.13Laplace's equation (elliptic) — physical meaning (steady-state)
  14. 4.7.14Laplace on rectangle — separation of variables
  15. 4.7.15Laplace on disk — polar coordinates, Bessel functions connection
  16. 4.7.16Neumann and Dirichlet boundary conditions
  17. 4.7.17Sturm-Liouville theory — eigenvalue problems, orthogonality of eigenfunctions
  18. 4.7.18Fourier transform — definition, properties
  19. 4.7.19Solving PDEs with Fourier transforms (heat equation on infinite domain)
  20. 4.7.20Convolution with Fourier transform
  21. 4.7.21Intro to finite difference methods for PDEs
4.8Numerical Methods0 / 29
  1. 4.8.1Sources of error — truncation error, round-off error
  2. 4.8.2IEEE 754 floating-point standard — significant bits, special values
  3. 4.8.3Machine epsilon — what it means in practice
  4. 4.8.4Condition number — absolute, relative; ill-conditioned problems
  5. 4.8.5Numerical stability vs instability — catastrophic cancellation
  6. 4.8.6Root finding — bisection method (convergence analysis)
  7. 4.8.7Fixed-point iteration — convergence conditions
  8. 4.8.8Newton-Raphson method — derivation, quadratic convergence
  9. 4.8.9Secant method
  10. 4.8.10Polynomial interpolation — Lagrange form, Newton's divided differences
  11. 4.8.11Error in polynomial interpolation
  12. 4.8.12Cubic spline interpolation — natural, clamped
  13. 4.8.13Numerical differentiation — forward, backward, central differences
  14. 4.8.14Error analysis of finite differences
  15. 4.8.15Numerical integration — trapezoidal rule (composite), error
  16. 4.8.16Simpson's 1 - 3 rule, 3 - 8 rule (composite) — derivation
  17. 4.8.17Gaussian quadrature — Gauss-Legendre
  18. 4.8.18Solving linear systems — Gaussian elimination with partial pivoting
  19. 4.8.19LU decomposition (numerical)
  20. 4.8.20Iterative methods — Jacobi, Gauss-Seidel, convergence
  21. 4.8.21Eigenvalue computation — power method, inverse iteration
  22. 4.8.22ODE solvers — Euler's method (derivation, global error)
  23. 4.8.23Modified Euler (Heun's method)
  24. 4.8.24Runge-Kutta 4th order (RK4) — derivation
  25. 4.8.25Adaptive step-size — RK45, error control
  26. 4.8.26Stiff equations — implicit methods, backward Euler
  27. 4.8.27Systems of ODEs — RK4 for systems
  28. 4.8.28Boundary value problems — shooting method, finite difference
  29. 4.8.29Solving nonlinear systems — Newton's method in n dimensions
4.9Probability Theory & Statistics0 / 25
  1. 4.9.1Probability space — sample space Ω, sigma-algebra F, measure P — Kolmogorov axioms
  2. 4.9.2Inclusion-exclusion principle
  3. 4.9.3Discrete random variables — PMF, CDF
  4. 4.9.4Expected value, variance, standard deviation — properties
  5. 4.9.5Moment generating function (MGF) — definition, use
  6. 4.9.6Common discrete distributions — Bernoulli, Binomial, Poisson, Geometric, Negative Binomial
  7. 4.9.7Continuous random variables — PDF, CDF, percentiles
  8. 4.9.8Common continuous distributions — Uniform, Normal, Exponential, Gamma, Beta
  9. 4.9.9Chi-squared, t, F distributions — definition, degrees of freedom
  10. 4.9.10Joint distributions — joint PMF - PDF, marginal, conditional
  11. 4.9.11Independence of random variables — formal definition
  12. 4.9.12Covariance and correlation
  13. 4.9.13Conditional expectation
  14. 4.9.14Transformations of random variables — change-of-variable technique
  15. 4.9.15Central Limit Theorem — statement, proof sketch, significance
  16. 4.9.16Law of Large Numbers — weak and strong
  17. 4.9.17Statistical estimation — MLE, method of moments
  18. 4.9.18Properties of estimators — unbiasedness, consistency, efficiency
  19. 4.9.19Confidence intervals — derivation for mean, proportion
  20. 4.9.20Hypothesis testing — null - alternative, test statistic, p-value, errors (Type I & II)
  21. 4.9.21z-test, t-test, chi-squared goodness of fit, F-test
  22. 4.9.22Linear regression — least squares, inference on coefficients
  23. 4.9.23Multiple regression
  24. 4.9.24Bayesian statistics — prior, likelihood, posterior (intro)
  25. 4.9.25Monte Carlo simulation — law of large numbers basis
4.10Advanced Topics (Elite Level)0 / 27
  1. 4.10.1Complex analysis — analytic functions, Cauchy-Riemann equations
  2. 4.10.2Complex integration — contour integrals
  3. 4.10.3Cauchy's integral theorem and formula
  4. 4.10.4Laurent series — principal part, annulus of convergence
  5. 4.10.5Residues and poles
  6. 4.10.6Residue theorem — computing real integrals
  7. 4.10.7Tensor analysis — scalars, vectors, rank-2 tensors
  8. 4.10.8Covariant and contravariant components
  9. 4.10.9Einstein summation convention
  10. 4.10.10Metric tensor — raising - lowering indices
  11. 4.10.11Christoffel symbols — intro
  12. 4.10.12Calculus of variations — functionals, functional derivative
  13. 4.10.13Euler-Lagrange equation — derivation
  14. 4.10.14Brachistochrone problem
  15. 4.10.15Hamilton's principle — least action
  16. 4.10.16Isoperimetric problems — constraints (Lagrange multipliers in variational sense)
  17. 4.10.17Convex optimization — convex sets, convex functions
  18. 4.10.18First-order optimality conditions — gradient = 0
  19. 4.10.19KKT conditions for constrained optimization
  20. 4.10.20Gradient descent and variants — convergence analysis
  21. 4.10.21Linear programming — simplex method (intro)
  22. 4.10.22Real analysis — rigorous epsilon-delta, metric spaces
  23. 4.10.23Uniform continuity — difference from pointwise
  24. 4.10.24Uniform convergence of function sequences
  25. 4.10.25Measure theory — Lebesgue measure (intro)
  26. 4.10.26Fourier analysis — DFT, FFT algorithm (Cooley-Tukey)
  27. 4.10.27Stochastic processes — Markov chains, steady-state, random walks

AI-ML

0 / 398 · 0%
1.1Linear Algebra Essentials0 / 18
  1. 1.1.1Scalars, vectors, matrices, and tensors definitions
  2. 1.1.2Vector addition, scalar multiplication, and geometric interpretation
  3. 1.1.3Dot product and its geometric meaning (projection, angle)
  4. 1.1.4Vector norms (L1, L2, L-infinity, Lp)
  5. 1.1.5Matrix multiplication rules and dimensionality
  6. 1.1.6Identity, diagonal, symmetric, and orthogonal matrices
  7. 1.1.7Matrix transpose and properties
  8. 1.1.8Matrix inverse and conditions for invertibility
  9. 1.1.9Determinant computation and meaning
  10. 1.1.10Rank, column space, null space
  11. 1.1.11Linear independence and basis vectors
  12. 1.1.12Solving linear systems (Gaussian elimination)
  13. 1.1.13Eigenvalues and eigenvectors
  14. 1.1.14Eigendecomposition of matrices
  15. 1.1.15Singular Value Decomposition (SVD) intuition and computation
  16. 1.1.16Trace operator and properties
  17. 1.1.17Positive definite and semidefinite matrices
  18. 1.1.18Quadratic forms
1.2Calculus & Optimization Basics0 / 14
  1. 1.2.1Functions, limits, and continuity
  2. 1.2.2Derivatives and rules (product, quotient, chain)
  3. 1.2.3Partial derivatives
  4. 1.2.4Gradients and directional derivatives
  5. 1.2.5The Jacobian matrix
  6. 1.2.6The Hessian matrix
  7. 1.2.7Taylor series approximation
  8. 1.2.8Convex vs non-convex functions
  9. 1.2.9Local vs global minima - maxima
  10. 1.2.10Critical points and saddle points
  11. 1.2.11Lagrange multipliers for constrained optimization
  12. 1.2.12Gradient descent intuition and update rule
  13. 1.2.13Learning rate effects on convergence
  14. 1.2.14Chain rule for multivariate functions (backprop foundation)
1.3Probability & Statistics0 / 21
  1. 1.3.1Sample spaces, events, and axioms of probability
  2. 1.3.2Conditional probability
  3. 1.3.3Bayes' theorem and applications
  4. 1.3.4Independence and mutual exclusivity
  5. 1.3.5Random variables (discrete and continuous)
  6. 1.3.6Probability mass and density functions
  7. 1.3.7Cumulative distribution functions
  8. 1.3.8Expectation, variance, and standard deviation
  9. 1.3.9Covariance and correlation
  10. 1.3.10Common distributions (Bernoulli, Binomial, Poisson)
  11. 1.3.11Gaussian - Normal distribution properties
  12. 1.3.12Uniform, Exponential, and Beta distributions
  13. 1.3.13Joint, marginal, and conditional distributions
  14. 1.3.14Law of large numbers
  15. 1.3.15Central limit theorem
  16. 1.3.16Maximum likelihood estimation (MLE)
  17. 1.3.17Maximum a posteriori estimation (MAP)
  18. 1.3.18Entropy and KL divergence
  19. 1.3.19Cross-entropy concept
  20. 1.3.20Hypothesis testing and p-values
  21. 1.3.21Confidence intervals
1.4Python & Scientific Computing0 / 12
  1. 1.4.1Python syntax, data types, control flow
  2. 1.4.2Functions, classes, and modules
  3. 1.4.3List - dict comprehensions and generators
  4. 1.4.4NumPy arrays and vectorized operations
  5. 1.4.5NumPy broadcasting rules
  6. 1.4.6Pandas DataFrames and Series basics
  7. 1.4.7Data loading (CSV, JSON, parquet)
  8. 1.4.8Matplotlib and Seaborn visualization
  9. 1.4.9Jupyter notebooks workflow
  10. 1.4.10Virtual environments and pip - conda
  11. 1.4.11Git version control basics
  12. 1.4.12Reading documentation and debugging
2.1Data Preprocessing & Feature Engineering0 / 15
  1. 2.1.1Types of data (numerical, categorical, ordinal, text)
  2. 2.1.2Handling missing values (deletion, imputation strategies)
  3. 2.1.3Outlier detection and treatment
  4. 2.1.4Feature scaling - normalization vs standardization
  5. 2.1.5Min-max scaling and z-score normalization
  6. 2.1.6One-hot encoding and label encoding
  7. 2.1.7Ordinal and target encoding
  8. 2.1.8Binning and discretization
  9. 2.1.9Log and power transformations
  10. 2.1.10Feature creation and interaction terms
  11. 2.1.11Handling imbalanced datasets (SMOTE, undersampling)
  12. 2.1.12Train - validation - test splitting
  13. 2.1.13Data leakage identification and prevention
  14. 2.1.14Exploratory data analysis (EDA) workflow
  15. 2.1.15Correlation analysis and multicollinearity
2.2Linear & Logistic Regression0 / 16
  1. 2.2.1Simple linear regression model
  2. 2.2.2Multiple linear regression
  3. 2.2.3Ordinary least squares derivation
  4. 2.2.4Cost function (MSE) and gradient descent fitting
  5. 2.2.5Normal equation closed-form solution
  6. 2.2.6Polynomial regression
  7. 2.2.7Assumptions of linear regression
  8. 2.2.8R-squared and adjusted R-squared
  9. 2.2.9Logistic regression and the sigmoid function
  10. 2.2.10Log-loss - binary cross-entropy
  11. 2.2.11Decision boundaries
  12. 2.2.12Multinomial - softmax regression
  13. 2.2.13L1 (Lasso) regularization
  14. 2.2.14L2 (Ridge) regularization
  15. 2.2.15Elastic Net regularization
  16. 2.2.16Interpreting model coefficients
2.3Tree-Based & Instance Methods0 / 17
  1. 2.3.1Decision tree structure and terminology
  2. 2.3.2Entropy and information gain
  3. 2.3.3Gini impurity
  4. 2.3.4Tree pruning techniques
  5. 2.3.5Overfitting in decision trees
  6. 2.3.6Bagging and bootstrap aggregating
  7. 2.3.7Random forest algorithm
  8. 2.3.8Feature importance from trees
  9. 2.3.9Out-of-bag error estimation
  10. 2.3.10Boosting concept and intuition
  11. 2.3.11AdaBoost algorithm
  12. 2.3.12Gradient Boosting Machines
  13. 2.3.13XGBoost fundamentals and tuning
  14. 2.3.14LightGBM and CatBoost overview
  15. 2.3.15K-Nearest Neighbors algorithm
  16. 2.3.16Distance metrics (Euclidean, Manhattan, cosine)
  17. 2.3.17Choosing K and the curse of dimensionality
2.4SVM, Naive Bayes & Probabilistic Models0 / 11
  1. 2.4.1Support Vector Machine maximum margin concept
  2. 2.4.2Hard vs soft margin classifiers
  3. 2.4.3The kernel trick
  4. 2.4.4Linear, polynomial, and RBF kernels
  5. 2.4.5Hyperparameters C and gamma
  6. 2.4.6Support vectors interpretation
  7. 2.4.7Naive Bayes assumption
  8. 2.4.8Gaussian Naive Bayes
  9. 2.4.9Multinomial and Bernoulli Naive Bayes
  10. 2.4.10Laplace smoothing
  11. 2.4.11Naive Bayes for text classification
2.5Unsupervised Learning0 / 13
  1. 2.5.1K-Means clustering algorithm
  2. 2.5.2Choosing K (elbow method, silhouette score)
  3. 2.5.3K-Means++ initialization
  4. 2.5.4Hierarchical clustering (agglomerative - divisive)
  5. 2.5.5Dendrograms and linkage methods
  6. 2.5.6DBSCAN density-based clustering
  7. 2.5.7Gaussian Mixture Models and EM algorithm
  8. 2.5.8Principal Component Analysis (PCA) theory
  9. 2.5.9PCA via eigendecomposition and SVD
  10. 2.5.10Explained variance and choosing components
  11. 2.5.11t-SNE for visualization
  12. 2.5.12UMAP for dimensionality reduction
  13. 2.5.13Anomaly detection methods
2.6Model Evaluation & Selection0 / 16
  1. 2.6.1Bias-variance tradeoff
  2. 2.6.2Underfitting vs overfitting diagnosis
  3. 2.6.3Training, validation, and test error
  4. 2.6.4K-fold cross-validation
  5. 2.6.5Stratified and leave-one-out cross-validation
  6. 2.6.6Confusion matrix interpretation
  7. 2.6.7Accuracy, precision, recall, F1-score
  8. 2.6.8Precision-recall tradeoff and curves
  9. 2.6.9ROC curve and AUC
  10. 2.6.10Regression metrics (MAE, MSE, RMSE, MAPE)
  11. 2.6.11Log-loss and calibration
  12. 2.6.12Learning curves analysis
  13. 2.6.13Grid search and random search
  14. 2.6.14Bayesian hyperparameter optimization
  15. 2.6.15Cross-validation pitfalls and nested CV
  16. 2.6.16Ensemble methods (voting, stacking, blending)
3.1Neural Network Fundamentals0 / 13
  1. 3.1.1The perceptron model and history
  2. 3.1.2Multi-layer perceptron architecture
  3. 3.1.3Forward propagation computation
  4. 3.1.4Activation functions - sigmoid, tanh
  5. 3.1.5ReLU and variants (Leaky ReLU, ELU, GELU)
  6. 3.1.6Softmax for output layers
  7. 3.1.7Universal approximation theorem
  8. 3.1.8Loss functions - MSE, cross-entropy
  9. 3.1.9Backpropagation algorithm derivation
  10. 3.1.10Computational graphs and autograd
  11. 3.1.11Vanishing and exploding gradients
  12. 3.1.12Weight initialization (Xavier, He)
  13. 3.1.13Bias terms and their role
3.2Training Deep Networks0 / 15
  1. 3.2.1Stochastic gradient descent (SGD)
  2. 3.2.2Mini-batch gradient descent
  3. 3.2.3Momentum and Nesterov momentum
  4. 3.2.4AdaGrad and RMSprop
  5. 3.2.5Adam and AdamW optimizers
  6. 3.2.6Learning rate scheduling
  7. 3.2.7Learning rate warmup
  8. 3.2.8Batch normalization
  9. 3.2.9Layer normalization
  10. 3.2.10Dropout regularization
  11. 3.2.11Early stopping
  12. 3.2.12L1 - L2 weight decay in deep nets
  13. 3.2.13Data augmentation strategies
  14. 3.2.14Gradient clipping
  15. 3.2.15Hyperparameter tuning for deep nets
3.3Deep Learning Frameworks0 / 11
  1. 3.3.1PyTorch tensors and operations
  2. 3.3.2Autograd and computational graphs in PyTorch
  3. 3.3.3Building models with nn.Module
  4. 3.3.4Datasets and DataLoaders
  5. 3.3.5Training loops from scratch
  6. 3.3.6GPU acceleration and device management
  7. 3.3.7Saving and loading models (checkpoints)
  8. 3.3.8TensorFlow - Keras basics
  9. 3.3.9Mixed precision training
  10. 3.3.10TensorBoard - Weights & Biases logging
  11. 3.3.11Distributed training overview
3.4Convolutional Neural Networks0 / 15
  1. 3.4.1Convolution operation and filters
  2. 3.4.2Stride, padding, and dilation
  3. 3.4.3Pooling layers (max, average)
  4. 3.4.4Feature maps and receptive fields
  5. 3.4.5CNN architecture design
  6. 3.4.6LeNet and AlexNet
  7. 3.4.7VGG networks
  8. 3.4.8Inception - GoogLeNet
  9. 3.4.9ResNet and skip connections
  10. 3.4.10DenseNet and EfficientNet
  11. 3.4.11Transfer learning and fine-tuning
  12. 3.4.12Image classification pipeline
  13. 3.4.13Object detection (R-CNN, YOLO, SSD)
  14. 3.4.14Semantic segmentation (U-Net, FCN)
  15. 3.4.15Data augmentation for images
3.5Sequence Models0 / 14
  1. 3.5.1Recurrent Neural Networks (RNN) architecture
  2. 3.5.2Backpropagation through time
  3. 3.5.3Vanishing gradients in RNNs
  4. 3.5.4Long Short-Term Memory (LSTM) cells
  5. 3.5.5Gated Recurrent Units (GRU)
  6. 3.5.6Bidirectional RNNs
  7. 3.5.7Sequence-to-sequence models
  8. 3.5.8Encoder-decoder architecture
  9. 3.5.9The attention mechanism intuition
  10. 3.5.10Bahdanau and Luong attention
  11. 3.5.11Word embeddings (Word2Vec, GloVe)
  12. 3.5.12Handling variable-length sequences
  13. 3.5.13Teacher forcing
  14. 3.5.14Beam search decoding
4.1Transformer Architecture0 / 14
  1. 4.1.1Limitations of RNNs motivating transformers
  2. 4.1.2Self-attention mechanism in detail
  3. 4.1.3Query, key, value matrices
  4. 4.1.4Scaled dot-product attention
  5. 4.1.5Multi-head attention
  6. 4.1.6Positional encodings (sinusoidal)
  7. 4.1.7Rotary positional embeddings (RoPE)
  8. 4.1.8Feed-forward network sublayers
  9. 4.1.9Residual connections and layer norm placement
  10. 4.1.10Encoder vs decoder vs encoder-decoder
  11. 4.1.11Masked attention for autoregression
  12. 4.1.12The original - Attention is All You Need - architecture
  13. 4.1.13Computational complexity of attention
  14. 4.1.14Flash attention and efficient attention
4.2Tokenization & Language Modeling0 / 10
  1. 4.2.1Tokenization fundamentals
  2. 4.2.2Byte-Pair Encoding (BPE)
  3. 4.2.3WordPiece and SentencePiece
  4. 4.2.4Vocabulary size tradeoffs
  5. 4.2.5Embedding layers and tied weights
  6. 4.2.6Causal language modeling objective
  7. 4.2.7Masked language modeling (BERT)
  8. 4.2.8Next sentence prediction
  9. 4.2.9Perplexity as a metric
  10. 4.2.10Context window and sequence length
4.3Pretraining & Fine-Tuning LLMs0 / 14
  1. 4.3.1GPT family architecture evolution
  2. 4.3.2BERT and encoder models
  3. 4.3.3T5 and text-to-text framework
  4. 4.3.4Pretraining data curation and cleaning
  5. 4.3.5Self-supervised pretraining objectives
  6. 4.3.6Full fine-tuning vs feature extraction
  7. 4.3.7Parameter-efficient fine-tuning (PEFT)
  8. 4.3.8LoRA and QLoRA
  9. 4.3.9Adapter layers and prefix tuning
  10. 4.3.10Instruction tuning
  11. 4.3.11Supervised fine-tuning (SFT)
  12. 4.3.12Catastrophic forgetting
  13. 4.3.13Quantization (INT8, INT4, GPTQ)
  14. 4.3.14Knowledge distillation
4.4Alignment, Prompting & RAG0 / 16
  1. 4.4.1Reinforcement Learning from Human Feedback (RLHF)
  2. 4.4.2Reward modeling
  3. 4.4.3Proximal Policy Optimization for LLMs
  4. 4.4.4Direct Preference Optimization (DPO)
  5. 4.4.5Constitutional AI overview
  6. 4.4.6Zero-shot and few-shot prompting
  7. 4.4.7Chain-of-thought prompting
  8. 4.4.8Self-consistency and tree-of-thought
  9. 4.4.9In-context learning mechanisms
  10. 4.4.10Prompt engineering best practices
  11. 4.4.11Retrieval-Augmented Generation (RAG) architecture
  12. 4.4.12Vector databases and embeddings
  13. 4.4.13Chunking strategies for retrieval
  14. 4.4.14Reranking and hybrid search
  15. 4.4.15Hallucination mitigation
  16. 4.4.16Evaluation of LLMs (benchmarks, LLM-as-judge)
4.5Generative Models0 / 17
  1. 4.5.1Generative vs discriminative models
  2. 4.5.2Autoencoders fundamentals
  3. 4.5.3Variational Autoencoders (VAE) theory
  4. 4.5.4Reparameterization trick
  5. 4.5.5ELBO objective and KL term
  6. 4.5.6Generative Adversarial Networks (GAN) framework
  7. 4.5.7Generator and discriminator dynamics
  8. 4.5.8GAN training instability and mode collapse
  9. 4.5.9DCGAN, WGAN, StyleGAN
  10. 4.5.10Diffusion models forward - reverse process
  11. 4.5.11Denoising diffusion probabilistic models (DDPM)
  12. 4.5.12Noise scheduling
  13. 4.5.13Score-based generative models
  14. 4.5.14Classifier-free guidance
  15. 4.5.15Latent diffusion (Stable Diffusion)
  16. 4.5.16Text-to-image conditioning (CLIP)
  17. 4.5.17Evaluating generative models (FID, IS)
5.1Reinforcement Learning Foundations0 / 13
  1. 5.1.1Agent, environment, state, action, reward
  2. 5.1.2Markov Decision Processes (MDP)
  3. 5.1.3Policies and value functions
  4. 5.1.4State-value and action-value functions
  5. 5.1.5Bellman equations
  6. 5.1.6Discount factor and returns
  7. 5.1.7Exploration vs exploitation tradeoff
  8. 5.1.8Epsilon-greedy strategy
  9. 5.1.9Dynamic programming (value - policy iteration)
  10. 5.1.10Monte Carlo methods
  11. 5.1.11Temporal Difference learning
  12. 5.1.12SARSA algorithm
  13. 5.1.13Q-learning algorithm
5.2Deep & Advanced RL0 / 14
  1. 5.2.1Deep Q-Networks (DQN)
  2. 5.2.2Experience replay
  3. 5.2.3Target networks
  4. 5.2.4Double DQN and Dueling DQN
  5. 5.2.5Policy gradient methods
  6. 5.2.6REINFORCE algorithm
  7. 5.2.7Actor-critic methods
  8. 5.2.8Advantage Actor-Critic (A2C - A3C)
  9. 5.2.9Proximal Policy Optimization (PPO)
  10. 5.2.10Trust Region Policy Optimization (TRPO)
  11. 5.2.11Soft Actor-Critic (SAC)
  12. 5.2.12Multi-agent reinforcement learning
  13. 5.2.13Reward shaping and sparse rewards
  14. 5.2.14Model-based RL overview
5.3MLOps & Deployment0 / 18
  1. 5.3.1ML project lifecycle
  2. 5.3.2Experiment tracking and reproducibility
  3. 5.3.3Model versioning and registries
  4. 5.3.4Data versioning (DVC)
  5. 5.3.5Feature stores
  6. 5.3.6Model serving (REST APIs, FastAPI)
  7. 5.3.7Batch vs real-time inference
  8. 5.3.8Containerization with Docker
  9. 5.3.9Kubernetes for ML workloads
  10. 5.3.10Model serving frameworks (TorchServe, Triton)
  11. 5.3.11CI - CD pipelines for ML
  12. 5.3.12Model monitoring and observability
  13. 5.3.13Data drift and concept drift detection
  14. 5.3.14A - B testing for models
  15. 5.3.15Model retraining pipelines
  16. 5.3.16Cost optimization and inference latency
  17. 5.3.17Edge deployment and ONNX
  18. 5.3.18LLM serving (vLLM, quantized inference)
6.1Scaling & Efficient Architectures0 / 13
  1. 6.1.1Neural scaling laws (Chinchilla, compute-optimal)
  2. 6.1.2Compute-data-parameter tradeoffs
  3. 6.1.3Emergent abilities in large models
  4. 6.1.4Mixture-of-Experts (MoE) architecture
  5. 6.1.5Sparse routing and gating networks
  6. 6.1.6Load balancing in MoE
  7. 6.1.7Model parallelism (tensor, pipeline)
  8. 6.1.8Data parallelism and ZeRO optimization
  9. 6.1.9FSDP and sharded training
  10. 6.1.10Long-context architectures
  11. 6.1.11State-space models (Mamba, S4)
  12. 6.1.12Speculative decoding
  13. 6.1.13KV-cache optimization
6.2AI Agents & Tool Use0 / 10
  1. 6.2.1Agent architectures and reasoning loops
  2. 6.2.2ReAct (reasoning + acting) framework
  3. 6.2.3Tool use and function calling
  4. 6.2.4Planning and task decomposition
  5. 6.2.5Memory systems for agents
  6. 6.2.6Multi-agent collaboration
  7. 6.2.7Agentic frameworks (LangChain, LlamaIndex)
  8. 6.2.8Code-generation agents
  9. 6.2.9Autonomous agent evaluation
  10. 6.2.10Guardrails and constrained generation
6.3Interpretability & Explainability0 / 11
  1. 6.3.1Importance of interpretability
  2. 6.3.2Feature attribution (SHAP, LIME)
  3. 6.3.3Saliency maps and Grad-CAM
  4. 6.3.4Attention visualization and limitations
  5. 6.3.5Probing classifiers
  6. 6.3.6Mechanistic interpretability
  7. 6.3.7Circuits and superposition
  8. 6.3.8Sparse autoencoders for features
  9. 6.3.9Activation patching
  10. 6.3.10Counterfactual explanations
  11. 6.3.11Concept-based explanations
6.4AI Safety & Alignment0 / 15
  1. 6.4.1The alignment problem definition
  2. 6.4.2Outer vs inner alignment
  3. 6.4.3Reward hacking and specification gaming
  4. 6.4.4Goal misgeneralization
  5. 6.4.5Scalable oversight
  6. 6.4.6Red-teaming language models
  7. 6.4.7Jailbreaks and adversarial prompts
  8. 6.4.8Adversarial examples and robustness
  9. 6.4.9Bias, fairness, and discrimination metrics
  10. 6.4.10Privacy (differential privacy, membership inference)
  11. 6.4.11Data poisoning and backdoor attacks
  12. 6.4.12Watermarking and provenance
  13. 6.4.13AI governance and regulation (EU AI Act)
  14. 6.4.14Existential and catastrophic risk frameworks
  15. 6.4.15Responsible AI deployment practices
6.5Research Frontiers & Practice0 / 12
  1. 6.5.1Reading and reproducing ML papers
  2. 6.5.2Implementing models from scratch
  3. 6.5.3Benchmark design and evaluation rigor
  4. 6.5.4Self-supervised and contrastive learning (SimCLR, CLIP)
  5. 6.5.5Multimodal models (vision-language)
  6. 6.5.6World models and embodied AI
  7. 6.5.7Continual and lifelong learning
  8. 6.5.8Federated learning
  9. 6.5.9Neuro-symbolic AI
  10. 6.5.10Open problems and future directions
  11. 6.5.11Contributing to open-source ML
  12. 6.5.12Building a portfolio and research roadmap

Coding

0 / 527 · 0%
1.1How Computers Work0 / 13
  1. 1.1.1Binary number system — conversions from - to decimal, counting in binary
  2. 1.1.2Hexadecimal and octal — conversions, why they're used
  3. 1.1.3Boolean algebra — AND, OR, NOT, XOR, NAND, NOR operations
  4. 1.1.4Truth tables — all 16 binary operations
  5. 1.1.5Logic gates — physical gate symbols, transistor implementation idea
  6. 1.1.6Combinational logic — half adder, full adder, multiplexer, decoder
  7. 1.1.7Flip-flops — SR, D, JK — storing one bit
  8. 1.1.8Registers — N flip-flops storing N bits
  9. 1.1.9Memory hierarchy — registers, cache (L1 - L2 - L3), RAM, SSD, HDD — speed - size trade-offs
  10. 1.1.10The CPU — ALU, control unit, registers
  11. 1.1.11Fetch-decode-execute cycle — step by step
  12. 1.1.12Machine code and assembly — what actually runs
  13. 1.1.13Operating system role — resource manager, abstraction layer
1.2Introduction to Programming (Python)0 / 39
  1. 1.2.1Installing Python + VS Code — environment setup
  2. 1.2.2`print()`, comments, code structure
  3. 1.2.3Variables — naming rules, assignment, reassignment
  4. 1.2.4Data types — int, float, str, bool, NoneType
  5. 1.2.5Type checking with `type()`, type conversion `int()`, `float()`, `str()`
  6. 1.2.6Arithmetic operators — +, −, - , - , - , %, - (floor div, modulo, power)
  7. 1.2.7Comparison operators — ==, !=, - , - , - =, - =
  8. 1.2.8Logical operators — and, or, not, short-circuit evaluation
  9. 1.2.9Bitwise operators — &, - , ^, ~, - , -
  10. 1.2.10String operations — concatenation, repetition
  11. 1.2.11String indexing and slicing — `s[0]`, `s[-1]`, `s[2 - 5]`, `s[ - 2]`
  12. 1.2.12String methods — upper, lower, strip, split, join, replace, find, format
  13. 1.2.13f-strings — embedding expressions
  14. 1.2.14Input with `input()` — always returns string, conversion needed
  15. 1.2.15if - elif - else — syntax, indentation rules
  16. 1.2.16Nested conditionals
  17. 1.2.17while loop — condition-based, infinite loop dangers
  18. 1.2.18for loop — iterating over sequences
  19. 1.2.19`range()` — start, stop, step
  20. 1.2.20break, continue, pass — when and why
  21. 1.2.21Lists — creation, indexing, slicing, mutability
  22. 1.2.22List methods — append, insert, remove, pop, sort, reverse, count, index
  23. 1.2.23Tuples — immutability, use cases
  24. 1.2.24Dictionaries — key-value pairs, access, methods (keys, values, items, get, update)
  25. 1.2.25Sets — unique elements, set operations (union, intersection, difference)
  26. 1.2.26Nested data structures — list of dicts, dict of lists
  27. 1.2.27Functions — def, parameters, return, docstrings
  28. 1.2.28Default parameters, keyword arguments
  29. 1.2.29` - args` and ` - kwargs` — flexible argument passing
  30. 1.2.30Variable scope — LEGB rule (Local, Enclosing, Global, Built-in)
  31. 1.2.31global and nonlocal keywords
  32. 1.2.32Lambda functions — anonymous, used with map - filter
  33. 1.2.33Built-in functions — map, filter, zip, enumerate, sorted, reversed, min, max, sum, any, all
  34. 1.2.34List comprehensions — `[expr for x in iterable if condition]`
  35. 1.2.35Dictionary and set comprehensions
  36. 1.2.36Generator expressions — memory efficiency
  37. 1.2.37Recursion — call stack visualization, base case, recursive case
  38. 1.2.38Classic recursion — factorial, Fibonacci, binary search
  39. 1.2.39Recursion depth limit — stack overflow
1.3Python Intermediate0 / 12
  1. 1.3.1Modules — import, from…import, as aliasing
  2. 1.3.2Standard library — math, random, os, sys, datetime, time, collections, itertools, functools
  3. 1.3.3File I - O — open modes (r, w, a, rb), read, readline, readlines, write
  4. 1.3.4Context managers — with statement, `__enter__` - `__exit__`
  5. 1.3.5Exception handling — try, except (specific), else, finally
  6. 1.3.6Raising exceptions — raise, custom exception classes
  7. 1.3.7Exception hierarchy
  8. 1.3.8Decorators — function decorators, @, wraps
  9. 1.3.9Generators — yield, generator functions, send(), next()
  10. 1.3.10Iterators — `__iter__`, `__next__`, StopIteration
  11. 1.3.11Regular expressions — re module, patterns, groups, findall, sub
  12. 1.3.12Virtual environments — venv, pip, requirements.txt
2.1OOP Fundamentals0 / 16
  1. 2.1.1Class vs object — blueprint vs instance
  2. 2.1.2`__init__` constructor — initializing attributes
  3. 2.1.3Instance attributes vs class attributes
  4. 2.1.4Instance methods, class methods (`@classmethod`), static methods (`@staticmethod`)
  5. 2.1.5`self` — what it is and how Python passes it
  6. 2.1.6Encapsulation — hiding internal state, name mangling (`__name`)
  7. 2.1.7Properties — `@property`, `@setter`, `@deleter` for controlled access
  8. 2.1.8Inheritance — single inheritance, method resolution order (MRO)
  9. 2.1.9`super()` — calling parent methods
  10. 2.1.10Multiple inheritance — Python's C3 linearization algorithm
  11. 2.1.11Method overriding — when and why
  12. 2.1.12Polymorphism — duck typing, same interface different behavior
  13. 2.1.13Abstract base classes — ABC module, `@abstractmethod`
  14. 2.1.14Operator overloading — dunder methods (`__add__`, `__eq__`, `__lt__`, `__len__`, `__str__`, `__repr__`, `__hash__`)
  15. 2.1.15Composition — has-a relationship vs is-a
  16. 2.1.16Dataclasses — `@dataclass` decorator, `__post_init__`
2.2Design Principles0 / 12
  1. 2.2.1DRY — Don't Repeat Yourself
  2. 2.2.2KISS — Keep It Simple
  3. 2.2.3YAGNI — You Aren't Gonna Need It
  4. 2.2.4SOLID — Single Responsibility Principle
  5. 2.2.5SOLID — Open - Closed Principle
  6. 2.2.6SOLID — Liskov Substitution Principle
  7. 2.2.7SOLID — Interface Segregation Principle
  8. 2.2.8SOLID — Dependency Inversion Principle
  9. 2.2.9Separation of concerns
  10. 2.2.10Design Patterns — Creational - Singleton, Factory Method, Abstract Factory, Builder, Prototype
  11. 2.2.11Design Patterns — Structural - Adapter, Bridge, Composite, Decorator, Facade, Flyweight, Proxy
  12. 2.2.12Design Patterns — Behavioral - Observer, Strategy, Command, Iterator, State, Template Method, Chain of Responsibility,
3.1Complexity Analysis0 / 9
  1. 3.1.1Big-O notation — formal definition, mathematical
  2. 3.1.2Common complexities — O(1), O(log n), O(n), O(n log n), O(n²), O(n³), O(2ⁿ), O(n!)
  3. 3.1.3Best, worst, average case — with examples
  4. 3.1.4Space complexity — auxiliary vs total
  5. 3.1.5Amortized analysis — aggregate, accounting, potential methods
  6. 3.1.6Tight bounds — Θ notation; lower bounds — Ω notation
  7. 3.1.7Master theorem — solving recurrences T(n) = aT(n - b) + f(n)
  8. 3.1.8Substitution method for recurrences
  9. 3.1.9Recursion tree method
3.2Linear Data Structures0 / 9
  1. 3.2.1Array — static, dynamic; cache locality; amortized O(1) append
  2. 3.2.2Linked list — singly - node structure, traversal, insert head - tail - middle, delete
  3. 3.2.3Doubly linked list — bidirectional traversal
  4. 3.2.4Circular linked list — applications
  5. 3.2.5Stack — LIFO semantics, push - pop - peek, array and linked list implementations
  6. 3.2.6Stack applications — balanced parentheses, infix-to-postfix, function call stack
  7. 3.2.7Queue — FIFO semantics, enqueue - dequeue, circular array implementation
  8. 3.2.8Deque (double-ended queue) — operations, use cases
  9. 3.2.9Priority Queue — concept (heap-based implementation covered later)
3.3Hashing0 / 10
  1. 3.3.1Hash function — properties - deterministic, uniform, fast
  2. 3.3.2Hash table — structure, open addressing vs chaining
  3. 3.3.3Chaining — linked lists in buckets, load factor, resizing
  4. 3.3.4Open addressing — linear probing, quadratic probing, double hashing
  5. 3.3.5Deletion in open addressing — tombstone markers
  6. 3.3.6Load factor — when to resize, rehashing cost
  7. 3.3.7Amortized O(1) operations
  8. 3.3.8Universal hashing — probabilistic guarantee
  9. 3.3.9Python dict and set internals
  10. 3.3.10Applications — frequency counting, two-sum problem, caching (LRU)
3.4Trees0 / 16
  1. 3.4.1Tree terminology — root, leaf, height, depth, degree, subtree
  2. 3.4.2Binary tree — structure, traversals - preorder, inorder, postorder (recursive and iterative)
  3. 3.4.3Level-order traversal — BFS with queue
  4. 3.4.4Binary Search Tree (BST) — BST property, insert, search, delete (3 cases)
  5. 3.4.5BST — inorder gives sorted order
  6. 3.4.6BST — worst case O(n) — motivation for balancing
  7. 3.4.7AVL tree — balance factor, rotations (LL, RR, LR, RL), insert, delete
  8. 3.4.8Red-Black tree — properties, rotations + recoloring (conceptual understanding)
  9. 3.4.9B-tree and B+ tree — motivation (disk storage), properties
  10. 3.4.10Heap — max-heap and min-heap properties
  11. 3.4.11Heapify — bottom-up O(n) build
  12. 3.4.12Heap operations — insert O(log n), extract-max - min O(log n), decrease-key
  13. 3.4.13Heap sort — in-place, O(n log n)
  14. 3.4.14Trie (prefix tree) — insert, search, startsWith, applications (autocomplete, spell check)
  15. 3.4.15Segment tree — build, range query, point update
  16. 3.4.16Fenwick tree (Binary Indexed Tree) — prefix sums, O(log n) update and query
3.5Graphs0 / 17
  1. 3.5.1Graph definitions — directed, undirected, weighted, unweighted, simple, multigraph
  2. 3.5.2Representations — adjacency matrix (space O(V²)), adjacency list (space O(V+E))
  3. 3.5.3Incidence matrix
  4. 3.5.4BFS — algorithm, queue-based, O(V+E), shortest path in unweighted graphs
  5. 3.5.5DFS — algorithm, stack - recursion, O(V+E), visited array
  6. 3.5.6DFS applications — cycle detection (directed and undirected)
  7. 3.5.7Topological sort — DFS-based, Kahn's algorithm (BFS-based)
  8. 3.5.8Strongly Connected Components (SCC) — Kosaraju's algorithm, Tarjan's algorithm
  9. 3.5.9Articulation points and bridges — Tarjan's low-link values
  10. 3.5.10Dijkstra's algorithm — greedy, priority queue, O((V+E) log V) — no negative edges
  11. 3.5.11Bellman-Ford algorithm — DP approach, negative cycles detection, O(VE)
  12. 3.5.12Floyd-Warshall — all-pairs shortest paths, O(V³)
  13. 3.5.13A - algorithm — heuristic, admissibility, consistency — important for GNC
  14. 3.5.14Minimum Spanning Tree — Kruskal's (Union-Find), Prim's (priority queue)
  15. 3.5.15Disjoint Set Union (Union-Find) — path compression + union by rank → α(n)
  16. 3.5.16Network flow — max-flow min-cut theorem, Ford-Fulkerson, Edmonds-Karp
  17. 3.5.17Bipartite graphs — 2-coloring test, bipartite matching — Hopcroft-Karp
3.6Sorting & Searching0 / 11
  1. 3.6.1Bubble sort, selection sort, insertion sort — O(n²), when insertion sort wins
  2. 3.6.2Merge sort — divide and conquer, O(n log n), stable, proof of correctness
  3. 3.6.3Quick sort — Lomuto - Hoare partition, pivot strategies, expected O(n log n), worst case
  4. 3.6.4Quick sort randomization — expected O(n log n)
  5. 3.6.5Heap sort — O(n log n), in-place, not stable
  6. 3.6.6Counting sort — O(n + k), integer keys only
  7. 3.6.7Radix sort — LSD, MSD; O(d(n+k))
  8. 3.6.8Bucket sort — uniform distributions
  9. 3.6.9Lower bound for comparison sorts — Ω(n log n) proof via decision trees
  10. 3.6.10Linear time selection — median of medians algorithm
  11. 3.6.11Binary search — iterative, recursive; O(log n); searching in sorted - rotated arrays
3.7Algorithm Paradigms0 / 20
  1. 3.7.1Brute force — exhaustive search, when acceptable
  2. 3.7.2Divide and conquer — template, correctness, recurrence
  3. 3.7.3Greedy — exchange argument proof technique
  4. 3.7.4Greedy problems — activity selection, fractional knapsack, Huffman coding (full algorithm)
  5. 3.7.5When greedy fails — 0 - 1 knapsack counter-example
  6. 3.7.6Dynamic programming — overlapping subproblems, optimal substructure
  7. 3.7.7Memoization (top-down DP) — recursive + memo dict
  8. 3.7.8Tabulation (bottom-up DP) — iterative
  9. 3.7.9DP problems — Fibonacci, coin change (count + min), 0 - 1 knapsack
  10. 3.7.10DP problems — Longest Common Subsequence (LCS)
  11. 3.7.11DP problems — Longest Increasing Subsequence (LIS) — O(n²) and O(n log n)
  12. 3.7.12DP problems — edit distance (Levenshtein)
  13. 3.7.13DP problems — matrix chain multiplication
  14. 3.7.14DP problems — rod cutting, egg drop, DP on trees
  15. 3.7.15Bitmask DP — TSP intro
  16. 3.7.16Backtracking — state-space tree, pruning
  17. 3.7.17Backtracking problems — N-Queens, Sudoku solver, all permutations - subsets
  18. 3.7.18Branch and bound
  19. 3.7.19Randomized algorithms — Las Vegas, Monte Carlo
  20. 3.7.20Bit manipulation — XOR tricks, LSB, counting set bits
3.8String Algorithms0 / 9
  1. 3.8.1Naive pattern matching — O(nm)
  2. 3.8.2KMP algorithm — failure function, O(n+m) — full derivation
  3. 3.8.3Rabin-Karp — rolling hash, O(n+m) expected
  4. 3.8.4Z-algorithm — Z-array construction, O(n+m)
  5. 3.8.5Boyer-Moore — bad character, good suffix heuristics
  6. 3.8.6Aho-Corasick — multiple pattern search, automaton
  7. 3.8.7Suffix array — construction O(n log n), LCP array
  8. 3.8.8Suffix tree (conceptual)
  9. 3.8.9Palindrome algorithms — Manacher's algorithm
4.1Computer Architecture (Deep)0 / 27
  1. 4.1.1Von Neumann architecture — components, bottleneck
  2. 4.1.2Harvard architecture — separate instruction - data memory
  3. 4.1.3ISA (Instruction Set Architecture) — RISC vs CISC
  4. 4.1.4ARM architecture intro — used in embedded - aerospace
  5. 4.1.5Registers — general purpose, special (PC, SP, LR, CPSR)
  6. 4.1.6ALU — operations, flags (zero, carry, overflow, negative)
  7. 4.1.7Instruction formats — R-type, I-type, J-type (MIPS - RISC-V)
  8. 4.1.8Memory addressing modes — immediate, register, direct, indirect, indexed
  9. 4.1.9Cache organization — direct-mapped, n-way set associative, fully associative
  10. 4.1.10Cache lines, tags, index, offset
  11. 4.1.11Replacement policies — LRU, LFU, FIFO, Random
  12. 4.1.12Write policies — write-through, write-back, write-allocate
  13. 4.1.13Cache coherence — MESI protocol in multicore
  14. 4.1.14Virtual memory — concept, page table, virtual-to-physical translation
  15. 4.1.15TLB — structure, TLB miss handling
  16. 4.1.16Page replacement — FIFO, LRU, Clock, Optimal
  17. 4.1.17Working set model, thrashing
  18. 4.1.18Pipelining — 5-stage pipeline, each stage
  19. 4.1.19Pipeline hazards — structural, data (RAW - WAR - WAW), control
  20. 4.1.20Hazard mitigation — stalling, forwarding - bypassing, branch prediction
  21. 4.1.21Branch prediction — static, dynamic (2-bit predictor, BTB)
  22. 4.1.22Out-of-order execution — Tomasulo algorithm (conceptual)
  23. 4.1.23Superscalar — multiple execution units
  24. 4.1.24SIMD — vector instructions, SSE - AVX
  25. 4.1.25GPU architecture — SIMT, warps, CUDA model
  26. 4.1.26Memory models — sequential consistency, TSO, relaxed
  27. 4.1.27Multicore coherence protocols
4.2Operating Systems0 / 41
  1. 4.2.1OS roles — resource management, hardware abstraction, protection
  2. 4.2.2OS structure — monolithic, microkernel, hybrid
  3. 4.2.3System calls — user mode vs kernel mode, trap mechanism
  4. 4.2.4Processes — PCB, states (new - ready - running - blocked - terminated)
  5. 4.2.5Process creation — fork(), exec(), wait(), exit()
  6. 4.2.6Context switch — what gets saved, overhead
  7. 4.2.7Threads — user-level vs kernel-level, one-to-one, many-to-many
  8. 4.2.8Thread synchronization needs — shared memory issues
  9. 4.2.9Scheduling goals — CPU utilization, throughput, turnaround, waiting, response
  10. 4.2.10Scheduling algorithms — FCFS, SJF (preemptive = SRTF), Round Robin, Priority
  11. 4.2.11Multi-level feedback queue (MLFQ) — promotion, demotion rules
  12. 4.2.12Scheduling on multiprocessors — load balancing, affinity
  13. 4.2.13Race condition — example, why it's a problem
  14. 4.2.14Critical section — mutual exclusion, progress, bounded waiting
  15. 4.2.15Mutex — implementation using hardware atomics (test-and-set, CAS)
  16. 4.2.16Semaphores — binary and counting, P() and V() operations
  17. 4.2.17Monitors — condition variables, wait, signal, broadcast
  18. 4.2.18Classic problems — Producer-Consumer, Readers-Writers (three variants), Dining Philosophers
  19. 4.2.19Deadlock — four necessary conditions (Coffman)
  20. 4.2.20Deadlock prevention — break each condition
  21. 4.2.21Deadlock avoidance — Banker's algorithm
  22. 4.2.22Deadlock detection and recovery
  23. 4.2.23Memory allocation — contiguous (first-fit, best-fit, worst-fit)
  24. 4.2.24Fragmentation — internal vs external, compaction
  25. 4.2.25Paging — page - frame size, page table structure
  26. 4.2.26Multi-level page tables — why, overhead
  27. 4.2.27Segmentation — segment table, protection
  28. 4.2.28Demand paging — page fault handling steps
  29. 4.2.29Copy-on-write
  30. 4.2.30Memory-mapped files
  31. 4.2.31File system concepts — file, directory, path, inode
  32. 4.2.32File operations — open, read, write, seek, close
  33. 4.2.33Directory structure — tree, DAG (hard links, symbolic links)
  34. 4.2.34File allocation — contiguous, linked, indexed (inode)
  35. 4.2.35ext4 structure — superblock, block groups, inodes
  36. 4.2.36Journaling — why, how it works
  37. 4.2.37I - O management — polling, interrupt-driven, DMA
  38. 4.2.38Disk scheduling — FCFS, SCAN, C-SCAN, LOOK
  39. 4.2.39RAID — levels 0, 1, 5, 6, 10 — trade-offs
  40. 4.2.40Virtualization — type 1 and type 2 hypervisors
  41. 4.2.41Containers — namespaces, cgroups, difference from VMs
4.3Computer Networks0 / 31
  1. 4.3.1OSI model — 7 layers, responsibilities, PDU names
  2. 4.3.2TCP - IP model — 4 layers, mapping to OSI
  3. 4.3.3Physical layer — encoding (NRZ, Manchester), bandwidth, Nyquist, Shannon-Hartley
  4. 4.3.4Data link layer — framing, error detection (CRC computation), MAC
  5. 4.3.5Ethernet (IEEE 802.3) — CSMA - CD, frame format
  6. 4.3.6Wi-Fi (IEEE 802.11) — CSMA - CA, bands
  7. 4.3.7Switching — circuit, packet, virtual circuit
  8. 4.3.8IPv4 — address format, classes, subnetting, CIDR notation
  9. 4.3.9Subnetting — subnet mask, network - host bits, VLSM
  10. 4.3.10NAT — why, how, types (SNAT, DNAT, PAT)
  11. 4.3.11IPv6 — address format, why needed, key differences
  12. 4.3.12ARP — address resolution, ARP cache, gratuitous ARP
  13. 4.3.13Routing — forwarding table, routing table
  14. 4.3.14Static routing vs dynamic routing
  15. 4.3.15Distance vector routing — RIP, Bellman-Ford, count-to-infinity
  16. 4.3.16Link state routing — OSPF, Dijkstra
  17. 4.3.17BGP — path vector, AS, policy routing
  18. 4.3.18UDP — header, use cases, checksum
  19. 4.3.19TCP — header, connection (3-way handshake, 4-way termination)
  20. 4.3.20TCP reliability — seq - ack numbers, retransmission, cumulative ACK
  21. 4.3.21TCP flow control — sliding window, receive buffer
  22. 4.3.22TCP congestion control — slow start, congestion avoidance, fast retransmit, CUBIC
  23. 4.3.23DNS — recursive vs iterative query, hierarchy, record types (A, AAAA, CNAME, MX, NS)
  24. 4.3.24HTTP - 1.1 — methods, status codes, headers, persistent connections
  25. 4.3.25HTTP - 2 — multiplexing, header compression (HPACK), server push
  26. 4.3.26HTTP - 3 — QUIC, UDP-based, why
  27. 4.3.27HTTPS — TLS handshake, certificates, CA
  28. 4.3.28Socket programming — TCP server - client, UDP server - client in Python
  29. 4.3.29Firewalls — stateless vs stateful packet filtering
  30. 4.3.30NAT traversal, VPN, tunneling
  31. 4.3.31Network security — DDoS, man-in-the-middle, replay attacks, countermeasures
4.4Databases0 / 28
  1. 4.4.1Relational model — tables, rows, columns, NULL
  2. 4.4.2Keys — primary, candidate, super, foreign, natural vs surrogate
  3. 4.4.3SQL DDL — CREATE, ALTER, DROP, TRUNCATE
  4. 4.4.4SQL DML — SELECT, INSERT, UPDATE, DELETE
  5. 4.4.5SQL clauses — WHERE, GROUP BY, HAVING, ORDER BY, LIMIT
  6. 4.4.6Joins — INNER, LEFT, RIGHT, FULL OUTER, CROSS, SELF
  7. 4.4.7Subqueries — correlated vs uncorrelated
  8. 4.4.8Aggregate functions — COUNT, SUM, AVG, MIN, MAX
  9. 4.4.9Window functions — ROW_NUMBER, RANK, DENSE_RANK, LAG, LEAD
  10. 4.4.10CTEs (WITH clause) — recursive CTEs
  11. 4.4.11Views — creating, updatable views
  12. 4.4.12Stored procedures, triggers, functions
  13. 4.4.13Indexing — B-tree index, hash index, full-text
  14. 4.4.14Composite indexes, covering indexes
  15. 4.4.15EXPLAIN — reading query plans, cost estimation
  16. 4.4.16Transactions — ACID properties (each one in detail)
  17. 4.4.17Transaction isolation levels — READ UNCOMMITTED, READ COMMITTED, REPEATABLE READ, SERIALIZABLE
  18. 4.4.18Concurrency anomalies — dirty read, non-repeatable read, phantom read
  19. 4.4.19Locking — shared, exclusive, intent locks
  20. 4.4.20Optimistic vs pessimistic concurrency control
  21. 4.4.21Normalization — 1NF, 2NF, 3NF, BCNF — anomalies each resolves
  22. 4.4.22Denormalization — when and why
  23. 4.4.23ER diagrams — entities, attributes, relationships, cardinality
  24. 4.4.24NoSQL — document (MongoDB), key-value (Redis), column (Cassandra), graph (Neo4j)
  25. 4.4.25CAP theorem — consistency, availability, partition tolerance
  26. 4.4.26BASE vs ACID
  27. 4.4.27Distributed databases — sharding strategies, replication
  28. 4.4.28MVCC — multi-version concurrency control
4.5Software Engineering0 / 24
  1. 4.5.1SDLC — waterfall, V-model, iterative, agile
  2. 4.5.2Agile — Scrum (sprints, roles, ceremonies), Kanban
  3. 4.5.3Requirements — functional vs non-functional, user stories, acceptance criteria
  4. 4.5.4UML — use case, class, sequence, activity, state machine, component diagrams
  5. 4.5.5Software architecture — layered, MVC, event-driven, microservices, serverless
  6. 4.5.6REST API design — resources, HTTP methods, status codes, versioning, pagination
  7. 4.5.7Git internals — objects (blob, tree, commit, tag), DAG structure
  8. 4.5.8Git operations — branch, merge, rebase, cherry-pick, stash, bisect
  9. 4.5.9Git workflows — Gitflow, trunk-based development
  10. 4.5.10CI - CD — pipeline stages, GitHub Actions - GitLab CI concepts
  11. 4.5.11Docker — images, containers, Dockerfile, docker-compose
  12. 4.5.12Kubernetes — pods, deployments, services, ingress (concepts)
  13. 4.5.13Testing — unit, integration, system, acceptance, smoke, regression
  14. 4.5.14TDD — Red-Green-Refactor cycle
  15. 4.5.15Code coverage — line, branch, path coverage
  16. 4.5.16Mutation testing
  17. 4.5.17Property-based testing
  18. 4.5.18Code review — what to look for
  19. 4.5.19Refactoring — code smells, common refactorings (extract method, rename, etc.)
  20. 4.5.20Technical debt — types, managing
  21. 4.5.21Documentation — inline comments, docstrings, README, ADRs
  22. 4.5.22Logging and monitoring — structured logging, metrics, alerting
  23. 4.5.23Security — OWASP Top 10, input validation, authentication vs authorization
  24. 4.5.24Performance profiling — CPU, memory, I - O profiling
4.6Theory of Computation0 / 29
  1. 4.6.1Alphabet, string, language — formal definitions
  2. 4.6.2Finite automata — DFA - formal definition (5-tuple), state diagrams
  3. 4.6.3NFA — formal definition, epsilon transitions
  4. 4.6.4NFA to DFA conversion — subset construction
  5. 4.6.5Regular expressions — equivalence with finite automata
  6. 4.6.6Regular languages — closed under union, intersection, complement, concatenation, Kleene star
  7. 4.6.7Pumping lemma for regular languages — proof and using to show non-regularity
  8. 4.6.8Context-free grammars (CFG) — productions, derivations, parse trees
  9. 4.6.9Chomsky Normal Form (CNF) — conversion
  10. 4.6.10Pushdown automata (PDA) — configuration, acceptance by empty stack - final state
  11. 4.6.11Equivalence of CFGs and PDAs
  12. 4.6.12Pumping lemma for CFLs
  13. 4.6.13Turing machines — formal definition, computation, configurations
  14. 4.6.14Variants — multi-tape TM, non-deterministic TM, all equivalent
  15. 4.6.15Church-Turing thesis
  16. 4.6.16Universal Turing machine
  17. 4.6.17Decidability — decidable (recursive) and recognizable (recursively enumerable) languages
  18. 4.6.18Halting problem — undecidability proof by diagonalization
  19. 4.6.19Reducibility — many-one reductions
  20. 4.6.20Rice's theorem
  21. 4.6.21Complexity — DTIME, DSPACE, complexity classes
  22. 4.6.22P — polynomial time
  23. 4.6.23NP — non-deterministic polynomial, verifier definition
  24. 4.6.24P vs NP — statement, why it matters
  25. 4.6.25NP-completeness — Cook's theorem (SAT is NP-complete), reduction
  26. 4.6.26NP-complete problems — 3-SAT, Vertex Cover, Clique, Hamiltonian Path, TSP, Subset Sum
  27. 4.6.27NP-hard — harder than NP, may not be in NP
  28. 4.6.28PSPACE — Quantified Boolean Formula
  29. 4.6.29Approximation algorithms — approximation ratio, examples
5.1C Programming0 / 33
  1. 5.1.1C compilation — preprocessor, compiler, assembler, linker
  2. 5.1.2Data types — char, short, int, long, float, double, size_t
  3. 5.1.3Type sizes — sizeof, platform dependency, stdint.h (int32_t etc.)
  4. 5.1.4Operators — arithmetic, relational, logical, bitwise, assignment, comma
  5. 5.1.5Operator precedence — full table
  6. 5.1.6Control flow — if - else, switch, while, do-while, for, break, continue, goto
  7. 5.1.7Functions — declaration vs definition, prototypes, call by value
  8. 5.1.8Pointers — declaration, dereferencing ( - ), address-of (&)
  9. 5.1.9Pointer arithmetic — adding integers to pointers
  10. 5.1.10Arrays and pointers — array name decays to pointer
  11. 5.1.11Multi-dimensional arrays
  12. 5.1.12Pointer to pointer
  13. 5.1.13Function pointers — declaration, calling, use in callbacks
  14. 5.1.14Dynamic memory — malloc, calloc, realloc, free
  15. 5.1.15Memory layout — text, data, BSS, heap, stack segments
  16. 5.1.16Stack frames — how function calls work at the memory level
  17. 5.1.17Heap fragmentation
  18. 5.1.18Common memory errors — null dereference, buffer overflow, use-after-free, double free, memory leak
  19. 5.1.19Valgrind — detecting memory errors
  20. 5.1.20String handling — char arrays, null terminator, strcpy, strcat, strlen, sprintf (dangers)
  21. 5.1.21Safe alternatives — strncpy, snprintf, strlcpy
  22. 5.1.22Structures — declaration, accessing members (. and - - )
  23. 5.1.23Bit fields in structs
  24. 5.1.24Unions — overlapping memory
  25. 5.1.25Enumerations
  26. 5.1.26Typedef
  27. 5.1.27Preprocessor directives — #define, #ifdef, #ifndef, #include guards
  28. 5.1.28Macros vs inline functions
  29. 5.1.29Variadic functions — va_list, va_start, va_arg, va_end
  30. 5.1.30Undefined behavior — comprehensive list, why to avoid
  31. 5.1.31Compile-time assertions — static_assert
  32. 5.1.32restrict keyword — aliasing hint
  33. 5.1.33volatile keyword — preventing optimization of hardware registers
5.2C++ Programming0 / 32
  1. 5.2.1C++ as superset of C — key additions
  2. 5.2.2References — lvalue references, difference from pointers
  3. 5.2.3const correctness — const variables, const pointers, const member functions
  4. 5.2.4Namespaces — avoiding name collisions
  5. 5.2.5Classes — member functions, access specifiers (public, private, protected)
  6. 5.2.6Constructors — default, parameterized, copy, delegating
  7. 5.2.7Destructor — RAII principle
  8. 5.2.8Copy constructor and copy assignment — Rule of Three
  9. 5.2.9Move semantics — rvalue references (&&), std - move, std - forward
  10. 5.2.10Move constructor and move assignment — Rule of Five
  11. 5.2.11Rule of Zero — prefer compiler-generated specials
  12. 5.2.12Smart pointers — unique_ptr (sole ownership), shared_ptr (shared ownership, ref count), weak_ptr (break cycles)
  13. 5.2.13RAII — resource acquisition is initialization — why it's the key idiom
  14. 5.2.14Templates — function templates, class templates
  15. 5.2.15Template specialization — full and partial
  16. 5.2.16Variadic templates — parameter packs, fold expressions
  17. 5.2.17SFINAE — substitution failure is not an error
  18. 5.2.18Concepts (C++20) — constraining templates
  19. 5.2.19STL containers — vector, list, deque, array, set, multiset, map, multimap, unordered_map, unordered_set
  20. 5.2.20STL algorithms — sort, find, transform, accumulate, copy, all_of, any_of
  21. 5.2.21Iterators — input, output, forward, bidirectional, random access, contiguous
  22. 5.2.22Lambda expressions — capture list (by value, by reference)
  23. 5.2.23std - function and std - bind
  24. 5.2.24Concurrency — std - thread, std - mutex, std - lock_guard, std - unique_lock
  25. 5.2.25std - condition_variable
  26. 5.2.26std - atomic — lock-free operations
  27. 5.2.27Memory model — happens-before, acquire-release semantics
  28. 5.2.28std - promise and std - future
  29. 5.2.29Exception safety — basic, strong, no-throw guarantees
  30. 5.2.30noexcept specifier
  31. 5.2.31Inline namespaces, anonymous namespaces
  32. 5.2.32Modules (C++20) — concept and syntax
5.3Build Systems & Toolchain0 / 17
  1. 5.3.1Compilation stages — preprocessing, compilation, assembly, linking
  2. 5.3.2Object files — .o - .obj, symbol table, relocation entries
  3. 5.3.3Static libraries — .a - .lib, creation and linking
  4. 5.3.4Dynamic - shared libraries — .so - .dll, dynamic linking, PIC
  5. 5.3.5Symbol resolution — order matters
  6. 5.3.6Makefiles — targets, prerequisites, recipes, variables, automatic variables
  7. 5.3.7Phony targets, pattern rules, implicit rules
  8. 5.3.8CMake — CMakeLists.txt, add_executable, add_library, target_link_libraries
  9. 5.3.9CMake build types — Debug, Release, RelWithDebInfo
  10. 5.3.10Cross-compilation — toolchains, sysroot
  11. 5.3.11GCC - Clang flags — optimization (-O0 to -O3, -Os), warnings (-Wall, -Wextra), sanitizers
  12. 5.3.12Address Sanitizer (ASan) — detecting buffer overflows at runtime
  13. 5.3.13Undefined Behavior Sanitizer (UBSan)
  14. 5.3.14Thread Sanitizer (TSan)
  15. 5.3.15GDB debugging — breakpoints, watchpoints, step, next, backtrace
  16. 5.3.16Profiling — gprof, perf, Valgrind - Callgrind
  17. 5.3.17Disassembly — objdump, reading assembly
5.4Scientific Computing (Python)0 / 25
  1. 5.4.1NumPy — ndarray structure, dtype, shape, strides
  2. 5.4.2Array creation — np.zeros, np.ones, np.linspace, np.arange, np.random
  3. 5.4.3Indexing and slicing — basic, boolean masking, fancy indexing
  4. 5.4.4Broadcasting — rules, why it works, gotchas
  5. 5.4.5Vectorization — avoiding Python loops, speed comparison
  6. 5.4.6NumPy linear algebra — np.linalg.solve, eig, svd, norm, det
  7. 5.4.7NumPy FFT — np.fft module
  8. 5.4.8SciPy — overview of submodules
  9. 5.4.9scipy.integrate — odeint, solve_ivp (RK45, DOP853), quad
  10. 5.4.10scipy.optimize — minimize, fsolve, curve_fit, linprog
  11. 5.4.11scipy.linalg — more stable than numpy.linalg, lu, qr, schur
  12. 5.4.12scipy.signal — filtering, convolution, FFT-based analysis
  13. 5.4.13scipy.sparse — sparse matrix formats (CSR, CSC), sparse solvers
  14. 5.4.14scipy.stats — distributions, hypothesis tests
  15. 5.4.15Matplotlib — figure - axes architecture
  16. 5.4.162D plots — line, scatter, bar, histogram, contour, imshow
  17. 5.4.173D plots — surface, wireframe
  18. 5.4.18Animation — FuncAnimation
  19. 5.4.19Publication-quality figures — LaTeX labels, colormaps, DPI
  20. 5.4.20SymPy — symbolic algebra, calculus, ODE solving
  21. 5.4.21Pandas — Series, DataFrame, indexing, groupby, merge, pivot
  22. 5.4.22Floating point gotchas — catastrophic cancellation, associativity failure
  23. 5.4.23Implementing ODE solvers from scratch — Euler, RK4
  24. 5.4.24Implementing numerical integration from scratch — trapezoidal, Simpson's
  25. 5.4.25Implementing root-finding from scratch — Newton-Raphson, bisection
5.5Embedded Systems & Real-Time Software0 / 28
  1. 5.5.1Microcontroller architecture — ARM Cortex-M series (M0, M3, M4, M7)
  2. 5.5.2GPIO — input - output, pull-up - pull-down, interrupt on pin change
  3. 5.5.3Timers — PWM generation, input capture, output compare
  4. 5.5.4ADC - DAC — resolution, sampling rate, Nyquist
  5. 5.5.5Communication interfaces — UART, SPI, I2C (master - slave), CAN bus
  6. 5.5.6CAN bus — frame format, arbitration, error handling — critical in aerospace
  7. 5.5.7Interrupts — ISR design, NVIC priority, interrupt latency
  8. 5.5.8DMA — memory-to-memory, peripheral-to-memory without CPU
  9. 5.5.9RTOS concepts — task, scheduler, preemption, context switch
  10. 5.5.10FreeRTOS — task creation, priorities, xTaskCreate
  11. 5.5.11FreeRTOS IPC — queues, semaphores, mutexes, event groups
  12. 5.5.12Real-time constraints — hard and soft deadlines
  13. 5.5.13WCET (Worst Case Execution Time) analysis
  14. 5.5.14Priority inversion — problem and solutions (priority inheritance, priority ceiling)
  15. 5.5.15Bare-metal vs RTOS — when to use each
  16. 5.5.16Startup code — vector table, reset handler, stack initialization
  17. 5.5.17Linker scripts — memory regions, sections (.text, .data, .bss)
  18. 5.5.18Safety-critical standards — DO-178C (airborne software), IEC 61508, ISO 26262
  19. 5.5.19MISRA C — rules for safety-critical C code
  20. 5.5.20Software testing in embedded — unit tests on host, HIL testing
  21. 5.5.21Hardware-in-the-Loop (HIL) simulation — real hardware, simulated plant
  22. 5.5.22Software-in-the-Loop (SIL) simulation — all software, simulated hardware
  23. 5.5.23Watchdog timers — purpose, feeding, types
  24. 5.5.24Memory protection units (MPU) — preventing stack overflow, access faults
  25. 5.5.25Redundancy — TMR (triple modular redundancy), voting logic
  26. 5.5.26Fault tolerance — fail-safe vs fail-operational
  27. 5.5.27SpaceWire — high-speed serial link standard for spacecraft
  28. 5.5.28MIL-STD-1553 — military avionics bus
5.6Machine Learning (Aerospace Applications)0 / 19
  1. 5.6.1Linear regression — normal equation, gradient descent derivation
  2. 5.6.2Logistic regression — sigmoid, cross-entropy loss
  3. 5.6.3Regularization — L1 (lasso), L2 (ridge), dropout
  4. 5.6.4Bias-variance trade-off
  5. 5.6.5Cross-validation — k-fold
  6. 5.6.6Neural network fundamentals — neuron, activation functions (ReLU, sigmoid, tanh)
  7. 5.6.7Feedforward network — forward pass
  8. 5.6.8Backpropagation — chain rule, gradient computation
  9. 5.6.9Optimization — SGD, momentum, Adam — derivations
  10. 5.6.10Batch, mini-batch, stochastic gradient descent
  11. 5.6.11Convolutional neural networks — convolution operation, pooling
  12. 5.6.12Recurrent neural networks — hidden state, BPTT
  13. 5.6.13LSTM — gates, cell state
  14. 5.6.14Transformers — attention mechanism, self-attention
  15. 5.6.15Aerospace ML applications — fault detection, system identification
  16. 5.6.16System identification — learning dynamics from data
  17. 5.6.17Reinforcement learning — MDP, Bellman equation, Q-learning
  18. 5.6.18Policy gradient — REINFORCE
  19. 5.6.19Application to GNC — learned guidance laws

Hardware

0 / 334 · 0%
1.1Electricity & Charge Basics0 / 14
  1. 1.1.1Define electric charge, electron, proton, and the coulomb
  2. 1.1.2Understand conductors, insulators, and semiconductors
  3. 1.1.3Define voltage (potential difference) and its units
  4. 1.1.4Define current (flow of charge) and the ampere
  5. 1.1.5Define resistance and the ohm
  6. 1.1.6State and apply Ohm's Law (V = IR)
  7. 1.1.7Calculate electrical power (P = VI, P = I²R)
  8. 1.1.8Distinguish DC vs AC signals
  9. 1.1.9Understand conventional current vs electron flow direction
  10. 1.1.10Define electric field and electric potential
  11. 1.1.11Understand capacitance and the farad
  12. 1.1.12Understand inductance and the henry
  13. 1.1.13Define energy (joules) vs power (watts)
  14. 1.1.14Read and interpret circuit schematic symbols
1.2Circuit Analysis Fundamentals0 / 14
  1. 1.2.1Series vs parallel resistor combinations
  2. 1.2.2Compute equivalent resistance in mixed networks
  3. 1.2.3Apply Kirchhoff's Current Law (KCL)
  4. 1.2.4Apply Kirchhoff's Voltage Law (KVL)
  5. 1.2.5Build and analyze a voltage divider
  6. 1.2.6Build and analyze a current divider
  7. 1.2.7Understand RC charging - discharging time constants
  8. 1.2.8Understand RL transient behavior
  9. 1.2.9Use Thevenin equivalent circuits
  10. 1.2.10Use Norton equivalent circuits
  11. 1.2.11Apply superposition theorem
  12. 1.2.12Read multimeter measurements (V, I, R)
  13. 1.2.13Understand grounding and reference nodes
  14. 1.2.14Analyze simple AC circuits with reactance
1.3Materials & Atomic Structure0 / 10
  1. 1.3.1Bohr atomic model and electron shells
  2. 1.3.2Valence electrons and bonding
  3. 1.3.3Covalent bonding in silicon crystals
  4. 1.3.4Crystal lattice structure of silicon
  5. 1.3.5Intrinsic vs extrinsic semiconductors
  6. 1.3.6Electron-hole pair generation
  7. 1.3.7Concept of carrier mobility
  8. 1.3.8Thermal effects on conductivity
  9. 1.3.9Why silicon dominates over germanium
  10. 1.3.10Compound semiconductors (GaN, GaAs, SiC) overview
2.1Band Theory & Carrier Physics0 / 13
  1. 2.1.1Energy bands - valence band and conduction band
  2. 2.1.2Band gap and its meaning for conductivity
  3. 2.1.3Compare band gaps - conductor - semiconductor - insulator
  4. 2.1.4Fermi level and Fermi-Dirac distribution
  5. 2.1.5Direct vs indirect band gap materials
  6. 2.1.6Carrier concentration equations (n, p, ni)
  7. 2.1.7Mass action law (np = ni²)
  8. 2.1.8Drift current and electric field
  9. 2.1.9Diffusion current and concentration gradient
  10. 2.1.10Einstein relation between mobility and diffusion
  11. 2.1.11Recombination and generation mechanisms
  12. 2.1.12Minority vs majority carriers
  13. 2.1.13Temperature dependence of carrier concentration
2.2Doping & PN Junctions0 / 13
  1. 2.2.1N-type doping with donor atoms (phosphorus, arsenic)
  2. 2.2.2P-type doping with acceptor atoms (boron)
  3. 2.2.3Donor - acceptor energy levels in the band gap
  4. 2.2.4Formation of a PN junction
  5. 2.2.5Depletion region and space charge
  6. 2.2.6Built-in potential of a junction
  7. 2.2.7Forward bias behavior
  8. 2.2.8Reverse bias behavior
  9. 2.2.9Diode I-V characteristic curve
  10. 2.2.10Shockley diode equation
  11. 2.2.11Junction capacitance (depletion + diffusion)
  12. 2.2.12Reverse breakdown - avalanche vs Zener
  13. 2.2.13Reverse saturation current
2.3Diodes & Applications0 / 10
  1. 2.3.1Rectifier diodes and half-wave rectification
  2. 2.3.2Full-wave and bridge rectifiers
  3. 2.3.3Zener diodes for voltage regulation
  4. 2.3.4Light-emitting diodes (LED) operation
  5. 2.3.5Photodiodes and solar cells
  6. 2.3.6Schottky diodes and metal-semiconductor junctions
  7. 2.3.7Varactor diodes
  8. 2.3.8Diode clipping and clamping circuits
  9. 2.3.9Diode logic gate basics
  10. 2.3.10Datasheet parameters (Vf, Ir, max ratings)
2.4Chapter 2.40 / 17
  1. 2.4.1BJT structure (NPN and PNP)
  2. 2.4.2BJT operating regions (cutoff, active, saturation)
  3. 2.4.3Current gain β (hFE) and α
  4. 2.4.4BJT as a switch
  5. 2.4.5BJT as an amplifier (common emitter)
  6. 2.4.6BJT biasing techniques
  7. 2.4.7JFET structure and operation
  8. 2.4.8MOSFET structure (gate, source, drain, body)
  9. 2.4.9Enhancement vs depletion mode MOSFETs
  10. 2.4.10NMOS vs PMOS
  11. 2.4.11Threshold voltage (Vth)
  12. 2.4.12MOSFET I-V curves (triode and saturation)
  13. 2.4.13Transconductance (gm)
  14. 2.4.14MOSFET as a switch
  15. 2.4.15Channel length and short-channel effects
  16. 2.4.16Body effect and substrate bias
  17. 2.4.17Subthreshold leakage current
3.1Boolean Algebra & Logic Gates0 / 15
  1. 3.1.1Binary number system and bit - byte concepts
  2. 3.1.2Hexadecimal and octal representation
  3. 3.1.3Two's complement signed numbers
  4. 3.1.4Boolean variables and operations (AND, OR, NOT)
  5. 3.1.5Truth tables construction
  6. 3.1.6XOR, NAND, NOR, XNOR gates
  7. 3.1.7Boolean algebra laws (commutative, associative, distributive)
  8. 3.1.8De Morgan's theorems
  9. 3.1.9Sum of products (SOP) form
  10. 3.1.10Product of sums (POS) form
  11. 3.1.11Karnaugh map simplification (2,3,4 variables)
  12. 3.1.12Don't-care conditions in K-maps
  13. 3.1.13Quine-McCluskey method
  14. 3.1.14Universal gates (NAND - NOR completeness)
  15. 3.1.15Logic gate propagation delay
3.2CMOS Circuit Design0 / 13
  1. 3.2.1CMOS inverter structure and operation
  2. 3.2.2Pull-up and pull-down networks
  3. 3.2.3CMOS NAND and NOR gate design
  4. 3.2.4Static vs dynamic power dissipation
  5. 3.2.5Voltage transfer characteristic (VTC)
  6. 3.2.6Noise margins (NMH, NML)
  7. 3.2.7Propagation delay and rise - fall times
  8. 3.2.8Fan-in and fan-out limits
  9. 3.2.9Transmission gates
  10. 3.2.10Pass-transistor logic
  11. 3.2.11Dynamic CMOS logic
  12. 3.2.12Domino logic
  13. 3.2.13Power-delay product
3.3Combinational Circuits0 / 14
  1. 3.3.1Half adder and full adder
  2. 3.3.2Ripple-carry adder
  3. 3.3.3Carry-lookahead adder
  4. 3.3.4Subtractors
  5. 3.3.5Multiplexers (2 - 1, 4 - 1, n - 1)
  6. 3.3.6Demultiplexers
  7. 3.3.7Encoders and priority encoders
  8. 3.3.8Decoders (2 - 4, 3 - 8)
  9. 3.3.9Comparators
  10. 3.3.10Parity generators - checkers
  11. 3.3.11Barrel shifters
  12. 3.3.12Combinational multipliers
  13. 3.3.13ALU design fundamentals
  14. 3.3.14Hazards (static and dynamic) in combinational logic
3.4Sequential Circuits0 / 15
  1. 3.4.1SR latch operation
  2. 3.4.2D latch and gated latches
  3. 3.4.3Edge-triggered D flip-flop
  4. 3.4.4JK and T flip-flops
  5. 3.4.5Setup and hold time constraints
  6. 3.4.6Clock-to-Q delay
  7. 3.4.7Registers and shift registers
  8. 3.4.8Synchronous vs asynchronous counters
  9. 3.4.9Ring and Johnson counters
  10. 3.4.10Finite state machines (Mealy and Moore)
  11. 3.4.11State diagram and state table design
  12. 3.4.12State minimization techniques
  13. 3.4.13Metastability and synchronizers
  14. 3.4.14Clock domain crossing
  15. 3.4.15Clock skew and jitter
3.5HDL & Digital Design Flow0 / 10
  1. 3.5.1Verilog - VHDL syntax basics
  2. 3.5.2Combinational logic in HDL
  3. 3.5.3Sequential logic and always blocks
  4. 3.5.4Blocking vs non-blocking assignments
  5. 3.5.5Testbenches and simulation
  6. 3.5.6RTL (register transfer level) design
  7. 3.5.7Synthesis to gate-level netlist
  8. 3.5.8FPGA vs ASIC design flow
  9. 3.5.9Timing analysis basics (static timing)
  10. 3.5.10Critical path identification
4.1Memory Technologies0 / 15
  1. 4.1.1SRAM 6T cell structure and operation
  2. 4.1.2SRAM read - write operations
  3. 4.1.3DRAM 1T1C cell structure
  4. 4.1.4DRAM refresh and charge leakage
  5. 4.1.5Row - column addressing and sense amplifiers
  6. 4.1.6SDRAM and DDR (DDR2 - 3 - 4 - 5) evolution
  7. 4.1.7ROM, PROM, EPROM, EEPROM
  8. 4.1.8Flash memory (NOR vs NAND)
  9. 4.1.9Floating gate transistor operation
  10. 4.1.10Multi-level cell (MLC - TLC - QLC) flash
  11. 4.1.11Wear leveling and flash controllers
  12. 4.1.12Emerging memories (MRAM, ReRAM, PCM)
  13. 4.1.13Content-addressable memory (CAM)
  14. 4.1.14Memory bandwidth and latency metrics
  15. 4.1.15ECC and memory error correction
4.2VLSI Design0 / 15
  1. 4.2.1Moore's Law and scaling trends
  2. 4.2.2Dennard scaling and its breakdown
  3. 4.2.3Full custom vs standard cell design
  4. 4.2.4Standard cell libraries
  5. 4.2.5Place and route (P&R)
  6. 4.2.6Floorplanning and power planning
  7. 4.2.7Clock tree synthesis
  8. 4.2.8Design rule checking (DRC)
  9. 4.2.9Layout vs schematic (LVS)
  10. 4.2.10Parasitic extraction (RC)
  11. 4.2.11Signal integrity and crosstalk
  12. 4.2.12Power grid and IR drop analysis
  13. 4.2.13Design for testability (DFT)
  14. 4.2.14Scan chains and BIST
  15. 4.2.15Low-power design techniques (clock - power gating)
4.3Semiconductor Fabrication0 / 22
  1. 4.3.1Silicon wafer production (Czochralski process)
  2. 4.3.2Wafer cleaning and preparation
  3. 4.3.3Oxidation (thermal SiO2 growth)
  4. 4.3.4Photolithography process steps
  5. 4.3.5Photoresist (positive and negative)
  6. 4.3.6Masks - reticles and projection systems
  7. 4.3.7Deep UV (DUV) lithography
  8. 4.3.8Extreme UV (EUV) lithography
  9. 4.3.9Multi-patterning techniques
  10. 4.3.10Etching (wet vs dry - plasma)
  11. 4.3.11Ion implantation and diffusion
  12. 4.3.12Chemical vapor deposition (CVD)
  13. 4.3.13Physical vapor deposition (PVD - sputtering)
  14. 4.3.14Atomic layer deposition (ALD)
  15. 4.3.15Chemical mechanical planarization (CMP)
  16. 4.3.16Metallization and interconnect layers
  17. 4.3.17Copper damascene process
  18. 4.3.18Process nodes (28nm→7nm→5nm→3nm→2nm)
  19. 4.3.19FinFET transistor structure
  20. 4.3.20Gate-all-around (GAA) nanosheet transistors
  21. 4.3.21Yield, defect density, and binning
  22. 4.3.22Packaging and wire bonding - flip-chip
5.1Instruction Set Architecture (ISA)0 / 13
  1. 5.1.1CISC vs RISC philosophies
  2. 5.1.2Instruction formats and encoding
  3. 5.1.3Addressing modes
  4. 5.1.4Register file organization
  5. 5.1.5x86 architecture overview
  6. 5.1.6ARM architecture overview
  7. 5.1.7RISC-V base ISA (RV32I - RV64I)
  8. 5.1.8RISC-V extensions (M, A, F, D, V, C)
  9. 5.1.9Load - store architecture model
  10. 5.1.10Calling conventions and ABI
  11. 5.1.11Endianness (big vs little)
  12. 5.1.12Instruction-level semantics and exceptions
  13. 5.1.13System vs user mode and privilege levels
5.2Processor Datapath & Pipelining0 / 12
  1. 5.2.1Single-cycle datapath design
  2. 5.2.2Multi-cycle datapath
  3. 5.2.3Classic 5-stage pipeline (IF - ID - EX - MEM - WB)
  4. 5.2.4Pipeline registers and control signals
  5. 5.2.5Structural hazards
  6. 5.2.6Data hazards and forwarding - bypassing
  7. 5.2.7Load-use hazard and stalls
  8. 5.2.8Control hazards and pipeline flushes
  9. 5.2.9Pipeline throughput and CPI
  10. 5.2.10Hazard detection units
  11. 5.2.11Deep pipelining trade-offs
  12. 5.2.12Precise exceptions in pipelines
5.3Advanced Microarchitecture0 / 15
  1. 5.3.1Superscalar execution
  2. 5.3.2Out-of-order execution
  3. 5.3.3Tomasulo's algorithm
  4. 5.3.4Register renaming
  5. 5.3.5Reorder buffer (ROB)
  6. 5.3.6Reservation stations
  7. 5.3.7Branch prediction (static and dynamic)
  8. 5.3.82-bit saturating counter predictors
  9. 5.3.9Branch target buffer (BTB)
  10. 5.3.10Tournament and TAGE predictors
  11. 5.3.11Speculative execution
  12. 5.3.12Return address stack
  13. 5.3.13VLIW architectures
  14. 5.3.14Simultaneous multithreading (SMT - hyperthreading)
  15. 5.3.15Spectre - Meltdown speculative side channels
5.4Memory Hierarchy & Caches0 / 17
  1. 5.4.1Principle of locality (temporal - spatial)
  2. 5.4.2Cache organization (direct-mapped)
  3. 5.4.3Set-associative and fully associative caches
  4. 5.4.4Cache line size and tags
  5. 5.4.5Replacement policies (LRU, FIFO, random)
  6. 5.4.6Write-through vs write-back
  7. 5.4.7Write-allocate vs no-allocate
  8. 5.4.8Multi-level cache hierarchy (L1 - L2 - L3)
  9. 5.4.9Cache miss types (compulsory, capacity, conflict)
  10. 5.4.10Average memory access time (AMAT)
  11. 5.4.11Virtual memory and paging
  12. 5.4.12TLB (translation lookaside buffer)
  13. 5.4.13Page tables and multi-level paging
  14. 5.4.14Cache coherence problem
  15. 5.4.15MESI - MOESI coherence protocols
  16. 5.4.16Memory consistency models
  17. 5.4.17Prefetching strategies
6.1Parallelism & Multicore0 / 12
  1. 6.1.1Flynn's taxonomy (SISD - SIMD - MIMD)
  2. 6.1.2Instruction-level vs thread-level parallelism
  3. 6.1.3Amdahl's Law and Gustafson's Law
  4. 6.1.4Multicore vs manycore designs
  5. 6.1.5Shared memory vs distributed memory
  6. 6.1.6Cache coherence at scale (directory-based)
  7. 6.1.7NUMA architectures
  8. 6.1.8Synchronization primitives (locks, barriers)
  9. 6.1.9Atomic operations and CAS
  10. 6.1.10False sharing problem
  11. 6.1.11Vector - SIMD instructions (SSE, AVX, NEON)
  12. 6.1.12Heterogeneous computing concepts
6.2GPU Architecture0 / 15
  1. 6.2.1GPU vs CPU design philosophy
  2. 6.2.2Streaming multiprocessors (SM)
  3. 6.2.3CUDA cores and execution model
  4. 6.2.4SIMT (single instruction multiple thread)
  5. 6.2.5Warps and warp scheduling
  6. 6.2.6Thread blocks and grids
  7. 6.2.7Memory hierarchy (global, shared, registers)
  8. 6.2.8Coalesced memory access
  9. 6.2.9Bank conflicts in shared memory
  10. 6.2.10Occupancy and latency hiding
  11. 6.2.11Warp divergence penalties
  12. 6.2.12Tensor cores and matrix operations
  13. 6.2.13CUDA programming model basics
  14. 6.2.14GPU memory bandwidth optimization
  15. 6.2.15ROCm - OpenCL alternatives
6.3Interconnects, Buses & SoC0 / 12
  1. 6.3.1Bus topologies and arbitration
  2. 6.3.2PCI Express (PCIe) architecture and generations
  3. 6.3.3PCIe lanes, links, and bandwidth
  4. 6.3.4NVLink and GPU interconnects
  5. 6.3.5CXL (Compute Express Link)
  6. 6.3.6Network-on-Chip (NoC) topologies
  7. 6.3.7AXI - AMBA on-chip protocols
  8. 6.3.8DMA controllers
  9. 6.3.9System-on-Chip (SoC) integration
  10. 6.3.10IP cores and SoC bus fabric
  11. 6.3.11Infinity Fabric - mesh interconnects
  12. 6.3.12Serial vs parallel signaling (SerDes)
6.4Power, Thermal & Reliability0 / 10
  1. 6.4.1Dynamic vs static power consumption
  2. 6.4.2Dynamic voltage and frequency scaling (DVFS)
  3. 6.4.3Thermal design power (TDP)
  4. 6.4.4Power gating and clock gating
  5. 6.4.5Heat dissipation and cooling solutions
  6. 6.4.6Thermal throttling mechanisms
  7. 6.4.7Dark silicon problem
  8. 6.4.8Electromigration reliability
  9. 6.4.9Voltage droop and decoupling capacitors
  10. 6.4.10Energy efficiency (performance per watt)
6.5Advanced & Emerging Architectures0 / 18
  1. 6.5.1Chiplets and multi-die integration
  2. 6.5.22.5D packaging and interposers
  3. 6.5.33D stacking and through-silicon vias (TSV)
  4. 6.5.4High Bandwidth Memory (HBM - HBM2 - HBM3)
  5. 6.5.5Processing-in-memory (PIM)
  6. 6.5.6Domain-specific accelerators
  7. 6.5.7Google TPU architecture and systolic arrays
  8. 6.5.8Neural processing units (NPUs)
  9. 6.5.9Dataflow architectures
  10. 6.5.10FPGA-based acceleration
  11. 6.5.11RISC-V custom extensions for accelerators
  12. 6.5.12Open hardware ecosystem (OpenRISC, OpenTitan)
  13. 6.5.13Quantum computing hardware basics
  14. 6.5.14Neuromorphic computing
  15. 6.5.15Photonic and optical interconnects
  16. 6.5.16Approximate computing techniques
  17. 6.5.17Wafer-scale engines (Cerebras-style)
  18. 6.5.18Co-packaged optics trends

Stock-Market

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1.1What Markets Are0 / 12
  1. 1.1.1Define a financial market and its economic purpose
  2. 1.1.2Understand capital allocation and price discovery
  3. 1.1.3Differentiate stock exchanges vs over-the-counter (OTC) markets
  4. 1.1.4Learn what a stock exchange physically - electronically does
  5. 1.1.5Understand role of NSE and BSE in India
  6. 1.1.6Learn about major global exchanges (NYSE, NASDAQ, LSE, TSE)
  7. 1.1.7Understand trading hours and time zones
  8. 1.1.8Define liquidity and why it matters
  9. 1.1.9Understand market capitalization (large - mid - small - micro cap)
  10. 1.1.10Learn what a ticker symbol - scrip code is
  11. 1.1.11Understand bid, ask, and spread basics
  12. 1.1.12Define bull, bear, and sideways markets
1.2Shares, Ownership & Indices0 / 13
  1. 1.2.1Understand what a share - stock represents (ownership)
  2. 1.2.2Differentiate common vs preferred shares
  3. 1.2.3Learn about voting rights and shareholder rights
  4. 1.2.4Understand dividends and dividend yield
  5. 1.2.5Learn about stock splits and bonus shares
  6. 1.2.6Understand buybacks and rights issues
  7. 1.2.7Define face value vs market value
  8. 1.2.8Understand authorized, issued, and outstanding shares
  9. 1.2.9Learn what a market index is and how it's built
  10. 1.2.10Understand Nifty 50, Sensex composition
  11. 1.2.11Learn about S&P 500, Dow Jones, NASDAQ Composite
  12. 1.2.12Understand free-float vs price-weighted indices
  13. 1.2.13Learn about sectoral and thematic indices
1.3Primary vs Secondary Market & IPOs0 / 11
  1. 1.3.1Differentiate primary and secondary markets
  2. 1.3.2Understand the IPO process end to end
  3. 1.3.3Learn about book building vs fixed price IPOs
  4. 1.3.4Understand the role of underwriters - merchant bankers
  5. 1.3.5Read a red herring prospectus (DRHP)
  6. 1.3.6Understand IPO price band, lot size, cut-off price
  7. 1.3.7Learn about IPO allotment and listing gains
  8. 1.3.8Understand FPO (Follow-on Public Offer)
  9. 1.3.9Learn about OFS (Offer for Sale)
  10. 1.3.10Understand QIP and private placements
  11. 1.3.11Learn about anchor investors and grey market premium
1.4Market Participants0 / 10
  1. 1.4.1Identify retail investors vs institutions
  2. 1.4.2Understand FIIs and DIIs and their impact
  3. 1.4.3Learn roles of mutual funds and pension funds
  4. 1.4.4Understand hedge funds and prop trading firms
  5. 1.4.5Learn about market makers and their function
  6. 1.4.6Understand brokers and sub-brokers
  7. 1.4.7Learn about depositories (NSDL, CDSL)
  8. 1.4.8Understand clearing corporations and settlement
  9. 1.4.9Learn role of SEBI as regulator
  10. 1.4.10Understand stock exchange listing requirements
1.5Brokerage, Demat & Account Setup0 / 10
  1. 1.5.1Understand demat account vs trading account
  2. 1.5.2Learn the account opening (KYC) process
  3. 1.5.3Understand T+1 settlement cycle in India
  4. 1.5.4Learn about full-service vs discount brokers
  5. 1.5.5Understand brokerage charges and pricing models
  6. 1.5.6Learn about DP charges, AMC, and statutory fees
  7. 1.5.7Understand power of attorney - DDPI
  8. 1.5.8Learn about linking bank account and UPI mandates
  9. 1.5.9Understand contract notes and ledger statements
  10. 1.5.10Learn how to read a holdings - portfolio statement
1.6Order Types & Mechanics0 / 12
  1. 1.6.1Understand market orders vs limit orders
  2. 1.6.2Learn stop-loss and stop-limit orders
  3. 1.6.3Understand GTT (Good Till Triggered) orders
  4. 1.6.4Learn about IOC, FOK, and day orders
  5. 1.6.5Understand bracket and cover orders
  6. 1.6.6Learn about AMO (after-market orders)
  7. 1.6.7Understand intraday vs delivery (CNC vs MIS)
  8. 1.6.8Learn how the order book - matching engine works
  9. 1.6.9Understand circuit limits and price bands
  10. 1.6.10Learn about pre-open session and call auctions
  11. 1.6.11Understand slippage and partial fills
  12. 1.6.12Learn how to read Level-1 quote data
2.1Equity & Fixed Income0 / 10
  1. 2.1.1Deepen understanding of equity as an asset class
  2. 2.1.2Understand bonds - coupon, maturity, face value
  3. 2.1.3Learn about government vs corporate bonds
  4. 2.1.4Understand yield and yield-to-maturity (YTM)
  5. 2.1.5Learn the inverse price-yield relationship
  6. 2.1.6Understand credit ratings and default risk
  7. 2.1.7Learn about the yield curve and its shapes
  8. 2.1.8Understand duration and interest rate sensitivity
  9. 2.1.9Learn about debentures and convertible bonds
  10. 2.1.10Understand zero-coupon bonds
2.2Funds, ETFs & Pooled Vehicles0 / 11
  1. 2.2.1Understand mutual funds and NAV
  2. 2.2.2Differentiate active vs passive funds
  3. 2.2.3Learn about index funds and ETFs
  4. 2.2.4Understand expense ratios and tracking error
  5. 2.2.5Learn about SIP vs lumpsum investing
  6. 2.2.6Understand equity, debt, and hybrid funds
  7. 2.2.7Learn about ELSS and tax-saving funds
  8. 2.2.8Understand exit loads and direct vs regular plans
  9. 2.2.9Learn about gold ETFs and international funds
  10. 2.2.10Understand REITs and InvITs
  11. 2.2.11Learn about fund of funds and closed-end funds
2.3Commodities, Forex & Crypto0 / 12
  1. 2.3.1Understand commodity markets (gold, silver, crude, agri)
  2. 2.3.2Learn about MCX and commodity exchanges
  3. 2.3.3Understand spot vs futures pricing in commodities
  4. 2.3.4Learn forex basics - currency pairs and quotes
  5. 2.3.5Understand base vs quote currency and pips
  6. 2.3.6Learn about major, minor, and exotic pairs
  7. 2.3.7Understand USD - INR and currency derivatives
  8. 2.3.8Learn cryptocurrency fundamentals (blockchain basics)
  9. 2.3.9Understand Bitcoin, Ethereum, and altcoins
  10. 2.3.10Learn about crypto exchanges and wallets
  11. 2.3.11Understand stablecoins and DeFi basics
  12. 2.3.12Learn about crypto volatility and risk
2.4Financial Statements0 / 13
  1. 2.4.1Read and interpret the income statement
  2. 2.4.2Understand revenue, COGS, gross profit
  3. 2.4.3Learn operating income vs net income
  4. 2.4.4Read the balance sheet structure
  5. 2.4.5Understand assets, liabilities, and equity
  6. 2.4.6Learn about current vs non-current items
  7. 2.4.7Read the cash flow statement (3 sections)
  8. 2.4.8Understand operating, investing, financing flows
  9. 2.4.9Learn the difference between profit and cash
  10. 2.4.10Understand working capital and its cycle
  11. 2.4.11Learn about depreciation and amortization
  12. 2.4.12Understand notes to accounts and footnotes
  13. 2.4.13Learn to spot accounting red flags
2.5Financial Ratios0 / 12
  1. 2.5.1Calculate and interpret EPS
  2. 2.5.2Understand P - E ratio and its uses - limits
  3. 2.5.3Learn P - B, P - S, and EV - EBITDA
  4. 2.5.4Understand ROE, ROA, and ROCE
  5. 2.5.5Learn about net, operating, and gross margins
  6. 2.5.6Understand current ratio and quick ratio
  7. 2.5.7Learn debt-to-equity and interest coverage
  8. 2.5.8Understand inventory and receivables turnover
  9. 2.5.9Learn about dividend payout and yield
  10. 2.5.10Understand PEG ratio
  11. 2.5.11Learn DuPont analysis decomposition
  12. 2.5.12Understand free cash flow and FCF yield
2.6Valuation Methods0 / 10
  1. 2.6.1Understand intrinsic value vs market price
  2. 2.6.2Learn discounted cash flow (DCF) modeling
  3. 2.6.3Understand WACC and discount rate calculation
  4. 2.6.4Learn about terminal value and growth assumptions
  5. 2.6.5Understand relative - comparable valuation
  6. 2.6.6Learn dividend discount model (DDM)
  7. 2.6.7Understand sum-of-the-parts valuation
  8. 2.6.8Learn sensitivity and scenario analysis
  9. 2.6.9Understand margin of safety concept
  10. 2.6.10Learn about reverse DCF
2.7Economic Moats & Macro0 / 11
  1. 2.7.1Understand competitive advantage - economic moats
  2. 2.7.2Learn moat types (network, cost, brand, switching)
  3. 2.7.3Understand management quality assessment
  4. 2.7.4Learn industry and sector analysis
  5. 2.7.5Understand Porter's Five Forces
  6. 2.7.6Learn about GDP, inflation, and CPI - WPI
  7. 2.7.7Understand interest rates and central bank policy
  8. 2.7.8Learn RBI monetary policy and repo rate
  9. 2.7.9Understand how rates affect equities and bonds
  10. 2.7.10Learn about currency, trade, and fiscal deficit
  11. 2.7.11Understand business cycles and sector rotation
3.1Charts, Trends & Dow Theory0 / 10
  1. 3.1.1Understand line, bar, and candlestick charts
  2. 3.1.2Learn how to read OHLC data
  3. 3.1.3Understand timeframes and multi-timeframe analysis
  4. 3.1.4Learn Dow Theory tenets
  5. 3.1.5Understand primary, secondary, and minor trends
  6. 3.1.6Learn to identify uptrends, downtrends, ranges
  7. 3.1.7Understand higher highs - higher lows logic
  8. 3.1.8Learn trendlines and channels
  9. 3.1.9Understand the role of volume confirmation
  10. 3.1.10Learn about log vs linear price scales
3.2Candlestick Patterns0 / 13
  1. 3.2.1Understand candlestick anatomy (body, wicks)
  2. 3.2.2Learn doji and its variants
  3. 3.2.3Understand hammer and hanging man
  4. 3.2.4Learn inverted hammer and shooting star
  5. 3.2.5Understand bullish and bearish engulfing
  6. 3.2.6Learn piercing line and dark cloud cover
  7. 3.2.7Understand morning star and evening star
  8. 3.2.8Learn three white soldiers - three black crows
  9. 3.2.9Understand harami and harami cross
  10. 3.2.10Learn spinning tops and marubozu
  11. 3.2.11Understand tweezer tops and bottoms
  12. 3.2.12Learn rising and falling three methods
  13. 3.2.13Practice combining patterns with context
3.3Support, Resistance & Price Action0 / 10
  1. 3.3.1Understand support and resistance concepts
  2. 3.3.2Learn to draw horizontal S - R levels
  3. 3.3.3Understand role reversal of S - R
  4. 3.3.4Learn about supply and demand zones
  5. 3.3.5Understand swing highs and swing lows
  6. 3.3.6Learn about breakouts and false breakouts
  7. 3.3.7Understand retests and confirmation
  8. 3.3.8Learn about psychological round numbers
  9. 3.3.9Understand pivot points and calculation
  10. 3.3.10Learn about price action without indicators
3.4Indicators & Oscillators0 / 14
  1. 3.4.1Understand simple vs exponential moving averages
  2. 3.4.2Learn MA crossover signals (golden - death cross)
  3. 3.4.3Understand RSI and overbought - oversold
  4. 3.4.4Learn RSI divergence
  5. 3.4.5Understand MACD line, signal, histogram
  6. 3.4.6Learn MACD crossovers and divergence
  7. 3.4.7Understand Bollinger Bands and squeezes
  8. 3.4.8Learn the stochastic oscillator
  9. 3.4.9Understand ADX and trend strength
  10. 3.4.10Learn about VWAP and its uses
  11. 3.4.11Understand ATR for volatility measurement
  12. 3.4.12Learn about OBV and volume indicators
  13. 3.4.13Understand Ichimoku cloud basics
  14. 3.4.14Learn to avoid indicator overload
3.5Chart Patterns0 / 11
  1. 3.5.1Understand head and shoulders (and inverse)
  2. 3.5.2Learn double top and double bottom
  3. 3.5.3Understand triple top and triple bottom
  4. 3.5.4Learn ascending, descending, symmetrical triangles
  5. 3.5.5Understand flags and pennants
  6. 3.5.6Learn rectangles and ranges
  7. 3.5.7Understand cup and handle
  8. 3.5.8Learn rising and falling wedges
  9. 3.5.9Understand rounding tops and bottoms
  10. 3.5.10Learn measured move targets from patterns
  11. 3.5.11Understand continuation vs reversal patterns
3.6Volume, Fibonacci & Elliott Wave0 / 11
  1. 3.6.1Understand volume analysis fundamentals
  2. 3.6.2Learn volume spread analysis basics
  3. 3.6.3Understand accumulation and distribution
  4. 3.6.4Learn Fibonacci retracement levels
  5. 3.6.5Understand Fibonacci extensions and targets
  6. 3.6.6Learn to combine Fib with S - R
  7. 3.6.7Understand Elliott Wave theory basics
  8. 3.6.8Learn impulse and corrective wave structure
  9. 3.6.9Understand the 5-3 wave count
  10. 3.6.10Learn wave rules and guidelines
  11. 3.6.11Understand limitations of Elliott Wave
4.1Trading vs Investing & Styles0 / 10
  1. 4.1.1Differentiate trading from investing mindset
  2. 4.1.2Understand scalping characteristics and demands
  3. 4.1.3Learn intraday - day trading approach
  4. 4.1.4Understand swing trading timeframe
  5. 4.1.5Learn positional - trend trading
  6. 4.1.6Understand momentum trading
  7. 4.1.7Learn mean-reversion trading
  8. 4.1.8Understand which style fits your personality
  9. 4.1.9Learn capital and time requirements per style
  10. 4.1.10Understand realistic return expectations
4.2What to Trade0 / 10
  1. 4.2.1Choose between stocks, indices, and derivatives
  2. 4.2.2Understand trading liquid vs illiquid stocks
  3. 4.2.3Learn index trading (Nifty, Bank Nifty)
  4. 4.2.4Understand F&O instruments for trading
  5. 4.2.5Learn commodity trading basics
  6. 4.2.6Understand currency pair trading
  7. 4.2.7Learn how to build a watchlist
  8. 4.2.8Understand stock screening for trades
  9. 4.2.9Learn about sector leaders and relative strength
  10. 4.2.10Understand correlation between instruments
4.3How to Trade — Execution & Platforms0 / 11
  1. 4.3.1Master order execution mechanics
  2. 4.3.2Learn to use trading platforms efficiently
  3. 4.3.3Understand hotkeys and fast order entry
  4. 4.3.4Learn charting platform setup
  5. 4.3.5Understand position sizing formulas
  6. 4.3.6Learn leverage and margin mechanics
  7. 4.3.7Understand margin calls and square-off
  8. 4.3.8Learn about intraday leverage rules (SEBI peak margin)
  9. 4.3.9Understand spread and execution cost impact
  10. 4.3.10Learn to manage multiple positions
  11. 4.3.11Understand using alerts and notifications
4.4When to Trade — Timing & Sessions0 / 12
  1. 4.4.1Understand market session phases
  2. 4.4.2Learn pre-market session behavior
  3. 4.4.3Understand the opening range and first 15-30 min
  4. 4.4.4Learn about midday lull and low liquidity
  5. 4.4.5Understand power hour - closing session
  6. 4.4.6Learn to read the economic calendar
  7. 4.4.7Understand news events and their impact
  8. 4.4.8Learn about earnings season trading
  9. 4.4.9Understand volatility windows (events, expiry)
  10. 4.4.10Learn weekly - monthly options expiry effects
  11. 4.4.11Understand times and days to avoid
  12. 4.4.12Learn about overnight and gap risk
4.5Entry, Exit & Trade Management0 / 12
  1. 4.5.1Define a trading setup with clear rules
  2. 4.5.2Learn entry signals and confirmation
  3. 4.5.3Understand stop-loss placement methods
  4. 4.5.4Learn fixed, ATR-based, and structure stops
  5. 4.5.5Understand target setting and profit booking
  6. 4.5.6Learn trailing stop techniques
  7. 4.5.7Understand risk-reward ratio (minimum 1 - 2)
  8. 4.5.8Learn R-multiples and expectancy
  9. 4.5.9Understand scaling in and scaling out
  10. 4.5.10Learn to manage a winning trade
  11. 4.5.11Understand cutting losers quickly
  12. 4.5.12Learn break-even stop management
4.6Trading Strategies0 / 14
  1. 4.6.1Master breakout trading strategy
  2. 4.6.2Learn pullback - retracement entries
  3. 4.6.3Understand trend-following systems
  4. 4.6.4Learn reversal trading setups
  5. 4.6.5Understand gap trading (gap up - down - fill)
  6. 4.6.6Learn range trading techniques
  7. 4.6.7Master Opening Range Breakout (ORB)
  8. 4.6.8Learn moving-average crossover systems
  9. 4.6.9Understand RSI-based trading systems
  10. 4.6.10Learn MACD-based systems
  11. 4.6.11Master pure price action trading
  12. 4.6.12Understand supply-demand zone trading
  13. 4.6.13Learn scalping setups and execution
  14. 4.6.14Understand VWAP-based intraday strategies
4.7Risk & Money Management0 / 10
  1. 4.7.1Define risk per trade (1-2% rule)
  2. 4.7.2Calculate position size from stop distance
  3. 4.7.3Understand maximum drawdown limits
  4. 4.7.4Learn daily loss limits and circuit breakers
  5. 4.7.5Understand the Kelly Criterion
  6. 4.7.6Learn total portfolio exposure limits
  7. 4.7.7Understand correlation risk across positions
  8. 4.7.8Learn hedging basics for protection
  9. 4.7.9Understand risk of ruin concept
  10. 4.7.10Learn to size up and down with performance
4.8Trading Psychology0 / 12
  1. 4.8.1Understand discipline and consistency
  2. 4.8.2Learn to manage fear and greed
  3. 4.8.3Understand and avoid FOMO
  4. 4.8.4Learn to prevent revenge trading
  5. 4.8.5Understand tilt and emotional control
  6. 4.8.6Build a written trading plan
  7. 4.8.7Learn to keep a detailed trade journal
  8. 4.8.8Understand backtesting strategies properly
  9. 4.8.9Learn to use paper - demo trading
  10. 4.8.10Understand process over outcome focus
  11. 4.8.11Learn to handle losing streaks
  12. 4.8.12Develop pre-market routine and review habits
5.1Futures0 / 10
  1. 5.1.1Understand futures contract fundamentals
  2. 5.1.2Learn contract specs, lot size, expiry
  3. 5.1.3Understand margin (SPAN + exposure)
  4. 5.1.4Learn mark-to-market settlement
  5. 5.1.5Understand contango and backwardation
  6. 5.1.6Learn about basis and cost of carry
  7. 5.1.7Understand rollover and rollover cost
  8. 5.1.8Learn hedging with futures
  9. 5.1.9Understand speculation with futures
  10. 5.1.10Learn index vs stock futures
5.2Options Basics0 / 10
  1. 5.2.1Understand calls and puts
  2. 5.2.2Learn strike price, premium, expiry
  3. 5.2.3Understand ITM, ATM, OTM
  4. 5.2.4Learn intrinsic vs time value
  5. 5.2.5Understand option buyer vs seller payoffs
  6. 5.2.6Learn about option chain reading
  7. 5.2.7Understand open interest and PCR
  8. 5.2.8Learn assignment and exercise
  9. 5.2.9Understand European vs American style
  10. 5.2.10Learn moneyness and breakeven points
5.3The Greeks0 / 10
  1. 5.3.1Understand Delta and directional exposure
  2. 5.3.2Learn Gamma and delta sensitivity
  3. 5.3.3Understand Theta and time decay
  4. 5.3.4Learn Vega and volatility sensitivity
  5. 5.3.5Understand Rho and interest rate impact
  6. 5.3.6Learn implied vs historical volatility
  7. 5.3.7Understand volatility skew and smile
  8. 5.3.8Learn the IV crush around events
  9. 5.3.9Understand Black-Scholes intuition
  10. 5.3.10Learn to manage a position's Greeks
5.4Options Strategies0 / 13
  1. 5.4.1Master covered call
  2. 5.4.2Learn protective put
  3. 5.4.3Understand bull call spread
  4. 5.4.4Learn bear put spread
  5. 5.4.5Understand bull put and bear call spreads
  6. 5.4.6Learn long straddle and strangle
  7. 5.4.7Understand short straddle and strangle
  8. 5.4.8Learn iron condor
  9. 5.4.9Understand iron butterfly
  10. 5.4.10Learn calendar and diagonal spreads
  11. 5.4.11Understand ratio spreads
  12. 5.4.12Learn collar strategy
  13. 5.4.13Understand strategy selection by view & IV
5.5Portfolio Theory0 / 10
  1. 5.5.1Understand diversification benefits
  2. 5.5.2Learn correlation and covariance
  3. 5.5.3Understand Markowitz mean-variance optimization
  4. 5.5.4Learn about the efficient frontier
  5. 5.5.5Understand CAPM and beta
  6. 5.5.6Learn the security market line
  7. 5.5.7Understand systematic vs unsystematic risk
  8. 5.5.8Learn the Sharpe ratio
  9. 5.5.9Understand Sortino and Treynor ratios
  10. 5.5.10Learn alpha and benchmark comparison
5.6Asset Allocation & Rebalancing0 / 10
  1. 5.6.1Understand strategic asset allocation
  2. 5.6.2Learn tactical asset allocation
  3. 5.6.3Understand age - risk-based allocation models
  4. 5.6.4Learn about rebalancing strategies
  5. 5.6.5Understand calendar vs threshold rebalancing
  6. 5.6.6Learn about core-satellite portfolios
  7. 5.6.7Understand goal-based investing
  8. 5.6.8Learn dollar - rupee cost averaging
  9. 5.6.9Understand tax-efficient allocation
  10. 5.6.10Learn portfolio drift and management
6.1Algorithmic & Quant Trading0 / 11
  1. 6.1.1Understand algorithmic trading fundamentals
  2. 6.1.2Learn the components of a trading system
  3. 6.1.3Understand strategy idea generation
  4. 6.1.4Learn about signal generation and rules
  5. 6.1.5Understand statistical arbitrage basics
  6. 6.1.6Learn pairs trading and cointegration
  7. 6.1.7Understand mean-reversion quant models
  8. 6.1.8Learn momentum quant strategies
  9. 6.1.9Understand machine learning in trading (caution)
  10. 6.1.10Learn about overfitting and curve fitting
  11. 6.1.11Understand walk-forward analysis
6.2Backtesting Frameworks0 / 11
  1. 6.2.1Understand backtesting methodology
  2. 6.2.2Learn about clean historical data sourcing
  3. 6.2.3Understand survivorship bias
  4. 6.2.4Learn look-ahead bias avoidance
  5. 6.2.5Understand transaction cost modeling
  6. 6.2.6Learn about slippage assumptions
  7. 6.2.7Understand in-sample vs out-of-sample testing
  8. 6.2.8Learn Python tools (pandas, backtrader, zipline)
  9. 6.2.9Understand performance metrics (CAGR, max DD)
  10. 6.2.10Learn Monte Carlo simulation of returns
  11. 6.2.11Understand paper trading before going live
6.3Market Microstructure0 / 10
  1. 6.3.1Understand order book dynamics
  2. 6.3.2Learn about limit order book depth
  3. 6.3.3Understand price impact and market depth
  4. 6.3.4Learn about adverse selection
  5. 6.3.5Understand bid-ask spread components
  6. 6.3.6Learn about tick size and lot size effects
  7. 6.3.7Understand auction mechanisms
  8. 6.3.8Learn about latency and co-location
  9. 6.3.9Understand dark pools and hidden liquidity
  10. 6.3.10Learn about iceberg orders
6.4Order Flow & Tape Reading0 / 10
  1. 6.4.1Understand Level-2 - market depth data
  2. 6.4.2Learn to read the order book
  3. 6.4.3Understand time and sales (tape reading)
  4. 6.4.4Learn about footprint and volume profile charts
  5. 6.4.5Understand absorption and exhaustion
  6. 6.4.6Learn about delta and cumulative delta
  7. 6.4.7Understand spoofing and layering (illegal patterns)
  8. 6.4.8Learn to identify large institutional orders
  9. 6.4.9Understand POC (point of control)
  10. 6.4.10Learn value area high - low concepts
6.5HFT & Advanced Concepts0 / 8
  1. 6.5.1Understand high-frequency trading basics
  2. 6.5.2Learn about market making at scale
  3. 6.5.3Understand latency arbitrage
  4. 6.5.4Learn about colocation and direct market access
  5. 6.5.5Understand smart order routing
  6. 6.5.6Learn about regulatory views on HFT
  7. 6.5.7Understand flash crashes and circuit breakers
  8. 6.5.8Learn about execution algorithms (TWAP, VWAP, POV)
6.6Factor & Behavioral Finance0 / 10
  1. 6.6.1Understand factor investing fundamentals
  2. 6.6.2Learn value, momentum, quality factors
  3. 6.6.3Understand size and low-volatility factors
  4. 6.6.4Learn Fama-French three - five factor models
  5. 6.6.5Understand smart beta strategies
  6. 6.6.6Learn about behavioral finance biases
  7. 6.6.7Understand anchoring and confirmation bias
  8. 6.6.8Learn loss aversion and disposition effect
  9. 6.6.9Understand herding and recency bias
  10. 6.6.10Learn about market efficiency (EMH) debate
6.7Indian Market Specifics0 / 14
  1. 6.7.1Understand NSE and BSE market structure
  2. 6.7.2Learn SEBI regulations and investor protection
  3. 6.7.3Understand F&O lot sizes and contract specs
  4. 6.7.4Learn intraday and peak margin rules
  5. 6.7.5Understand STT (Securities Transaction Tax)
  6. 6.7.6Learn about stamp duty, GST, exchange charges
  7. 6.7.7Understand short-term vs long-term capital gains tax
  8. 6.7.8Learn taxation of intraday and F&O (business income)
  9. 6.7.9Understand turnover calculation and tax audit
  10. 6.7.10Learn about LTCG exemption and grandfathering
  11. 6.7.11Understand dividend taxation rules
  12. 6.7.12Learn about ASM - GSM surveillance lists
  13. 6.7.13Understand circuit filters and ban periods in F&O
  14. 6.7.14Learn about weekly expiry products in India