Basic English Grammar, Tenses, Articles and Adjectives, Prepositions, Conjunctions, Verb-Subject Agreement, Vocabulary: Idioms and Words in Context, Reading Comprehension, Sequencing of Ideas, Critical Reasoning and Verbal Deduction

Data Interpretation: Tables, Graphs and Charts, Numerical Computation and Estimation, Ratios, Percentages, Powers and Exponents, Logarithms, Permutations and Combinations, Mensuration, Geometry and Elementary Statistics, Probability

Logic: Deduction and Induction, Analogy, Numerical Relations and Reasoning

Transformation of Shapes: Translation, Rotation, Scaling, Mirroring, Assembling and Grouping, Paper Folding, Cutting and Inking, Patterns in 2 and 3 Dimensions

Vector Spaces and Operators, Eigenvalues and Diagonalisation, Tensors

Analytic Functions and Cauchy Theorem, Residue Theorem, Fourier and Laplace Transforms, Green's Functions

Legendre, Hermite, Laguerre and Bessel Functions, Sturm-Liouville Theory

Newton's Equations and Conservation Laws, Damped and Driven Oscillations, Lagrangian Mechanics and Constraints, Hamiltonian Formalism and Canonical Transformations, Hamilton's and Lagrange's Equations, Central Force Motion and Kepler Problem, Special Relativity: Lorentz Transformations, Relativistic Kinematics

Gauss', Ampere's and Faraday's Laws, Solution of Electrostatics Problems: Poisson and Laplace Equations, Maxwell's Equations and Electromagnetic Waves, Wave Propagation in Dispersive Media, Waveguides and Transmission Lines, Radiation from Moving Charges: Larmor Formula

Wave-Particle Duality and Uncertainty Principle, Schrödinger Equation and Solutions: Potential Wells, Harmonic Oscillator, Orbital Angular Momentum and Spherical Harmonics, Hydrogen Atom

Operator Formalism and Dirac Notation, Perturbation Theory: Time-Independent and Time-Dependent, WKB Approximation, Variational Method, Spin, Identical Particles and Pauli Principle, Addition of Angular Momenta

Laws of Thermodynamics and Thermodynamic Potentials, Maxwell Relations and Phase Transitions, Macro and Micro States and Entropy, Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac Distributions, Partition Functions and Applications, Black Body Radiation and Planck Distribution, Ideal Fermi and Bose Gases

Semiconductor Devices: Diodes, Transistors, FETs, Op-Amp Circuits and Active Filters, Oscillators and Feedback, Digital Electronics: Logic Gates, Flip-Flops, Counters, ADC and DAC

Measurement Instruments: CRO, Multimeters, Error Analysis and Curve Fitting, Signal Averaging and Lock-in Detection, Vacuum Techniques and Cryogenics Basics

Fine Structure and Hyperfine Structure, Zeeman and Stark Effects, LS and JJ Coupling, Laser Physics: Population Inversion, Cavity Modes, Raman and Infrared Spectroscopy

Crystal Structures and Bravais Lattices, Reciprocal Lattice and Diffraction: Bragg Law, Lattice Vibrations and Phonons, Free Electron Theory and Band Theory of Solids, Metals, Insulators and Semiconductors, Magnetic Properties: Dia, Para, Ferro and Antiferro, Superconductivity: Type I and II, BCS Basics

Nuclear Radius, Mass and Binding Energy, Nuclear Models: Liquid Drop, Shell Model, Alpha, Beta and Gamma Decay, Nuclear Reactions and Fission/Fusion, Nuclear Detectors and Accelerators

Fundamental Interactions and Elementary Particles, Symmetries and Conservation Laws, Quarks and the Standard Model Basics