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math

algebra — Exponents & logs, sequences & series, counting & binomial, polynomials, partial fractions, proof, linear systems.

complex numbers — Cartesian, polar & Euler forms, De Moivre, nth roots, polynomials & the complex exponential.

functions — Notation & inverses, lines, transformations, quadratics, rational functions & asymptotes, graph features.

geometry — Coordinate geometry, areas & volumes of standard figures and solids.

trigonometry — Unit circle, exact values, identities, compound & double angles, trig equations, triangle rules.

vectors — Dot & cross products, lines and planes in 3D, angles, intersections, distances.

linear algebra — Spans & independence, linear systems & row reduction, matrices & linear maps, determinants, eigenvalues & diagonalization.

probability — Probability laws, conditional & Bayes, discrete & continuous random variables, binomial & normal.

statistics — Descriptive statistics, variance, correlation & regression.

calculus — Limits, differentiation, integration, kinematics, sequences & series, Taylor series.

multivariable calculus — Partial derivatives & chain rule, gradient, optimization & Lagrange multipliers, multiple integrals, line & surface integrals, Green, Stokes & divergence theorems.

differential equations — First & second order ODEs, linear systems, resonance, Fourier series, PDEs & Fourier transforms, Laplace transforms.

analysis — Sets, functions & cardinality, proof technique, axioms of the numbers, construction of the reals, sequences & convergence, open & closed sets.

functional analysis — L² & Hilbert spaces, distributions, orthonormal bases & completeness, hermitian & unitary operators, spectral theory, boundary value problems, Bessel & Legendre functions.