Math
From foundational arithmetic to the abstract structures that underlie modern science. Each chapter is a self-contained area of mathematics; each topic inside is a single focused lesson.
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Arithmetic
Counting, place value, the four operations, integers, fractions, decimals, percentages — and a financial-literacy capstone applying it all to real money decisions.
Pre-Algebra
Order of operations, ratios and proportions, exponents and roots, and the move from numbers to symbols.
Logic & Set Theory
The grammar of mathematics. Propositions, proof techniques, sets, and the set-theoretic view of relations and functions.
Algebra
The language of equations: variables, lines, systems, polynomials, and the patterns that show up everywhere downstream.
Geometry
Shapes, proofs, and the spatial reasoning that turns informal intuition into rigorous argument.
Trigonometry
Angles, triangles, the unit circle, and the bridge into periodic functions and Fourier ideas.
Number Systems
The extension chain from ℕ to ℂ, each step forced by an equation the previous system couldn't solve — plus a sideways step into modular arithmetic and its finite cyclic ring structure.
Number Theory
The integers up close. Divisibility, primes, Diophantine equations, quadratic reciprocity, and a peek at the Riemann Hypothesis.
Precalculus
The bridge from algebra to calculus. Function transformations, composition, inverses, polynomial and rational behavior, and a first encounter with limits.
Linear Algebra
Vectors, matrices, transformations, vector spaces, inner products, and the four big matrix decompositions (LU, QR, eigen, SVD).
Calculus
Single-variable through multivariable. Limits, derivatives, integrals, series, partials, and vector calculus — the full classical sequence.
Differential Equations
Calculus as the language of dynamics. ODEs (separable, linear, second-order), the Laplace transform, and an introduction to PDEs.
Statistics & Probability
Combinatorics, random variables, distributions, inference, regression, and a closing Bayesian arc.
Discrete Math & Combinatorics
Generating functions and the foundations of graph theory — paths, cycles, coloring, and the standard algorithms (BFS, DFS, Dijkstra, MST).