Algebra Foundations — A compact algebra route from expressions and polynomials to complex roots and the theorem that every nonconstant polynomial has one.
Functions to Limits — The shortest useful bridge into calculus: functions, transformations, logs, trig, sequences, and the limit idea.
Pythagorean Theorem — A focused geometry climb: points, angles, triangles, area, and the right-triangle theorem that powers the rest.
Basic Algebra I — Build a solid Algebra I foundation, from expressions and equations through functions, coordinate problems, and inequalities.
Geometry Essentials — The core synthetic-geometry toolkit: points, angles, proof, triangles, Pythagoras, congruence, similarity, area, and circle facts.
Calculus Essentials — A fast single-variable calculus tour: limits, derivative rules, optimization, integrals, the FTC, and Taylor series.
Linear Algebra Essentials — The core language of vectors and matrices: row reduction, span, independence, rank, null spaces, determinants, linear maps, and eigenvalues.
Probability Essentials — A compact probability tour: sample spaces, conditioning, Bayes, random variables, expectation, variance, common distributions, and limit laws.
Quant Interview Prep — The probability that quant and trading interviews actually test: expectation tricks, conditioning, random walks and gambler's ruin, martingales and optional stopping, and growth-optimal betting.
Discrete Math Essentials — A high-speed tour of proof, sets, counting, induction, relations, and the graph language that underlies discrete math and CS.
Bayes' Theorem — Sample spaces and conditional probability, built just far enough to make Bayes and Monty Hall feel inevitable.
Rank-Nullity Theorem — Matrices, spans, independence, null spaces, and rank, arranged to land on the central dimension-counting theorem.
Ramsey's Theorem — A short combinatorial path from forced collisions to the theorem that large enough structures contain order.
Fermat's Little Theorem — Divisibility, the Euclidean algorithm, and modular arithmetic, aimed at Fermat's classic prime-modulus theorem.
Planar Graphs — Vertices, paths, trees, and Euler-style structure, focused on understanding when a graph can live in the plane.
Green's Theorem — The shortest useful vector-calculus path to turning a line integral around a curve into an area integral inside.
Jensen's Inequality — A focused inequality path: triangle inequality, AM-GM, Cauchy-Schwarz, convexity, and Jensen.
Heine-Borel Theorem — Completeness, convergence, closed sets, and subsequences, arranged to reach compactness on the real line.
Galois Theory — Groups, quotients, field extensions, and splitting fields, trimmed to the ideas that make Galois theory possible.
Channel Capacity Theorem — Entropy, mutual information, and noisy channels, focused on the theorem that defines reliable communication limits.
Ptolemy's Theorem — The circle-geometry ingredients needed for cyclic quadrilaterals and Ptolemy's elegant length relation.
The Central Limit Theorem — Random variables, expectation, variance, common distributions, and limit laws, aimed at the normal approximation miracle.
Max-Flow Min-Cut — The graph and algorithm ideas needed to understand the theorem equating maximum flow with minimum cut.
Naive Bayes Classifier — A probability-first machine-learning path to a small, useful classifier.
The Residue Theorem — Complex differentiability, contour integrals, Cauchy's theorems, Laurent series, and poles, all for residue computation.
The Halting Problem — Automata as a warm-up, then Turing machines and the first great impossibility theorem of computation.
The Fundamental Group — Open sets, continuity, homeomorphism, and homotopy, leading to the first algebraic invariant of a space.
The Chicken McNugget Theorem — GCDs and modular arithmetic build to the Frobenius result: for whole-number box sizes a,b > 1 with no common factor greater than 1, the largest number you cannot buy is ab - a - b.
Hamming Codes — A coding-theory path from bits and parity checks to the classic error-correcting Hamming code.
Infinity & the Continuum — How can one infinity be bigger than another? Sets, bijections, and cardinality build to Cantor's diagonal argument and the uncountability of the reals.
Symmetry & Counting — Group actions meet combinatorics: from counting and permutations through cyclic, dihedral, and symmetric groups to Burnside's lemma — count necklaces and colorings up to symmetry.
Gödel's Incompleteness — Climb from logical connectives and first-order logic through Cantor's diagonal and self-reference to the theorem that every rich, consistent system has true statements it cannot prove.
The Hairy Ball Theorem — A short topology path to a famous fact: you can't comb a hairy ball flat. Open sets, continuity, and the Euler characteristic lead to the Hairy Ball Theorem.