MathBuff: learn math from fractions to graduate level

One skill tree of 696 interactive math topics across 34 subjects. Every topic has a plain-language lesson, a guided walkthrough you answer step by step, and practice; the big theorems come with interactive proofs. Lessons, proofs and a daily workout are free.

Take the ten-question placement test · Browse all 696 topics · Follow a guided path

Subjects

• Basic Algebra — Elementary algebra from the ground up — variables, equations, lines, polynomials, factoring, fractions, and radicals, building to the Fundamental Theorem of…
• Basic Geometry — Standard school geometry: points and angles, triangles and the Pythagorean theorem, polygons and area, similarity, circles, solids, and transformations.
• Geometry — Advanced and olympiad geometry: triangle centers and the classical theorems, power of a point, cyclic quadrilaterals, inversion, and non-Euclidean geometry.
• Precalculus — Functions, logs, trig, sequences, and limits — the toolkit you need before calculus makes sense.
• Discrete Math — The language of proof, counting without listing, number theory classics, and the vocabulary of graphs.
• Graph Theory — Vertices and edges: connectivity, traversals, planarity, directed graphs and shortest paths, and the tree data structures built on them.
• Number Theory — The integers up close: divisibility and primes, gcd via the Euclidean algorithm, modular arithmetic and congruences, and the classical proofs.
• Calculus — Single-variable calculus: derivatives, integrals, the classic theorems, and their applications.
• Real Analysis — Calculus made rigorous: the completeness of ℝ and the supremum, the ε–N limit, sequences and series, compactness, and the Riemann integral.
• Multivariate Real Analysis — Rigorous analysis in ℝ^n: the total derivative as a linear map, the inverse and implicit function theorems, rigorous multivariable integration, and…
• Linear Algebra — Vectors, matrices, determinants, eigenvalues, and the structural identities of linear maps.
• Probability — From basic event probabilities through expectation and variance to concentration inequalities.
• Combinatorics — Counting identities plus the probabilistic and extremal methods built on them.
• Multivariable Calculus — Partial derivatives, gradients, multiple integrals, and the three great theorems of vector calculus.
• Abstract Algebra — Groups, rings, and fields — a Dummit & Foote arc from the group axioms to Galois theory.
• Combinatorial Optimization — Linear programming, duality, and submodular optimization over discrete structures.
• Inequalities — Classical and analytic inequalities at the heart of competition math and analysis.
• Logic — Self-reference, diagonalization, and the limits of formal systems.
• AI & ML — Regression, gradient descent, classification, and neural networks — the mathematical core of machine learning.
• Information Theory — Entropy, mutual information, KL divergence, and the limits of communication.
• Coding Theory — Bits, parity, and error-correcting codes from repetition to Hamming.
• Game Theory & Social Choice — Strategic play, voting, and the paradoxes of collective choice.
• Competition Math — The contest toolbox: Vieta's formulas, telescoping, invariants, the extremal principle, coloring arguments, and functional equations.
• Topology — Standard topology topics from the canonical curriculum.
• Complex Analysis — Standard complex analysis topics from the canonical curriculum.
• Algorithms — Standard algorithms topics from the canonical curriculum.
• Differential Geometry — Standard differential geometry topics from the canonical curriculum.
• Theory of Computation — Standard theory of computation topics from the canonical curriculum.
• Computational Complexity — Standard computational complexity topics from the canonical curriculum.
• Stochastic Processes — Randomness evolving in time — random walks and Markov-chain behavior through Poisson processes, martingales, Brownian motion, and Itô calculus.
• Mathematics of Finance — The mathematics of money and markets — interest and time value, bond valuation, portfolio risk, CAPM, utility, and growth-optimal betting.
• Convex Optimization — Why convex problems are the ones we can actually solve — recognizing convexity, the standard problem families, Lagrange duality and KKT, and the algorithms…
• Algebraic Topology — Turning shape into algebra — cell complexes, the fundamental group by pieces, homology and cohomology, and the classical fixed-point theorems they prove.
• Category Theory — The mathematics of structure itself — objects and arrows, functors and naturality, universal properties and limits, the Yoneda lemma, and adjunctions.

Guided paths

• Algebra Foundations
• Functions to Limits
• Pythagorean Theorem
• Basic Algebra I
• Geometry Essentials
• Calculus Essentials
• Linear Algebra Essentials
• Probability Essentials
• Quant Interview Prep
• Discrete Math Essentials
• The Fundamental Theorem of Calculus
• Bayes' Theorem
• Rank-Nullity Theorem
• Ramsey's Theorem
• Fermat's Little Theorem
• Planar Graphs
• Green's Theorem
• Jensen's Inequality
• Heine-Borel Theorem
• Galois Theory
• Channel Capacity Theorem
• Ptolemy's Theorem
• The Central Limit Theorem
• Max-Flow Min-Cut
• Naive Bayes Classifier
• The Residue Theorem
• The Halting Problem
• The Fundamental Group
• The Chicken McNugget Theorem
• Hamming Codes
• Infinity & the Continuum
• Symmetry & Counting
• Gödel's Incompleteness
• The Hairy Ball Theorem