mathbase
Learn · Structured proof curriculum

Work through a proof-first math track

Start with the core proof modules — what proofs are, logic, direct proof, contradiction, induction, and sets/functions — then branch into number theory, combinatorics, and graph theory. Every module is built to feed directly into contest math, olympiad-style problems, and proof-based courses.

Best for students aiming at AMC/AIME, olympiads, and proof courses
Each module has reading, practice, TL;DR, and proof-writing prompts

Core proof track

Go through these in order. They build the mental toolkit you’ll reuse in every branch of math.

Module 1Start here

What is a Proof?

What proofs are really doing, and how mathematicians think with them.

6 lessonsOpen module →
Module 2

Logic & Quantifiers

Propositions, implications, truth tables, and quantifiers.

6 lessonsOpen module →
Module 3

Direct Proofs

Turn definitions into step-by-step arguments using direct proof.

6 lessonsOpen module →
Module 4

Counterexamples

Disprove false claims and build minimal counterexamples.

6 lessonsOpen module →
Module 5

Proof by Contradiction & Contrapositive

Explore concepts and proof techniques in this topic.

6 lessonsOpen module →
Module 6

Mathematical Induction

Learn induction as a logical structure, not just a magic trick.

6 lessonsOpen module →
Module 7

Sets & Functions (Proof-Oriented)

Explore concepts and proof techniques in this topic.

6 lessonsOpen module →