Book of Proof
by Richard Hammack
Essential introduction to mathematical proof techniques covering logic, sets, relations, functions, and various proof methods for pure mathematics.
More resources on Logic
Gödel, Escher, Bach: An Eternal Golden Braid
Pulitzer Prize-winning exploration of consciousness, artificial intelligence, and meaning through connections between mathematics, art, music, and formal systems.
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
proofwiki.org
ProofWiki is a free, collaboratively edited online collection of mathematical proofs, theorems, and definitions organized by technique. It provides step-by-step proofs and explanations of proof strategies (such as induction, contradiction, and contrapositive) across a wide range of mathematical topics.
plato.stanford.edu
The Stanford Encyclopedia of Philosophy is a peer‑reviewed online encyclopedia of philosophy featuring in‑depth, scholarly articles written and regularly updated by experts, including comprehensive coverage of logic topics.
Logic II (MIT 24.242)
Computability theory followed by a detailed study of Gödel's incompleteness theorems and their applications, including Church's undecidability theorem and Tarski's theorem on the undefinability of truth. Lecture notes and problem sets with solutions let learners work through these proofs themselves.
Mathematics for Computer Science (MIT 6.042J)
Discrete mathematics for computer science with an emphasis on definitions and proofs: logic, induction, sets and relations, graph theory, modular arithmetic, asymptotics, counting and discrete probability. 25 lecture videos, problem sets and exams with solutions build fluency in writing proofs.