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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.
More resources on Proof Techniques
How to Solve It: A New Aspect of Mathematical Method
George Pólya's classic guide to mathematical problem solving, built around a four-step method of understanding, planning, carrying out and looking back, plus a dictionary of heuristics such as working backwards, auxiliary problems and generalization. Readers learn to attack unfamiliar problems and proofs systematically.
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.
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.
How to Read and Do Proofs - Daniel Solow
Introduces the "Forward-Backward" method to help students understand the structure and logic of mathematical proofs.
How to Prove It: A Structured Approach
Velleman builds proof-writing from propositional and predicate logic upward, then works through set theory, relations, functions, and induction. Exercises demand full written proofs. Standard bridge text for students moving from calculus to abstract mathematics.
Mathematical Proofs: A Transition to Advanced Mathematics
Mathematical Proofs: A Transition to Advanced Mathematics - A book resource