Notes on Mathematics

A transition-to-proof textbook built around logic, sets, proofs, functions, and relations. Designed to bridge calculus and upper-level abstract mathematics.

Patrick Keef, David Guichard

A problem-driven tour of mathematical thinking, using carefully chosen elementary problems to reveal the depth behind familiar topics. Rewards curiosity over rote technique.

Alexandre Borovik, Tony Gardiner

An accessible introduction to the language of proof and abstract mathematics, covering logic, sets, functions, and relations. A solid foundation for proof-based courses.

Dave Witte Morris, Joy Morris

A wide-ranging introduction to contemporary mathematics for general readers, exploring patterns, infinity, and reasoning. Emphasizes ideas and beauty over heavy machinery.

John Hutchinson

A practical mathematics course built in modules, from order of operations and fractions to measurement, geometry, and formulas. Aimed at applied and technical learners.

Morgan Chase