The Essence of Mathematics. Through Elementary Problems

Broad lecture notes spanning linear algebra, differential equations, and calculus. A compact reference for undergraduates who want core topics gathered in one place.

Peeyush Chandra, A. K. Lal, V. Raghavendra

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

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