Mathematical proofs

Readers who want to move from following mathematical arguments to constructing them will find this text useful. It shows how to read and assess existing proofs, and how to write new ones that are both correct and clearly expressed.

The core material covers relations, functions, and the comparison of set sizes through cardinality. Optional sections extend into number theory, combinatorics, and calculus for those who want to explore further.

Exercises guide learners from analyzing proofs toward producing well-built proofs on their own. Because of this, the book also works as a reference for later courses that involve reading or writing proofs. This is the fourth edition.