Book of Proof

About the book

Book of Proof is a textbook by Richard Hammack for students making the shift from calculation to proof-based mathematics. It treats propositional and predicate logic, set theory, relations, functions, and induction as tools a reader will use, not as separate topics to file away.

The premise is that proof writing is a craft with learnable conventions. Definitions and logical structure come first, then those pieces assemble into direct proofs, contrapositive arguments, contradiction, and induction. Sets and functions get extended treatment because they supply the vocabulary for most of what follows in abstract mathematics.

Hammack writes for self-study as well as coursework, with explanation followed by exercises. The emphasis falls on why a step is valid, not on memorizing templates for common proof types.

How to read it

Read with a pencil and try the exercises before looking at solutions. The material is cumulative. A shaky grasp of quantifiers or set notation will surface later as confusion about functions and induction. When a proof is presented, reconstruct its logical skeleton and identify which definition each step invokes.

The prose is plain and the pace moderate, though density rises once relations and functions arrive. Expect to reread. Work the early logic and set exercises carefully even when they seem elementary, since they establish the notation and habits the rest of the book assumes.

Who it suits

This suits undergraduates entering abstract mathematics, computer science students meeting formal logic, and independent learners who want to read proof-based texts without feeling locked out. Readers comfortable with high school algebra and willing to do written exercises will gain the most. It also helps instructors seeking a lean treatment of foundations.

Reading considerations

The book covers foundational material rather than analysis, algebra, or topology, so it prepares a reader for those subjects without teaching them. Exercise solutions and availability vary by edition and printing; check which version you hold before relying on a solutions section. Readers wanting extensive worked examples may find the exercise load demanding.