James Franklin and Albert Daoud (Quakers Hill Press, 1996/Kew Books, 2011) Proofs Book Picture

This is a small (98 page) textbook designed to teach mathematics and computer science students the basics of how to read and construct proofs.

Why do students take the instruction "prove" in examinations to mean "go to the next question"? Because they have not been shown the simple techniques of how to do it. Mathematicians meanwhile generate a mystique of proof, as if it requires an inborn and unteachable genius. True, creating research-level proofs does require talent; but reading and understanding the proof that the square of an even number is even is within the capacity of most mortals.

Proof in Mathematics: an Introduction takes a straightforward, no nonsense approach to explaining the core technique of mathematics.

"Mathematics teaches you to think" is often an empty marketing slogan. With this book, it can become a reality.

A short video on the basic ideas of the book.


For individual copies, BUY ONLINE (Amazon - including kindle version); BUY ONLINE (UNSW Bookshop)
Multiple copies for classroom use cost $US12 ($A12). Email James Franklin.

Praise for the first edition

(Introduction to Proofs in Mathematics, Prentice Hall, 1988)

"Delightfully written ..."

- Mathematics Teacher (USA) 82 (Dec 1989)

"does not cloud the issue with a sea of philosophical niceties, instead it takes a pragmatic approach that should prove appealing to students. The language is easy to read and stimulating for a student of average ability... This pragmatic and essentially elementary book on the nature of proof is A definite step in the right direction."

- Mathematical Gazette (UK) 73 (Oct 1989)

"should help students enormously in their appreciation of what mathematics is all about ... one cannot help being affected by the obvious enthusiasm of the authors, which I feel certain will be conveyed to students."

- Australian Math Soc Gazette 15 (5) (Oct 1988)

"The style is lucid and stimulating and does not oblige the reader to read through unnecessary padding ... without presenting this fundamental idea [proof] in mathematics can the accusation be made that students of mathematics are not being well taught?"

- Australian Mathematics Teacher 46 (3) (1990).

"can be warmly recommended especially to first-year university students and their teachers."

- New Zealand Mathematical Soc Newsletter 50 (Dec 1990)

The book has been used successfully for 30 years in the first year Discrete Mathematics courses at the University of New South Wales


  1. Proof
  2. "All" statements
  3. "If and only if" statements
  4. "Some" statements
  5. Multiple quantifiers
  6. "Not", contradiction and counterexample
  7. Sets
  8. Proof by mathematical induction
  9. Solutions

A short article on 'Proof in mathematics' gives some of the book's flavour.

Here, some brief comments on how to teach 'Mathematics for the intelligent'.

(Thanks to Mandy Taylor and Dawn Boos for the pdfs)

Back to J. Franklin home page.