Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series) Paperback – 19 Jan. 2021

TLDR: This book is a masterpiece.I have had a long and slow journey to mathematics and I find it a challenging subject. I find many books obscure and difficult to follow. I firmly believe this is not a necessary feature of the subject, for the most part, but is more often than not a failing in pedagogy. On the contrary Jay has, in my opinion, succeeded in teaching a subject that although difficult is entirely accessible.Almost by definition any book is going to be either too hard or too easy for most people. For myself - someone approximately at the beginning of undergraduate level in maths - who has never “got” proofs and wanted to start to understand them, I have found this the perfect introduction.

This book covers much the same ground as many other textbooks on proofs, particularly the discreet math books like the one by Epp. However, and compared to other dedicated proof books like the very popular Velleman, this one is much more readable in my opinion. It's also cheaper. I definitely recommend to any student who is struggling with some of the explanations of things like proof by strong mathematical induction given in other textbooks.

Always felt that my stdis left much to be desired on the subject of proofs. Managed to cope with what I had until now (20 years later). I'm a bit rusty anyway and I REALLY need to know my stuff in this area right now. An excellent book with excellent explanations and which enables rapid progress but has plenty of detail and help where you need it.NOTE: Cummings self publishes to keep the cost down, which is why this book is cheap in comparision.

The book has a wide selection of topics and unlike most maths books it provides clear concise and interesting explanatations. I bought this book to help with my proof writing ability in mathematical olympiads(the Irish Mathematical Olympiad IRMO), it helped a lot. The open questions and brief introductions into higher maths were very interesting and has sparked interest in maths beyond second level olympiads.I can't wait to read more of Jay's books.

It's a really good book which makes proofs accessible and fun. However, I think a way needs to be found to provide self-learners with solutions to the many exercises. Without access to these (or a teacher) a great deal of educational value is lost.

Very useful book

Excellent service! Product arrived on time and was in mint condition. Highly recommended 👌

Proofs are scary things, full of complicated notation and 'rigour' ... but it need not be so. Jay Cummings has written a brilliant book on proofs guiding the reader from simple to more complex examples in the most gentle and fun way possible. Finally here is a book that does not overwhelm the reader but focuses on teaching mathematics in a way that builds up understanding step by step. Where the book could do better is by providing solutions to at least some of the numerous exercises in each chapter, currently there are none.