Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series)

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.

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.

Easy to read and very useful.

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.

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.

Cummings does a good job of walking you through everything. Great introductory textbook.

A good introduction to mathematics proofs. Examples and diagrams are included. Handy as a reference.

I find that this book is sooo good all around the board. It has exercises which is always very important, and also the quality is perfect. Its big, wonderful, and cheap. What else can one ask for?

A pesar que no llego bien empacado, llego en buen estado, el libro tiene gran calidad en papel e impresión, es más grande de lo normal, valorando costo - beneficio es una gran compra.

Not only does this textbook introduce proof-writing in a wonderfully clear and organized way, the text is also full of wildly amusing footnotes. I've laughed out loud MULTIPLE times while reading this text as a supplement to the very staid text assigned for my Intro to Abstract Mathematics class.This proofs book feels like my friend. Seriously. It's weird. I love it so much. I truly, genuinely look forward to reading each section.If you are a math or CS major, buy this book. It will help mold your intuition. It will make math feel fuzzy and warm and exciting and delightful and fun. It will be a wonderful complement to the (probably) staid and formal textbook you have been assigned for your proofs book.THANK YOU, Professor Cummings!

Libro eccezionale che non richiede una conoscenza approfondita per poter essere compreso. Le spiegazioni sono molto chiare e le dimostrazioni piacevoli e divertenti da svolgere. L'approccio è molto informale ed aiuta a mantenere alto il livello di attenzione durante lo studio. Consigliatissimo!

The book is good, but I guess we are getting a trimmed down edition in India. The product description itself is not upto the mark. It says its width is 2.95 cm, but what I got is approx. 1.5 cm. The author's webpage and amazon.com says that the print length is 511 pages, but we get only 312 pages. No Appendices, Indexes, Preface, acknowledgement in Indian edition. The back cover says that we cover addtional topics like Ramsey theory, Real Analysis..... but these are not available in Indian edition. So, be careful. The pages quality is quite good, but binding is not proper. Pages will come out if not handled carefully. Enjoy!