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

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.

The book is lovely but had to knock a star off because it was not packaged to protect it and the cover is damaged.

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.

Ainda estou no começo, capítulo 2, mas já pude perceber a qualidade do produto. O autor conversa com você, comete erros junto com você, tem um tom mais informal e engraçado, começando pela dedicatória a sua esposa, que Léo I livro inteiro com exceção das partes de matemática, rsrsrs. Simplesmente sensacional, um curso de matemática dado por aquele tipo de professor que transforma sua visão de um determinado assunto e que cruzamos raramente na nossa carreira de estudos.

Great book for self study

The ‘Introduction To’ sections of the book were my favourite and I loved the inclusion of open problems as it builds a curiosity towards mathematics.

Very good Math book

The Long-Form is plesant to read. A Fresh new way to learn math thinking.