--- product_id: 271804487 title: "Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series)" price: "€ 44.06" currency: EUR in_stock: true reviews_count: 13 url: https://www.desertcart.pt/products/271804487-proofs-a-long-form-mathematics-textbook-the-long-form-math store_origin: PT region: Portugal --- # Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series) **Price:** € 44.06 **Availability:** ✅ In Stock ## Quick Answers - **What is this?** Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series) - **How much does it cost?** € 44.06 with free shipping - **Is it available?** Yes, in stock and ready to ship - **Where can I buy it?** [www.desertcart.pt](https://www.desertcart.pt/products/271804487-proofs-a-long-form-mathematics-textbook-the-long-form-math) ## Best For - Customers looking for quality international products ## Why This Product - Free international shipping included - Worldwide delivery with tracking - 15-day hassle-free returns ## Description This textbook is designed for students. Rather than the typical definition-theorem-proof-repeat style, this text includes much more commentary, motivation and explanation. The proofs are not terse, and aim for understanding over economy. Furthermore, dozens of proofs are preceded by "scratch work" or a proof sketch to give students a big-picture view and an explanation of how they would come up with it on their own.This book covers intuitive proofs, direct proofs, sets, induction, logic, the contrapositive, contradiction, functions and relations. The text aims to make the ideas visible, and contains over 200 illustrations. The writing is relaxed and conversational, and includes periodic attempts at humor.This text is also an introduction to higher mathematics. This is done in-part through the chosen examples and theorems. Furthermore, following every chapter is an introduction to an area of math. These include Ramsey theory, number theory, topology, sequences, real analysis, big data, game theory, cardinality and group theory.After every chapter are "pro-tips," which are short thoughts on things I wish I had known when I took my intro-to-proofs class. They include finer comments on the material, study tips, historical notes, comments on mathematical culture, and more. Also, after each chapter's exercises is an introduction to an unsolved problem in mathematics.In the first appendix we discuss some further proof methods, the second appendix is a collection of particularly beautiful proofs, and the third is some writing advice. Review: Masterpiece - 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. Review: A very readable introduction to proof reading and writing - 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. ## Technical Specifications | Specification | Value | |---------------|-------| | Best Sellers Rank | 20,279 in Books ( See Top 100 in Books ) 1 in Discrete Mathematics (Books) 17 in Mathematical Logic (Books) 541 in Mathematics Teaching Aids | | Customer Reviews | 4.8 out of 5 stars 1,024 Reviews | ## Images ![Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series) - Image 1](https://m.media-amazon.com/images/I/51PuEwEYE+L.jpg) ## Customer Reviews ### ⭐⭐⭐⭐⭐ Masterpiece *by A***N on 27 September 2024* 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. ### ⭐⭐⭐⭐⭐ A very readable introduction to proof reading and writing *by Q***T on 22 February 2025* 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. ### ⭐⭐⭐⭐⭐ Wish I'd had this during my undergrad studies. *by R***N on 30 March 2023* 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. ## Frequently Bought Together - Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series) - Real Analysis: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series) - How to Prove It: A Structured Approach --- ## Why Shop on Desertcart? - 🛒 **Trusted by 1.3+ Million Shoppers** — Serving international shoppers since 2016 - 🌍 **Shop Globally** — Access 737+ million products across 21 categories - 💰 **No Hidden Fees** — All customs, duties, and taxes included in the price - 🔄 **15-Day Free Returns** — Hassle-free returns (30 days for PRO members) - 🔒 **Secure Payments** — Trusted payment options with buyer protection - ⭐ **TrustPilot Rated 4.5/5** — Based on 8,000+ happy customer reviews **Shop now:** [https://www.desertcart.pt/products/271804487-proofs-a-long-form-mathematics-textbook-the-long-form-math](https://www.desertcart.pt/products/271804487-proofs-a-long-form-mathematics-textbook-the-long-form-math) --- *Product available on Desertcart Portugal* *Store origin: PT* *Last updated: 2026-09-23*