--- product_id: 272088332 title: "Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series)" price: "NT$1665" currency: TWD in_stock: true reviews_count: 13 url: https://www.desertcart.tw/products/272088332-proofs-a-long-form-mathematics-textbook-the-long-form-math store_origin: TW region: Taiwan --- # Comprehensive Coverage In-Depth Explanations Rigorous Problem Sets Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series) **Price:** NT$1665 **Availability:** ✅ In Stock ## Summary > 📈 Elevate Your Math Game with Proofs! ## Quick Answers - **What is this?** Proofs: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series) - **How much does it cost?** NT$1665 with free shipping - **Is it available?** Yes, in stock and ready to ship - **Where can I buy it?** [www.desertcart.tw](https://www.desertcart.tw/products/272088332-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 ## Key Features - • **Structured Learning Path:** Follow a logical progression that builds your confidence and expertise. - • **Join a Community of Learners:** Collaborate and share insights with fellow math enthusiasts and professionals. - • **Master Problem-Solving Skills:** Tackle challenging exercises designed to enhance your analytical thinking. - • **Unlock the Secrets of Mathematics:** Dive deep into complex concepts with clarity and precision. - • **Engage with Real-World Applications:** Connect theoretical knowledge to practical scenarios for a richer understanding. ## Overview Proofs: A Long-Form Mathematics Textbook is an essential resource for students and professionals alike, offering a thorough exploration of mathematical principles, rigorous problem sets, and real-world applications to foster a deep understanding of the subject. ## 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: Tremendous - I can't say enough good things about this book. It's a math textbook that reads like an entertaining puzzle book. If, like me, you're interested in recreational mathematics, you will have encountered many of the examples before. Even so, you'll find many, many new insights. Lots of good exercises as well. And it goes beyond math; this is a great book on how to approach problem solving of any kind. The combination of rigor, rules-of-thumb, and intuition reminds me of Polya. Texts of this type should be required reading for college freshmen regardless. Plus, at this price, it's a real bargain! I plan to check out other books in this series. I bought it for the Kindle Fire, and it reads well on that device. Review: Learn Proof Writing From A Master - I just finished reading another wonderful book by Jay Cummings. The book is titled "Proofs" and is intended to help the reader learn how to write diverse kinds of proofs from many different areas of mathematics. I especially liked Chapter 4 on Induction because the writing is very clear and to the point. He discusses both weak and strong induction and his examples are extremely well chosen. I especially like his writing style. He also writes about math proofs by induction that contain mistakes that can mislead the reader. His example of how all people have the same name is the same as a similar example not in his book that all horses have the same color. Trying to find the mistakes in these proofs can be a real challenge, but once you do it you will understand math induction even better than you did before. This book has a rather ambitious aim, as proof writing is all anyone does in upper division math courses. Trying to learn how to write proofs in such a wide open field is not easy. However, the author does not try to teach you any advanced math and that is another reason I am so attracted to his writing style. Here is another small but important example. In discussing functions, Jay explains that writing f(x) is standard for a 1-tuple, but writing f((x,y)) with an order pair is not necessary. This a small notational convention that can trip up some students. Jay gives you permission to be confused at times and is aware that even very small things can make your life complicated! Jay has written three books that are all very different. I recently learned that I read his three books in the reverse time order in which he wrote them. Nonetheless, I think most people will find his books very worth while. The "Proofs" book is as good as any and contains a lot of information. ## Technical Specifications | Specification | Value | |---------------|-------| | Best Sellers Rank | #33,360 in Books ( See Top 100 in Books ) #3 in Discrete Mathematics (Books) #9 in Mathematical Logic #16 in Mathematics Study & Teaching (Books) | | Customer Reviews | 4.8 out of 5 stars 1,042 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 ### ⭐⭐⭐⭐⭐ Tremendous *by K***R on September 23, 2025* I can't say enough good things about this book. It's a math textbook that reads like an entertaining puzzle book. If, like me, you're interested in recreational mathematics, you will have encountered many of the examples before. Even so, you'll find many, many new insights. Lots of good exercises as well. And it goes beyond math; this is a great book on how to approach problem solving of any kind. The combination of rigor, rules-of-thumb, and intuition reminds me of Polya. Texts of this type should be required reading for college freshmen regardless. Plus, at this price, it's a real bargain! I plan to check out other books in this series. I bought it for the Kindle Fire, and it reads well on that device. ### ⭐⭐⭐⭐⭐ Learn Proof Writing From A Master *by J***Y on September 18, 2025* I just finished reading another wonderful book by Jay Cummings. The book is titled "Proofs" and is intended to help the reader learn how to write diverse kinds of proofs from many different areas of mathematics. I especially liked Chapter 4 on Induction because the writing is very clear and to the point. He discusses both weak and strong induction and his examples are extremely well chosen. I especially like his writing style. He also writes about math proofs by induction that contain mistakes that can mislead the reader. His example of how all people have the same name is the same as a similar example not in his book that all horses have the same color. Trying to find the mistakes in these proofs can be a real challenge, but once you do it you will understand math induction even better than you did before. This book has a rather ambitious aim, as proof writing is all anyone does in upper division math courses. Trying to learn how to write proofs in such a wide open field is not easy. However, the author does not try to teach you any advanced math and that is another reason I am so attracted to his writing style. Here is another small but important example. In discussing functions, Jay explains that writing f(x) is standard for a 1-tuple, but writing f((x,y)) with an order pair is not necessary. This a small notational convention that can trip up some students. Jay gives you permission to be confused at times and is aware that even very small things can make your life complicated! Jay has written three books that are all very different. I recently learned that I read his three books in the reverse time order in which he wrote them. Nonetheless, I think most people will find his books very worth while. The "Proofs" book is as good as any and contains a lot of information. ### ⭐⭐⭐⭐⭐ Incredible *by T***G on April 13, 2026* Exceptionally good textbook for self-learning and digestible explanations. ## 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.tw/products/272088332-proofs-a-long-form-mathematics-textbook-the-long-form-math](https://www.desertcart.tw/products/272088332-proofs-a-long-form-mathematics-textbook-the-long-form-math) --- *Product available on Desertcart Taiwan* *Store origin: TW* *Last updated: 2026-05-20*