--- product_id: 145453768 title: "Real Analysis: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series)" price: "£32.23" currency: GBP in_stock: true reviews_count: 13 url: https://www.desertcart.co.uk/products/145453768-real-analysis-a-long-form-mathematics-textbook-the-long-form store_origin: GB region: United Kingdom --- # Comprehensive Coverage In-Depth Examples Rigorous Proofs Real Analysis: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series) **Price:** £32.23 **Availability:** ✅ In Stock ## Summary > 📈 Elevate Your Math Game with Real Analysis! ## Quick Answers - **What is this?** Real Analysis: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series) - **How much does it cost?** £32.23 with free shipping - **Is it available?** Yes, in stock and ready to ship - **Where can I buy it?** [www.desertcart.co.uk](https://www.desertcart.co.uk/products/145453768-real-analysis-a-long-form-mathematics-textbook-the-long-form) ## 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 - • **Ideal for Self-Study:** Perfect for independent learners seeking a thorough and structured approach. - • **Extensive Problem Sets:** Sharpen your skills with a plethora of exercises designed to reinforce your understanding. - • **Master the Fundamentals:** Dive deep into the core concepts of real analysis with clarity and precision. - • **Real-World Applications:** Connect theoretical concepts to practical scenarios, enhancing your analytical thinking. - • **Rigorous and Accessible:** Experience a perfect blend of challenging material and approachable explanations. ## Overview Real Analysis: A Long-Form Mathematics Textbook is a comprehensive resource designed for students and professionals alike, offering rigorous proofs, extensive problem sets, and real-world applications to enhance understanding and analytical skills in the field of mathematics. ## 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. Examples often drive the narrative and challenge the intuition of the reader. The text also aims to make the ideas visible, and contains over 200 illustrations. The writing is relaxed and includes interesting historical notes, periodic attempts at humor, and occasional diversions into other interesting areas of mathematics. The text covers the real numbers, cardinality, sequences, series, the topology of the reals, continuity, differentiation, integration, and sequences and series of functions. Each chapter ends with exercises, and nearly all include some open questions. The first appendix contains a construction the reals, and the second is a collection of additional peculiar and pathological examples from analysis. The author believes most textbooks are extremely overpriced and endeavors to help change this.Hints and solutions to select exercises can be found at LongFormMath.com. This is the 2 + epsilon edition of this book. The second edition was published in July 2019. In January 2024, an epsilon of changes were made and the manuscript was updated, without officially creating a new edition. Review: A MUST HAVE BOOK! Beware of Low Reviews - As a student at one of the University of California schools taking Real Analysis, this book is perfect for both following along with the class and self-studying. I have been a mostly self-taught student, reading books prior to my classes, and found this book to be very engaging. It's an enjoyable read, providing insightful quips to keep your interest piqued. Context is thoroughly provided before entering a topic - whether it be historical or math relevant. Footnotes contain interesting comments along with additional commentary on harder topics; sometimes even jokes. Honestly, most books fail to connect to the reader - like they're some robot, but when I read this it's as if I'm talking to Jay Cummings himself. It's a human-to-human read. So far, Real Analysis tends to be hard because your intuition fails you at times. The book does its best to supplement the occasional topics that deceive your intuition. Most of the reviews seem to complain about not having enough examples, but in reality, there are plenty (along with ALOT of additional notes in footnotes!). There are also solutions posted to the exercises online (on the author's site iirc). There have been times when I couldn't understand something specific and had to seek other material on YouTube (and this is normal). Some topics click to others and some don't. Ultimately, you'll find yourself understanding 90% of the book alone. That's just how Real Analysis is and there are some parts of math that will be harder to understand and require extra care. For example, when the book covers convergent sequences there is a great emphasis on understanding the definitions and even gives you multiple "comments". Each comment provides a different perspective than the one before and ultimately gives you the best opportunity to learn. (I've attached an image of part of the convergent sequences). Something unique that the book does is it gives you a page of contents for every proposition, lemma, and definition given. Truly a convenience. Ultimately, this book rules. If you're a like-minded student, this is perfect for you. Provides amazing intuition and historical context which helps you understand the purpose of the math you are learning. The book is also easily read and funny. I rarely write reviews but I couldn't pass this book up. Good luck with Real Analysis. Also, if it means anything, The Math Sourcerer on Youtube reviewed this book and practically gave it a 10/10. So if my review doesn't convince fellow students, check out his review. Way more in-depth than mine probably. Review: A Most Outstanding Book - I just finished reading a most wonderful book on Real Analysis by Jay Cummings. As unusual as it may seem, I normally scan over a book before I begin reading it. In this case I actually read the Appendices first, before I began reading the book. The Appendices were fantastic and I had to keep reading them because they were so good. As an undergraduate I learned how to construct the real numbers by starting with nothing but the empty set. Jay does the same thing in Appendix A, but he cleverly avoids boring you with all the details. His summary is succinct and to the point and it is all outlined in just a few pages. His Appendix B contains classic pathological examples which motivate most of the subject of Real Analysis. You will know Jay is an expert when you finish Appendix B. The book's cover shows the graph of what is called Thomae's function (I had not seen this before in any of the books I have on Real Analysis). Later he proves this function is integrable. Strangely enough, I am probably one of the few people to take a full year course in Topology before I took my first course in Real Analysis. I found Topology fascinating, but you aren't supposed to take Topology before you take Real Analysis. How ironic then that in Jay's book Chapter 5 is a brief intro to Topology and this is before Chapter 6 which discusses Continuity. Little wonder that I felt right at home with this book. The author also very carefully introduces the concept of integrability and touches on measure theory. You immediately learn why the author is such an expert. The rest of the book is full of outstanding problems that will really help you learn the subject He also includes many open questions that will keep you entertained. I only wish I could have had this book when I took Real Analysis. It would have made my life much easier! ## Technical Specifications | Specification | Value | |---------------|-------| | Best Sellers Rank | #46,320 in Books ( See Top 100 in Books ) #4 in Mathematical Analysis (Books) #20 in Calculus (Books) #37 in Mathematics Study & Teaching (Books) | | Customer Reviews | 4.8 out of 5 stars 849 Reviews | ## Images ![Real Analysis: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series) - Image 1](https://m.media-amazon.com/images/I/51LQTavml+L.jpg) ## Customer Reviews ### ⭐⭐⭐⭐⭐ A MUST HAVE BOOK! Beware of Low Reviews *by K***N on August 15, 2023* As a student at one of the University of California schools taking Real Analysis, this book is perfect for both following along with the class and self-studying. I have been a mostly self-taught student, reading books prior to my classes, and found this book to be very engaging. It's an enjoyable read, providing insightful quips to keep your interest piqued. Context is thoroughly provided before entering a topic - whether it be historical or math relevant. Footnotes contain interesting comments along with additional commentary on harder topics; sometimes even jokes. Honestly, most books fail to connect to the reader - like they're some robot, but when I read this it's as if I'm talking to Jay Cummings himself. It's a human-to-human read. So far, Real Analysis tends to be hard because your intuition fails you at times. The book does its best to supplement the occasional topics that deceive your intuition. Most of the reviews seem to complain about not having enough examples, but in reality, there are plenty (along with ALOT of additional notes in footnotes!). There are also solutions posted to the exercises online (on the author's site iirc). There have been times when I couldn't understand something specific and had to seek other material on YouTube (and this is normal). Some topics click to others and some don't. Ultimately, you'll find yourself understanding 90% of the book alone. That's just how Real Analysis is and there are some parts of math that will be harder to understand and require extra care. For example, when the book covers convergent sequences there is a great emphasis on understanding the definitions and even gives you multiple "comments". Each comment provides a different perspective than the one before and ultimately gives you the best opportunity to learn. (I've attached an image of part of the convergent sequences). Something unique that the book does is it gives you a page of contents for every proposition, lemma, and definition given. Truly a convenience. Ultimately, this book rules. If you're a like-minded student, this is perfect for you. Provides amazing intuition and historical context which helps you understand the purpose of the math you are learning. The book is also easily read and funny. I rarely write reviews but I couldn't pass this book up. Good luck with Real Analysis. Also, if it means anything, The Math Sourcerer on Youtube reviewed this book and practically gave it a 10/10. So if my review doesn't convince fellow students, check out his review. Way more in-depth than mine probably. ### ⭐⭐⭐⭐⭐ A Most Outstanding Book *by J***Y on September 11, 2025* I just finished reading a most wonderful book on Real Analysis by Jay Cummings. As unusual as it may seem, I normally scan over a book before I begin reading it. In this case I actually read the Appendices first, before I began reading the book. The Appendices were fantastic and I had to keep reading them because they were so good. As an undergraduate I learned how to construct the real numbers by starting with nothing but the empty set. Jay does the same thing in Appendix A, but he cleverly avoids boring you with all the details. His summary is succinct and to the point and it is all outlined in just a few pages. His Appendix B contains classic pathological examples which motivate most of the subject of Real Analysis. You will know Jay is an expert when you finish Appendix B. The book's cover shows the graph of what is called Thomae's function (I had not seen this before in any of the books I have on Real Analysis). Later he proves this function is integrable. Strangely enough, I am probably one of the few people to take a full year course in Topology before I took my first course in Real Analysis. I found Topology fascinating, but you aren't supposed to take Topology before you take Real Analysis. How ironic then that in Jay's book Chapter 5 is a brief intro to Topology and this is before Chapter 6 which discusses Continuity. Little wonder that I felt right at home with this book. The author also very carefully introduces the concept of integrability and touches on measure theory. You immediately learn why the author is such an expert. The rest of the book is full of outstanding problems that will really help you learn the subject He also includes many open questions that will keep you entertained. I only wish I could have had this book when I took Real Analysis. It would have made my life much easier! ### ⭐⭐⭐⭐⭐ The perfect real analysis textbook *by C***N on February 25, 2026* I'm a mathematics and computer science undergraduate student and have found this book (and the mathematical proofs book) incredibly helpful. The content is rigorous while also interspersed with humor and interesting footnotes that help alleviate my "math anxiety." The scratch work, proofs, and layout are clear and approachable. If you're taking real analysis you should definitely add this book to your collection. ## Frequently Bought Together - Real Analysis: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series) - Proofs: 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.co.uk/products/145453768-real-analysis-a-long-form-mathematics-textbook-the-long-form](https://www.desertcart.co.uk/products/145453768-real-analysis-a-long-form-mathematics-textbook-the-long-form) --- *Product available on Desertcart United Kingdom* *Store origin: GB* *Last updated: 2026-06-07*