Real Analysis: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series)
Original price was: $37,99.$19,99Current price is: $19,99.
- 100% Satisfaction Guaranteed!
- Immediate Digital Delivery
- Download Risk-Free
✔ Digital file type(s): １𝐏𝐃𝐅
Part of: The Long-Form Math Textbook Series (2 books)
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.
51 reviews for Real Analysis: A Long-Form Mathematics Textbook (The Long-Form Math Textbook Series)
You must be logged in to post a review.
Related products
-
Essential Calculus Skills Practice Workbook with Full
Original price was: $33,00.$16,99Current price is: $16,99. -
Game Theory Unbound: Revolutionize Your Thinking and Learn How to Win in Life and Business. Think Like a Strategist, Predict Outcomes, Play Smarter, and Navigate Life’s Games with Confidence
Original price was: $44,99.$14,99Current price is: $14,99. -
Build a Mathematical Mind – Even If You Think You Can’t Have One: Become a Pattern Detective. Boost Your Critical and Logical Thinking Skills. (Advanced Thinking Skills)
Original price was: $42,00.$14,99Current price is: $14,99.
Jordan –
Real Analysis is an exceptional text book. Dr. Cummings has taken complicated material and has made it approachable engaging and fun. One mark of a great teacher is when their love of their subject matter is obvious, and contagious to their students. The philosophy/history in this book provide context and intrigue. The conversational /tutoring tone and interspersed jokes (even poetry) provide levity. The affordable price makes it accessible to students of all incomes.
dronno –
One the best thought out books on the subject.
Jonathan Cooke –
I have nothing but praise for Professor Cumming’s book. I love the expository writing style; most real analysis books have a much terser style. While I can understand mathematicians ultimately need to develop the mathematical maturity to understand terse works, the student new to proof style math will typically flounder. The book shows the reasoning behind proofs, and one gets to observe a professional mathematician’s reasoning. Without a doubt, one can gain mathematical maturity by studying the text. Among other strengths, the author offers the text at an extremely affordable price. I look forward to more of the author’s works.
Vladislav –
This book is a rare jewel. It is both casual and rigorous and introduces all necessary concepts in order to build the foundations of modern analysis. Dr. Cummings does a great job introducing concepts, theorems, and proof ideas by first focusing on the intuition behind every step. It is a great fit for a primary text in an undergraduate Analysis course, but is also a great supplement for those taking graduate Analysis. 11/10, would recommend!
Andrew Tran –
For me, this wasn’t a life-changing math book. It is not the type of thing you could hand to a non-math student and everything will instantly click. Even maybe a stats student wouldn’t get much from it. Also, the author still engages in some traditional math-isms such as leaving simple parts of the proof to the reader or not giving solutions to end-of-chapter questions.
But, that is basically me saying what I wanted or expected out of the book versus what I got. One thing is for certain though: when I had to self study in my analysis class, this book helped me immensely. I am by no means a natural at math, but I am probably more attracted to it than the average person and think I understood most of the high-level concepts. Anything I didn’t understand well, this book helped me greatly with. In fact, the author’s approach was actually an improvement, not some needless change (though, it is not a radical departure from other math books). And for the price, I would really recommend trying it out just to support trying to move math into a more accessible direction.
So, if you’re the type of person who normally bangs their head against the wall when studying math, I doubt this book will change that. But if you’re interested in math and generally try to find satisfying explanations for things, I would highly recommend this book.
Laura –
Engaging, readable and even funny! Numerous illustrations, historical examples and space for reflection and scratch work make this a great text!
Rafae –
I would recommend this as a prerequisite to Rudin’s principles of math analysis or as a supplementary book. In my opinion this book should be a required textbook alongside Rudin’s for every real analysis course out there.
BG –
This is THE book for a solid understanding of analysis at the introductory level. This can then be followed by Rudin’s book or any other “advance” book on the subject. “Advance” often is code for “terse”. This book intentionally avoids being “advance”. The goal is to teach fully and smoothly. It is also the best book for self-study. The author does a great job of demystifying the subject matter. It’s to the point and does exactly as it aims to do; and, it’s cheap!
David –
This is a great text book. Not like others I’ve read. Easy to understand and helpful.
Michelle N. –
The book is written super informally but in a way that makes it easy to understand. It has many jokes (truly LOL’d a few times). Lots of proof sketches are used so I know where the proofs come from. It also has a website (LongFormMath.com) that has hints to exercises and lots of great videos.
Charles Saunders –
This is book is a great addition to the real analysis literature for several reasons. First, it explains difficult concepts in a clear and engaging manner. Second, having Baby Rudin alongside works well as the two books together create a great synergy. Finally, the author has additional information available on the website (https://longformmath.com/). This book is highly recommended.
John –
Good book on elementary real analysis and is a perfect supplementary to Baby Rudin! But I am a self-study learner, need complete solutions plz!!
B. Padilla –
This book was recommended to me by a fellow Math Major. Real Analysis is not natural to me at all. While I still struggle, this book helps explain things a bit simpler to me and makes a bit more sense. Also, it’s nice because when I read it at times it feels like someone is sitting there explaining it to me. I actually had the 1st edition, but when noticed there was a 2nd edition, later on, I bought it (Hey, it’s only $16) and planning on passing the 1s edition to a friend.
You can also check out the Author’s longformath webpage that links to the book, which then has links to videos that go with some of the chapters.
Nehemiah Leong –
A humorous introduction to classical analysis. Although Jay is a Combinatorist, he writes like an analyst. Highly recommended for anyone who wants to learn elementary real analysis with lots of fun. Learning math ought to be fun and Jay has shown how to do it
Allan Ackerman –
Topics like Linear Algebra, Real Analysis, and Number Theory are very tough to learn unless one has a teaching type textbook and is not taking a formal class. I have had trouble finding such books for both Linear Algebra and Real Analysis that do work. Regarding the latter I am only in the first chapter but already can see how things are much better explained to the novice than most other books on Analysis (most such books are very thin). A vital tip off for the above book were the number of pages. I knew he would do a better job of explaining the concepts and so far I have been right. I look forward to the remainder of the book.
Kaíque –
Excelent book. Extremely resourceful when it comes to representing graphically definitions and theorems, so as to build intuition without abandoning the rigor necessary for a solid understanding of the subject.
Math Customer –
It’s a really great book.
Dave Eaton –
This is an accessible and remarkably entertaining introduction to real analysis. The style is at once inviting and informal while not ignoring rigor. I’m a chemist with a deep interest in mathematics, so I appreciate the extra effort to call out the especially interesting and fun parts of the subject. Maybe, if you think Rudin is for sissies, you won’t find it quite as engaging as I do. But if you are not from the planet Vulcan and need a little convincing why the subject is so nifty, this is the book to do it.
Benjamin Sipes –
This book is simply the most well-written math textbook I’ve ever encountered. I loved math growing up, but college calculus classes made me feel like an idiot. This book has practically re-taught me math. It’s written at this golden level where the expectation is that you’ve already taken calculus, but that you didn’t get much out of it. And I’m like, wow, that’s what I needed!
Not only is the exposition 10/10, but Dr Cummings is also very funny. How awesome it is to have a math textbook that teaches you advanced topics while making you laugh?!
My next request for you, Jay, is to write a real analysis textbook for kids. The way you present these topics already feel like they could be the foundation of a child’s math education. Teaching math in this way makes me wish I had this textbook a long time ago.
Thank you!
Rahul Madhavan –
What an enjoyable book! It simplifies real analysis to the point that it becomes a conversation. The author prefaces the formalism with the concept understanding to the point the formalism works as a tool to strengthen understanding than the means to it.
This is the best first text in real analysis I’ve seen (Rudin, Abbott can come after reading this). Excellent illustrative examples. Good coverage.
What about exercises – is it a classroom text?
The textbook is filled with exercises. Some of these are listed as important ones. I think it can work well for instructors in undergraduate mathematics.
Anthony Petrakian –
Amazingly explained
vm1980 –
Questo testo è il link ideale fra i corsi di Calculus e Analysis così come vengono chiamati in UK/US. In Italia siamo meno abituati a questa distinzione, perchè almeno i nostri vecchi corsi di Analisi assumevano l’una e l’altra veste: a lezione Analysis e Calculus ad esercitazione. In ogni caso, sia nello studio da autodidatta che di preparazione preliminare a corsi più avanzati, questo ottimo libro accompagna il lettore nel viaggio alla scoperta delle strategie di dimostrazione e del linguaggio tipico dell’Analisi Matematica. L’Inglese utilizzato è davvero di facile comprensione e l’esposizione è informale quando opportuno, al tempo stesso è rigorosa nella presentazione delle definizioni, teoremi e dimostrazioni finali (per alcune dimostrazioni si adotta una strategia graduale, prima una bozza informale e alla fine la “vera” dimostrazione. Inutile dire come questo abbia un gran valore pedagogico, cosa di cui i testi più comuni devono fare necessariamente a meno). Il contenuto copre gli argomenti tipici di un primo corso di Analisi: numeri reali, successioni e serie numeriche, limiti, continuità, differenziazione, integrazione, successioni e serie di funzioni.
Eric –
You can use any old analysis textbook to learn the important theorems of Analysis and their proofs. You’ll get axioms, lemmas, propositions, etc., thrown at you page after page. Most of the time, you’re expected to have a lecturer filling in the gaps, leading you to the intuition or insight that would help you replicate the proofs yourself.
This book is that lecturer. It’s a Long-Form Mathematics Textbook, so you’ll get all the same theorems, lemmas, and propositions as other terser books, sandwiched in between exposition that reads easily and spills all the secrets. You can treat it like unlimited access to your favorite professor’s office hours.
Sammy Melendez –
The book is very readable for an undergraduate math student with no real analysis background. It is logically organized and the author doesn’t make too many assumptions about your math ability except that you know basic proof writing.
I’ve enjoyed every chapter so far and have never been left confused at the end of one (which I definitely cannot say for other math textbooks). All in all, it is an approachable Intro to analysis and may very well become the next “industry standard” for such courses.
It’s worth every penny and then some, and has made me very excited for the author’s intro to proofs book!
lmata1981 –
If you are looking for a book that delivers mathematical maturity and professionalism, this book isn’t it. If you are looking for a light-hearted approach to a rather difficult subject and great examples and exercises, pick this book up. The author understands that Real Analysis is a difficult subject and he doesn’t make the material too terse or goes too fast for a student who has a lack of or small experience toward proofs.
Dimetrius –
I mean it’s still just another professor’s view about how Analysis ‘should’ be taught but I can definitely say that I like his descriptions about how to approach a different problems. He gives a nice amount of intuition in an approachable reading format. I definitely do like how he provides the Axioms for ZFC Set Theory ; I understand that they are important but I don’t see the pedagogical point of view to provide an overview of them in the text. How nice and pretty they are, I feel as though to have a discussion about them is more minutiae than actual substance pertaining to the core of the book, Analysis (granted they are featured towards the end). Overall , much better than a lot of analysis books I have come across.
William D. Fusfield –
li li –
Learned a lot, and was easy to understand
Maria A. –
This is a very informal book with tons of clearly thought examples. Every example is fully described in detail. The book does a great job in attracting a complicated subject and making it understandable. There are a lot of interesting applied and historical concepts roaming throughout the book. It is such a fascinating book to read. It’s funny, entertaining, informative, provides tons of examples, engaging and it guides you through the process all the way. It’s also very affordable, what more can you want?
Nicolò oldrini –
Perfect as a first book to enter the subject. The exposition is clear, rigorous when necessary without ever being overly complicated. I’m finishing the third chapter and each demonstration is always introduced by a ‘scratch work’ that shows the underlying intuition. Strongly recommended!
Thomas Chambrier –
If you are buying a first book in Real Analysis then this is the one, especially if you are quite new to proof in general.
This book is much less terse than your typical Analysis book. You can use this book to build mathematical maturity and then move on to the more concise books. The author has done an amazing job here and deserves a lot of credit.
Me –
This is it. The new paradigm is here. Down with the old “definition and proof” style of textbook, and long live Jay Cummings! Long live the king!
The text actually attempts to explain the ideas behind the theorems, definitions, corollaries, and proofs. It doesn’t just drop them in your lap and move on, assuming previous mastery of the subject. Mr. Jay understands that a proof is a demonstration, not a proof.
Just buy the book.
fugu –
I was looking for a textbook on real analysis that is rigorous, intuitive and not too expensive. This one scores highly on all accounts. The background is the following: my nine-year old daughter really enjoys math at school but it is not always challenging and naturally heavy on computing things as opposed to solving riddles, understanding concepts etc. So we do math instead of bed-time stories. Analysis is a particularly nice field to start with because many of the concepts are familiar (natural number, rational numbers, the axioms, the concept of a distance, summation of terms etc.) or they can be motivated easily (the reals, convergence, integration etc.). I was looking for a textbook which does university level analysis but with more intuition and examples than you would find in a definition-theorem-proof kind of textbook. Real Analysis – the long-form holds what it promises. It is a gentle introduction, has a lot of motivating examples and it starts very slowly (proof that |a| = |-a| kind of propositions). But importantly, it does define objects and it does prove rigorously. The coverage is very standard: The derivation and structure of the reals, sequences and series, continuity, differentiation and integration and sequences and series of functions. Each chapter has some open questions that invite the reader to marvel about the beauty of mathematics (is e+pi rational?).
With four-hundred pages, you get a lot of mathematics for your money, just be aware that it could be squashed into hundred pages without too much effort. So if you get impatient easily, this book is not for you. If however, you enjoy to read why an object is defined in a certain way or enjoy longer proofs that illustrate the core idea carefully, I would thoroughly recommend this book. Even for small children.
Cliente Math –
The style of the presentation is very clear and engaging. The inclusion of more solutions to exercises would be a big improvement to the learning experience the book provides to self-students.
Rob Mitra –
This book is a gem. It is exceptionally clear — the “long form” nature of the book means the author can take his time to thoroughly motivate and explain ideas. Furthermore, the price means that even if you have other Analysis textbooks, you can buy this one to obtain another point of view on a topic. For example, I also have Abbott and Rudin, both of which I also like for different reasons. But, I must say, Long Form has become my “go to” book over those two. If you’ve read Abbott, then you know that is high praise indeed. Cummings’ exposition is clear, the examples are well-chosen, and I especially like he describes some open problems in the field. I hope the author continues his “long form” tradition and writes on many other topics.
Brett Gregory –
This book really is amazing! Received it a few minutes ago and it was a lot bigger than I expected! I have skimmed through the content and I am so impressed by how the content is communicated to the reader. It will really help me a lot in my analysis module.
Considering getting Prof Cumming’s new proof book (I bet its just as good as this book if not better!)
JustAnother Math Customer –
Alan –
Livro parece bom para introdução a introdução a análise real. Veio rápido, e foi uma boa compra.
John –
By far, the best Real Analysis book on the market. The depth and clarity of this book is unmatched. It provides everything needed to master Real Analysis. It does so with detailed explanations of the concepts and procedures along with the most illuminating graphics that I have seen in a Real Analysis book. I would highly recommend this book to anyone looking to learn and understand the subject.
Lance Johnson –
This book was a lifesaver. Being able to read about a topic in this book and get the idea of it down before tackling the harder presentation in my course’s primary textbook made my learning more effective and easier. I recommend this book to anyone taking real analysis.
Daniel J. McKinley –
I like the author’s new approach to explaining the subject matter. Lots of good humor and personal asides about how amazing some of the definitions and theorems are. The author clearly loves this stuff.
It’s rigorous too, full of complicated epsilon-delta proofs. Another nice touch are his “Proof Sketches” that precede the formal proof, where he works out his method of attack.
Highly recommended.
Eric G. –
El libro explica lo básico del análisis real y lo hace de una manera muy buena y sencilla por si no tienes ninguna experiencia haciendo demostraciones matematicas. Pienso que es posible que sea uno de los mejores libros para introducirse de manera autodidacta en el análisis real. //
//
The book explains the basics of real analysis and does it in a very good and simple way in case you don’t have any experience doing mathematical proofs. I think it may be one of the best books for a self-studying an introduction to actual analysis.
cloudio_18 –
This book is much more approachable and enjoyable to read compared to other Real Analysis textbooks. It comes with both width and breadth of this subject, also with plenty of asides and notes which provide extra reference and insights. More importantly, you don’t need to pay a premium to access this amazing book. Highly recommended, I wish I could read this when I was studying RA back in university 😉
James –
I have a number of RA texts and I have to say this one really impressed. Obviously the thoroughness is there (it’s a big book for such a low price) but what impressed most is the sketches of proofs before the proofs and the explanations within. The author really goes to great depths to fully explain everything which makes this an excellent text for self learners. Highly recommend, along with the author’s other text on Proof. Hints to exercises are on his website, but I would have liked a more substantial bank of solutions.
kevin_HamptonMiddx –
All OK
alexander –
good way of presenting the matter
dottid –
Good, maybe, for an advanced undergrad but a bit more appropriate in a graduate course. More yet, it is great for a reference text.
SJ –
I got this book for my son. He’s in 11th grade. He found the book to be very helpful. It was much simpler than the MIT Real Analysis Lectures on YouTube and his other book “Real and Complex Analysis” by Shilov. He said that it is a good book to get him started and it’s providing him with a solid foundation for the hard stuff. There were some dents in the pages and it looked like it had been mishandled but everything else is perfect. I usually expect to order something new and get it in new condition though.
Libro en perfecto estado –
Vino un poco dañado en la parte de atrás pero adelante y adentro está excelente, se que acá hablan inglés pero recomendadisimo este libro para los que quieren aprender otro idioma y hacerlo a lo grande con este libro que sinceramente va a elabar mi y tú conocimiento. Es un increíble libro y mi opinión es que además de grande tamaño, tiene grande aporte a tu vida. Excelente.
Daniel McCormick –
Great product with great price… minor damage during shipping. Arrived as promised! Would buy from this seller again!
Perla –
The back of the book came damaged, it looks like it was bent on some parts and some of the back pages look a bit bent. Aside from that the book is good and is readable. I need it for school so I will not be returning it I just hope it doesn’t start tearing apart because of this.