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

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.

Ive been trying to self study real analysis. Here’s a list of some analysis books I've either read or skimmed through:- Understanding Analysis by Abbott- fundamentals of mathematical analysis Haggarty- analysis with an introduction to proof by Lay- introduction to real analysis by Silva- introduction to analysis by Mattuck- many, many more that i could get my hands onThis is the best one i could find. The author actually explains the motivation behind the proofs, and shows you how to *think* about them so you can derive the theorem and similar results on your own. This is in stark contrast to the presentation in many other books where a pretentious “polished” proof is shown with absolutely no hint as to *how* it was actually derived in the first place.Not so with this book. The author shows how the derivation is actually done by a human and not a computer.There are also plenty of illustrations in the book to provide an intuitive understanding of the proofs before giving the formal derivation.Each chapter comes with an introductory section providing the motivation for the topics about to be studied, which gets you curious about what you’re about to learn. This is the first math book I’ve read that I actually want to *read* for its own sake, not just use as something to “study” from.The only shortcoming is that there are no solutions to the exercises in the book, which often include crucial concepts (none that are needed for later chapters though; you can easily read the entire book and work on the examples without doing the exercises). The author does provide hints and partial solutions to some of the exercises on his website but i wish they were more comprehensive for those looking to self study.I also wish there was a section on metric spaces but really, i cant complain. This is such a well written book; it deserves nothing less than 5 stars. I haven’t listed the many books i tried to work through to understand analysis, this one just clicked for me very quickly. I even prefer it over Abbott’s as a first book on mathematical analysis, and I’ll be buying his other book on proof writing as well :)

Professor Jay Cummings is a king making math more accessible to 21st-century students.I'm taking a real analysis at a top private university. My professor is great, but this book also really helps when I'm confused about topics and need more explanation beyond my terse textbook!This one goes into a LOT of depth.

This is a great gentle introduction to real analysis. The range of topics neither deep nor detailed, but it's an entertaining and easy-to-read overview of what analysis is all about. You won't learn the differences between Darboux, Reimann-Stiltjes, and Lebesque integrals, but you will learn what is going on behind the scenes of the introductory calculus courses you took.

This is the funniest and best math textbook I have ever studied. If you want to go into Real Analysis, look at the seeming paradoxes in math, and find elegant solutions to messy problems with infinities I highly recommend this book to you.From a math text book I also wasn't expecting to literally break out laughing, but the foot notes provided some of the funniest information I've ever read. All this to say that this isn't a book you'll put down because of dryness but instead needing time to contemplate the material.Jay Cummings really made a terrific book, and has self published to keep the cost of the textbook affordable for the self studied. If you'd like to delve into self taught math, support your academic math, or just support a man trying to keep textbook prices from ballooning even more this is the book for you.I'm very glad Jay Cummings made the effort to create this book so that text book prices wouldn't be a barrier of entry for people trying to learn math.