Real Analysis: A Long-Form Mathematics Textbook

This Real Analysis book by Cummings is definitely the best math book ever written! I recommend it to anyone who may have noticed themselves having to read and reread a textbook in their mathematical journey and still felt lost. I say this because I loved how easy to read this real analysis textbook was for me. I have read many math books in the past and some can even get overwhelming with their technicality. I was able to follow easily and best part of this is the fact that you geniunly close the book with a better understanding of the topic. Learning to write proofs is difficult enough as it is, but this book helps you refresh your proof writing along the way! If you are a student that feels lost or overwhelmed with the topic of real analysis, please take a look at this book! With time and perserverance in reading the topics introduced in this book you will slowly notice the difference! I wish all authors would write in the style Cummings writes in. He writes in a way to make you feel like you are being tutored or in your class lecture. I am the type of student who sometimes would fear opening the books because I knew I would feel like I studied and got nothing out of the textbook. This is the only book so far where I have gone to lecture and felt comfortable and confident enough to read and tackle my homeworks afterwards! I hope other authors take the time to read this Real Analysis textbook and understand that students do not have their PhD's and need to write more clearly and easy to follow textbooks. I hope this author continues to publish amazing books like this and hope to see an abstract algebra proof book in the future!

Having read multiple real analysis books during my undergraduate studies, I can say without a shadow of a doubt that this is the best introductory real analysis book for the STUDENT. There are no skipped steps in proofs and Dr. Cummings spends quite a bit of time helping the student develop proof writing skills. The conversational style of writing makes the book a joy to read and the author can be quite funny at times!!!I believe that this book should precede baby Rudin and is well suited for self study. For a complete understanding of undergraduate analysis, I'd highly recommend building your foundations with this book and using Tao/Rudin to gain further insight into the topic. if you need to study real analysis or have any interest in the topic, then do yourself a favor a buy this book. You won't be disappointed.There are no solutions to the problems but the book includes many standard real analysis problems and any problem/solution analysis book will serve you well as a companion to the text.

From time to time, having a masochistic steak, I buy math books. Math is one of those subjects that I have always wanted to understand, but have been daunted by the (to me) impenetrable way in which such books are written. There seems to be a dichotomy. Either the books are aimed at a young audience and simply do not go far enough, or they quickly devolve into esoteric symbology.I realize that mathematical notation is the "language of math." But, like any language, one has to learn the language before understanding it. This is where most math books, especially those written for a more general audience, fall down. Those of us, whose day jobs are not "mathy," either never got a good foundation in the notation, or are rusty as hell.Cummings makes no assumptions regarding the reader's prior math-savvyness. There is enough English between the equations to understand and follow along. The introduction of the symbols is accompanied by lucid explanations and many examples that let the reader get comfortable with the concepts before building on them.Over the years, I have bought and ended up donating hundreds of dollars worth of books on math. This one I am keeping!

I struggled a lot in my Real Analysis courses as a undergraduate student. I used this book to brush up on the concepts before going back to grad school and wow....where was this textbook back then?! Not only is it an amazing price for textbook, I also love how easy it is to navigate through this book. The definitions are clear and relevant, the examples are great and helpful, and the exercises are straightforward and applicable. If you are currently a student or plan to take this course in the future (or if you're just a curious cat about real analysis! :P), I HIGHLY recommend checking out this affordable textbook

Excellent

Purchased this item for Real Analysis I-II in undergrad. Topics include the reals, cardinality, sequences, series, topology of R, continuity, differentiation, integration, and sequences and series of functions. Like most textbooks there is a table of contents and an index which make it easy to find what you're looking for but as an added bonus this textbook also contains a "list of results" in which you can find all the theorems, propositions, lemmas, and corollarys you are looking for.This is truly not your average real analysis textbook. The writing style is more conversational and utilizes humor and peculiar examples to facilitate learning. Considering most analysis textbooks run over $80, this one is a steal and has everything you need to know for undergrad real analysis. I included a picture of the beginning of Chapter 6 which is on Continuity. Read the text to see what I mean! Enjoy!

This is comparable to my RA text in college. I was expecting better explanations than was found in textbooks years ago but I did not find it here.

Dr. Cummings did a fantastic job with this textbook. As you can see, it is obviously the most affordable real analysis textbook you can find. On top of that, Dr. Cummings writes in a conversational tone reminiscent of an actual lecture, which is a much more pleasurable way to learn. In fact, the way the book is broken up into sections and subsections makes the (not very easy) material easily digestible. Highly recommended as either supplemental material or the main text for your Real Analysis journey.