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Understanding Analysis

4.34  ·  Rating details ·  232 ratings  ·  17 reviews
This book outlines an elementary, one-semester course that exposes students to both the process of rigor, and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim of a course in real analysis should be to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus atten ...more
Hardcover, 312 pages
Published August 22nd 2016 by Springer (first published January 1st 2000)
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Mar 13, 2016 rated it really liked it  ·  review of another edition
This is a fantastic introduction to real analysis. All the concepts are explained and motivated very well. It is great for self study, and requires only as much as the calculus sequence and a previous exposure to proofs. This is a relatively easy book, though some of the exercises are really good. Do them all if you can. My only gripes with this book is that it could at least attempt to be more ambitious in its complexity. For example, it describes the properties of the real numbers in the first ...more
Kiên Trần
Feb 22, 2016 rated it it was amazing  ·  review of another edition
Shelves: math
concise, crystal clear, complete core of calculus/real analysis.
James Povilonis
May 09, 2020 rated it it was amazing  ·  review of another edition
Easily the best math textbook I've ever used. One major frustration I have with university math texts that challenge their readers to think deeper is that the student's work can often feel useless or misguided. The writing can be unfocused or too presumptuous of what the the student can do. Yet, a balance must be struck against the other extreme: so simple and repetitive that a student begins to think of the concepts as a collection of algorithms to complete.

This book achieves a perfect balance
Owen Jepps
Dec 12, 2019 rated it really liked it  ·  review of another edition
I like this book very much as an introduction to analysis, because it motivates the concepts much more strongly than most books from the traditional canon. I use this book for a reading course in analysis: the chapters are well structured with a hook to motivate the content, and a nice summary at the end. I agree with another reviewer's comment that the treatment of the real numbers is a little confusing due to the order, and one student noted that with so many parts of proofs left as exercises ...more
Tim Wetzel
Feb 25, 2019 rated it it was amazing  ·  review of another edition
Shelves: education
Honestly the thing that pisses me off most about math books is when they're disorganized and written for the author, rather than for the students. This one has all the definitions, theorems, proofs, and problems arranged in a really digestible way. I really struggled with the concepts in this class (fuck series, am I right) but the book made it possible to teach myself a lot of the harder concepts, which is a tough feat especially for a proofs class. This is one of the notoriously hard classes a ...more
Davi Barreira
Jun 30, 2019 rated it it was amazing  ·  review of another edition
This is the best book I found for learning analysis the first time, specially for self-study! The exercises evolve in difficulty, which gives you confidence that you are actually learning the subject (because you are able to do the easy exercises as you read the chapter). Also, the examples and the writing are just great! It felt like a novel! I just wish I could find other textbooks with the same “spirit”.
Robbie Carlton
Jun 16, 2019 rated it it was amazing
This is the best presentation on Analysis I've read.

He does a really great job of motivating the ideas, and gives really interesting and unusual examples, not just the normal basic examples.

Lot's of exercises for each chapter ranging from simple to pretty involved proofs (no solutions).

Above all that it's just well written and a pleasure to read.
Nov 30, 2019 rated it it was amazing
Shelves: math-stats-cs
Great introductory book in analysis. Presents the material in a straightforward manner accessible to those with introductory calculus, and the many stories, backgrounds, and explorations the author offers help ground understanding. Just an all-around great introductory math text for building conceptual understanding of analysis as a first look.
May 14, 2017 rated it it was amazing  ·  review of another edition
Shelves: analysis, mathematics
Very nice introduction to analysis with good background and motivation of why we are interested in various theorems or problems. Even the chapter on Fourier series was excellent. Naturally, this book doesn't go too far so more difficult analysis must search elsewhere.
Ayush Bhat
Jul 02, 2017 rated it it was amazing  ·  review of another edition
Simple and great book to get started with real analysis.
Max Wang
Nov 26, 2019 rated it really liked it  ·  review of another edition
Beautifully written.
Mar 07, 2020 marked it as did-not-finish  ·  review of another edition
For clarification: Putting it down right now, not because it is bad.

I have plan to come towards it later.
Sep 14, 2017 rated it it was amazing  ·  review of another edition
Shelves: mathematics, owned
It's a fine book, but the second edition is much better in that it has several additional sections which cover the Lebesgue integral and some other very fine topics that the first edition doesn't cover at all. Not that there isn't plenty for a first-semester course in analysis in the 1st but the 2nd is just much better for that very reason.
Oct 01, 2008 rated it it was amazing  ·  review of another edition
This book was intense pain and utter pleasure for a class I worked extremely hard on - ultimately my favorite class. A great reference for me as I learned the proofs behind why Calculus works.
Arzu Erdem
Jan 01, 2014 rated it it was amazing  ·  review of another edition
Easy way to understand analysis
THis book is ok
Austin Hogie
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