What are the best introductions on analysis, to read for leisure?

Question

I was just wondering if anyone could recommend a book on mathematical analysis that is interesting enough to sit down and read for enjoyment alone? Something not written in the style of a textbook?

Does this answer your question? Good book for self study of a First Course in Real Analysis — user1110341, Oct 08 '23 at 18:51

score 2 · Answer 1 · answered Apr 08 '17 at 16:33

2

Counterexamples in Analysis is great for recreational reading.

answered Apr 08 '17 at 16:33

Paul

8,153

score 2 · Answer 2 · answered Apr 08 '17 at 16:42

2

Understanding Analysis is an awesome book in my opinion. It's concise and highly readable, but manages to not sacrifice too much rigor when doing so. I think it's a great book for someone who is interested in getting their hands on serious material, but in an accessible and easy to read fashion.

answered Apr 08 '17 at 16:42

Stella Biderman

31,155

+1 Its a great book, i forgot to write it in my answer. Now i remember – J. Deff Apr 08 '17 at 16:43

score 2 · Answer 3 · answered Apr 08 '17 at 16:50

Tom Körner's got a couple:

Calculus for the Ambitious
A Companion to Analysis: A second first and first second course in analysis.

All of his stuff is extremely readable, whether it's formatted like a textbook or otherwise. (His book on Fourier analysis is easily one of the best, but probably a bit advanced for what the OP has in mind.)

And of course I have to recommend Hardy's A Course in Pure Mathematics, even if it is explicitly a textbook. Boy did Hardy know how to write.

score 1 · Answer 4 · answered Apr 08 '17 at 16:31

1

I remember Visual Complex Analysis by Tristan Needham being enjoyable for armchair reading.

answered Apr 08 '17 at 16:31

Tim kinsella

5,903

score 1 · Answer 5 · answered Apr 08 '17 at 16:33

There are two books according to me

How to Think About Analysis 1st Edition by Lara Alcock

https://www.amazon.com/Think-About-Analysis-Lara-Alcock/dp/0198723539

2. The Real Analysis Lifesaver: All the Tools You Need to Understand Proofs (Princeton Lifesaver Study Guides) Reprint Edition by Raffi Grinberg

https://www.amazon.com/Real-Analysis-Lifesaver-Understand-Princeton/dp/0691172935/ref=sr_1_1?s=books&ie=UTF8&qid=1491669108&sr=1-1&keywords=analysis+lifesaver

Both these books are written in informal way suitable for self study

Hope it heps

score 1 · Answer 6 · answered Apr 08 '17 at 16:35

1

The Manga Guide to Calculus might be of use: The Mange Guide to Calculus

answered Apr 08 '17 at 16:35

alekscooper

952

score 1 · Answer 7 · answered Apr 08 '17 at 16:35

An Introduction to Mathematical Analysis by Burkill is nice and concise, yet still flows very well and has a few good exercises. Only covers basic analysis though, nothing beyond first or maybe second year undergrad. I also like that it is smaller so you can carry it around to read on a bench or on a train.

score 1 · Answer 8 · answered Apr 08 '17 at 16:46

1

Iosevich, A View from the Top : Analysis, Combinatorics and Number Theory

answered Apr 08 '17 at 16:46

Gabriel Romon

35,428
5
65
157

score 1 · Answer 9 · answered Apr 09 '17 at 04:13

1

For an easy and fun book read Understanding Analysis by Abbott. For a tougher read that is thorough and intuitive read Real Mathematical Analysis by C.C.Pugh.I would recommend this over Rudin anyday.

answered Apr 09 '17 at 04:13

CoffeeCCD

836

score 1 · Answer 10 · edited Jun 12 '20 at 10:38

1

I recommend

Analysis by its History by E. Hairer and G. Wanner

and

A Radical Approach to Real Analysis by D.M. Bressoud.

edited Jun 12 '20 at 10:38

Community

1

answered Apr 09 '17 at 13:14

Markus Scheuer

108,315

Yes · Answer 11 · 2017-04-08T16:40:50.877

0

Your description led me to think that you want a book speaking in a tone like you are strolling with a seasoned mathematician. Then two books came to my mind:

The Way of Analysis by R. S. Strichartz;
Analysis (three volumes) by R. Godement.

The latter one is in addition entertaining, in the sense that the author is actually a comedian whose sense of humor is unique and superb.

Also check out Princeton's Companion to Mathematics; you can get inspired as you can see mathematics from the viewpoints of the experts of the experts.

edited Apr 08 '17 at 16:40

answered Apr 08 '17 at 16:37

Yes

20,719

Are these suitable for beginners and self study? – J. Deff Apr 08 '17 at 16:39
@J.Deff, That is a separate question. Whether the OP is a beginner or not cannot be told from the OP's question itself. – Yes Apr 08 '17 at 16:42
I am asking for myself – J. Deff Apr 08 '17 at 16:42
@J.Deff The former is suitable for both. He does one rather bold thing for analysis which is using $1/n$ and $1/m$ instead of $\epsilon$ and $\delta$. This in and of itself I actually find to be a good thing because it emphasizes the idea that these are not just small positive numbers but small positive numbers that change (so I set $n=1$, I ask what $m$ can be; I set $n=2$; I ask what $m$ can be now; etc.) My one very serious gripe is that at one point in the book he, without comment, abruptly interchanges the role of $n$ and $m$, leaving it that way for the rest of the book. – Ian Apr 08 '17 at 16:44
@J.Deff, Oh haha :) Got'ya wrong. I would say it depends on your current working knowledge. If you already can follow the theorem-proof style exposition then probably you can follow the books. But if you currently can only do computation well, then I am not sure about it :). – Yes Apr 08 '17 at 16:45
@EricClapton no problem mate. i am just a starter – J. Deff Apr 08 '17 at 16:46
@J.Deff My other negative comment is not a complaint at all really, but I will say that Strichartz is an absolutely atrocious reference. It is definitely meant to be read, in the sense that there is substantive content embodied in the middle of paragraphs. But I do find this nearly unavoidable; it seems to me that a math book will almost always be either a bad reference or a bad linear read or both. – Ian Apr 08 '17 at 16:47
@Ian Okay thanks – J. Deff Apr 08 '17 at 16:47

What are the best introductions on analysis, to read for leisure?

11 Answers11

Linked