Intro to Analysis and Groups textbooks

[CAF123]

I am doing an introductory analysis and groups course next semester and I have a couple of questions about books. The course textbook is 'An introduction to Analysis' by W R Wade. Can anyone tell me if/when a new edition is expected and if not, what the current edition of the book is? I tried googling but couldn't see anything.

Also, I looked on amazon and this book has less than satisfactory reviews. This was similar to the reviews about the course textbook i had for probability, but in the end i found the book good. So just wondering: what introductory analysis/groups textbooks would you recommend, that you have perhaps found good when you did a similar course etc..

Many thanks.

 

[CAF123]

Does anyone have any recommendations at all?

 

[fourier jr]

it might just be that this sort of question comes up a lot. the contents aren't on amazon but judging by the reviews it looks like you're looking for a book that covers the same sort of stuff as small rudin. so how about
dieudonne
pfaffenberger/johnsonbaugh
bartle
kolmogorov/fomin

i've never heard of an analysis book that also does group theory, I learned that from general algebra books. i guess you could try either one by herstein. his "topics" book is a bit more advanced.

 

[CAF123]

Thanks for your reply. Sorry, I meant separate books on analysis and groups. I'll check out your suggestions now. Thanks!

 

[jgens]

I am not a huge fan of Wade, but you will learn the things that you need from there. If you really want an analysis book that covers some basic group theory, the text Fundamentals of Mathematical Analysis by P. Sally is great. It does not come out until March though.

 

[homeomorphic]

I learned it from Wade. It was okay, but kind of butchered some topics in my opinion, like the implicit function theorem, which is much more natural with better motivation.

The only other book I have read (though not cover to cover) that covers that stuff is A Radical Approach to Real Analysis, which is good for historical motivation, although perhaps, you might take the history with a grain of salt. One of the nice things here is that you learn how central uniform convergence is to the purpose of the subject, since it guarantees that your series or sequence can be integrated or differentiated term by term. You'll get that from any good analysis class to some degree, but it the point was driven home particularly well here. It conveys what analysis is good for and how it fits in with other things that you might care about, like Fourier series.

From what I have heard, if I had my memory erased and was forced to learn analysis from scratch, I would definitely go with Understanding Analysis, by Abbott. Sounds like sort of a well-motivated and intuitive approach, although this is just judging from second-hand information, since I haven't read it. And I would maybe supplement it with A Radical Approach to Real Analysis.

 

[Cod]

"Analysis: With An Introduction to Proofs" by Steven Lay is a very good beginning analysis text in my opinion. My university used it for an "analysis bridge" course and I thought it did a great job of setting the foundation for a rigorous analysis class. Check it out here: https://www.amazon.com/dp/0131481010/?tag=pfamazon01-20

I wish you would've posted this last month because I just sold my copy back to Amazon for $67. I would've given a PFer a huge discount since I was just making space on my bookshelf.

 

[A. Bahat]

Rudin is pretty standard for introductory real analysis, but is probably too slick for optimal learning. Besides, it seems that Wade works in substantially less generality than Rudin (i.e. on the real line and later in Euclidean space rather than in metric spaces). Perhaps try Lang's Undergraduate Analysis, it looks comparable and better. Disclaimer: I haven't used this book myself, but it's Lang and the table of contents looks promising.

 

[Sankaku]

From what I have heard, if I had my memory erased and was forced to learn analysis from scratch, I would definitely go with Understanding Analysis, by Abbott. Sounds like sort of a well-motivated and intuitive approach, although this is just judging from second-hand information, since I haven't read it. And I would maybe supplement it with A Radical Approach to Real Analysis.

I am a big fan of Abbott's Understanding Analysis. However, there is a very good free analysis book here:

Elementary Real Analysis (2nd Edition), B. S. Thomson, A. M. Bruckner, and J. B. Bruckner
http://www.classicalrealanalysis.info/com/FREE-PDF-DOWNLOADS.php

It takes the time to motivate the theory pretty well. The later sections (on Calculus in R^n) fall down a bit trying hard to avoid using linear algebra, but the first half is solid (except for some typos).

As you will see in lots of other threads, I recommend Pinter for anyone starting abstract algebra.

https://www.amazon.com/dp/0486474178/?tag=pfamazon01-20

 

[A. Bahat]

Oh, and for algebra, I recommend Artin.

 

[Vargo]

I used Lang's Undergraduate Analysis and I liked it at the time. My professor complained several times that he does not give the common names of many theorems (this is probably because so many theorems are attributed to the wrong names!). There are very few pictures. Generally I preferred the first half of the book to the second half because it was easier for me to understand. But that might just be because the latter half is just harder to learn.