What's a good book for Real Analysis independent studying?

[fleshette]

Planning to do self study in Real Analysis before I go to grad school in the Fall. Anyone have any favorites? What about user-friendly books?

 

EDIT: A book with complete solutions (or easy access to a complete manual) is also wanted!

[TheBrothersKaramazov]

User friendly?? I personally love

 

Stephan Lay's "Analysis: With an introduction to proof".

 

This was a nice introduction to future analysis work.

[polkaparty]

"Principles of Mathematical Analysis" 3rd edition (1974) by Walter Rudin is often the first choice. This book is lovely and elegant, but if you haven't had a couple of Def-Thm-Proof structured courses before, reading Rudin's book may be difficult.

 

A nice book I recommend for introductory analysis is "Understanding Analysis" (2002) by Stephen Abbott. It covers only typical first semester analysis material (less than Rudin), but it is extremely well written. Every chapter begins with an interesting discussion of problems and examples which motivate the various theorems and definitions.

 

Another good book similar to Rudin's is "Introduction to Analysis" (1968) by Maxwell Rosenlicht. This book parallels Rudin for the most part, and is slightly easier. Also, it costs only about $10, compared to Rudin: $150 hardcover, $75 soft and Abbott: $40.

[econandon]

abbott's understanding analysis is good

[kartelite]

We used Bartle. It was pretty good.

[econandon]

another good book is Problems and Solutions for Undergraduate Analysis

 

use it with another analysis book, because it is just lots of problems and solutions. without a teacher to correct your proofs, you want to be able to check your own work. a big part of the whole point of analysis is write proofs well.

[reactor]

guys, guys, we are looking for a book for self-study. baby rudin, rudin, royden, apostol, taylor etc etc have all very few (if any at all_ worked out examples.

 

fleshette: order now Mathematical Methods and Models for Economists by Angel de la Fuente. 1 copy for youserf and 1 copy for your best econ friend. :grad:

(i sent a copy as a gift to my gf. am'I too geeky?) :whistle:

 

I cannot say enough for this book. Just notice that contains complete solutions (not just out-of-nowhere answers, not just cryptic hints) to all problems in the book! (not to mention that costs less than $50! boy, de la Fuente is a true academic!)

 

review from amazon:

This an excellent book primarily for students in Economics either PhD or advanced Masters and/or students interested in Economics and who are coming from "rich in maths" fields. It contains a rigorous treatment of the mathematics used in graduate economics. The title "Mathematical Methods" may be somewhat misleading since the book adopts a rather rigorous approach instead of the "cook-book" approach. In many parts the book cannot be distinguished from a pure mathematics book but it includes plenty economic applications and examples.

 

One of the things I really loved in this book is that it is "self-contained"; at the end of the book you will find complete solutions (not merely answers) of all problems (and not just the odd/even ones). However make no mistake, this is an advanced book and for students with not strong background in maths I would recommend the the sequence (roughly): Alpha C. Chiang "Fundamental Methods of Mathematical Economics" after this, Simon & Blume "Mathematics for Economists" and then de la Fuente's book.

[econandon]

 

fleshette: order now Mathematical Methods and Models for Economists by Angel de la Fuente. 1 copy for youserf and 1 copy for your best econ friend. :grad:

 

yeah its good but its not a real analysis book, that is a complete treatment of what is typically covered in undergraduate analysis. it has topics covered in analysis but it leaves out a lot. fleshette was requesting an analysis book.

[reactor]

econandon: you're right. de la Fuente does not cover series or power series for example.

 

 

for an introduction:

Fundamentals of Mathematical Analysis by Rod Haggarty

which has complete solutions to most problems in the back of the book.

 

for further stuff:

Undergraduate Analysis by Serge Lang (there is also available a low-price student-version with chinese cover available from ebay) and its solutions manual: Problems and Solutions for Undergraduate Analysis by Rami Shakarchi and Serge Lang

[JAlfredPrufrock]

I liked "The Way of Analysis" By Robert S. Strichartz. He spends alot of time building up intuition for his proofs, although there are some proofs where he kinda waves his hands, and viola, but overall I thought it was usefull.

[reactor]

there are some proofs where he kinda waves his hands, and viola,

 

 

I totally agree on that.

[chauchau]

Yeah, strichartz is good for an introduction, b/c it's so wordy. I like Browder for a slightly more advanced, and much more concise, treatment.

[fleshette]

Anymore opinions? I'm only interested in buying one or two books and so far everyone has recommended many different books..

[Jhai]

It'd probably be a good idea to ask your math or econ professors, since they're the ones who know either the subject matter or how you're going to need it in grad school.

[EconChump]

i would not recommend asking professors anything... most of them are so out of touch with reality and how hard it can be to actually learn something new. i think asking people on a forum for advice is precisely the best way to go about it.

 

i have just ordered abbott and de la fuente. screw the money.

[apropos]

My undergraduate Analysis course was based on Pugh. I like this book but it's not perfect. The coolest thing about it is that it collects all of the point-set topology concepts into a single, compact (no pun intended) section that's easy to use for review and reference, and it covers somewhat more of point-set topology concepts than others. The section on the function spaces is a very good one too. My course covered only the first four sections, and then I skimmed over the rest of this book. I got a feeling that some of the proofs in the later sections, such as about analysis in R^n section, were too 'slick' and the author takes a bizarre approach towards the Lebesgue integral. He defines it as the measure of a function's undergraph, then derives all the usual properties, then shows than it's equivalent to the usual definition. This was two years ago and now I am reviewing real analysis using Serge Lang's book. I think this text is terrific. Unlike many other texts, it seems like the author is setting you up to study real analysis in R^n from the beginning, and he covers some subtle but important theorems that others don't (for example, did you know that _all_ possible norms in the finite dimensional vector spaces are equivalent to each other or how to Taylor expand a multivariable function?)

[phdphd]

I recommend Efe Ok's Real Analysis With Economic Aplications. It covers not only analysis in the real line but other topics that will be quite useful for you afterwards (fixed poin theorems, correspondences etc). Besides, the guy really has a good sense of humor, it's funny reading the book. Until recently it was possible to download the chapter's from the author's website but it's not possible anymore (http://homepages.nyu.edu/~eo1/). Anyway, if you want I can send you the whole book. Just PM me.

[JAlfredPrufrock]

I recommend Efe Ok's Real Analysis With Economic Aplications. It covers not only analysis in the real line but other topics that will be quite useful for you afterwards (fixed poin theorems, correspondences etc). Besides, the guy really has a good sense of humor, it's funny reading the book. Until recently it was possible to download the chapter's from the author's website but it's not possible anymore (http://homepages.nyu.edu/~eo1/). Anyway, if you want I can send you the whole book. Just PM me.

 

Did he get rid of the Measure theory notes too?

[Teazer]

although there are some proofs where he kinda waves his hands, and viola......

 

a musical instrument appears??

[Gogol]

a musical instrument appears??

 

That's kind of cheesy, but I laughed :D

[Prometheus_Econ]

I recommend Efe Ok's Real Analysis With Economic Aplications.

Yes, this is an excellent book because it is rigorous but puts a lot of emphasis on the topics that are really used in economic theory. It's at a higher level than any of the "math camp" books, and I would recommend anyone wanting to do theory to look at it. I'm eagerly awaiting the probability book by him to come out.

[Antichron]

I actually somewhat enjoyed the book "Fundamental Ideas of Analysis" by Michael Reed. It is written in a much more clear manner than any of my other analysis books. (I have Rudin, Kolmogorov and Fomin, Haaser and Sullivan, and Folland.) Also, Terence Tao (who recently won the field's medal) has a great set of notes available on his websites:

 

http://www.math.ucla.edu/~tao/resource/general/131ah.1.03w/

http://www.math.ucla.edu/~tao/resource/general/131bh.1.03s/

 

As with most math classes, the best way to learn the material is to do problems. Someone else suggested a book that contains problems and solutions, which could be good. Alternatively, if you want to learn using Reed, my solutions to two quarters worth of problem sets are available on my website at:

 

http://www.pareto-optimal.com/winter2005/math131a.htm

http://www.pareto-optimal.com/winter2005/math131b.htm

 

I make no guarantees that any of my solutions are correct, but they are detailed (often pedantically so) and could potentially be of some use. Good luck with analysis!

[fleshette]

econandon: you're right. de la Fuente does not cover series or power series for example.

 

 

for an introduction:

Fundamentals of Mathematical Analysis by Rod Haggarty

which has complete solutions to most problems in the back of the book.

 

for further stuff:

Undergraduate Analysis by Serge Lang (there is also available a low-price student-version with chinese cover available from ebay) and its solutions manual: Problems and Solutions for Undergraduate Analysis by Rami Shakarchi and Serge Lang

 

 

Maybe a stupid question: do I need to know this stuff to get through the first year? Can I just read de la Fuente and be good?

 

I don't want to waste time on what's not important...

[Stuy]

Guys, Ok's book is great and he is awesome teaching. At least that is what my classmates agree upon. But as he says it his book is not an introduction to Real Analysis. It somehow assumes you've already taken a serious introduction to the topics and it intends to be an introduction to advanced real analysis. Here at NYU that book is used after Stacchetti covered introduction to Real Analysis at the level of Rudin in his class. So even though I think that the book is really good I wouldn't start there. And just so you know the Probability book is being revised right now as he is currently teaching those topics.

[grahamcoxon]

I actually somewhat enjoyed the book "Fundamental Ideas of Analysis" by Michael Reed. It is written in a much more clear manner than any of my other analysis books. (I have Rudin, Kolmogorov and Fomin, Haaser and Sullivan, and Folland.) Also, Terence Tao (who recently won the field's medal) has a great set of notes available on his websites:

 

http://www.math.ucla.edu/~tao/resource/general/131ah.1.03w/

http://www.math.ucla.edu/~tao/resource/general/131bh.1.03s/

 

As with most math classes, the best way to learn the material is to do problems. Someone else suggested a book that contains problems and solutions, which could be good. Alternatively, if you want to learn using Reed, my solutions to two quarters worth of problem sets are available on my website at:

 

http://www.pareto-optimal.com/winter2005/math131a.htm

http://www.pareto-optimal.com/winter2005/math131b.htm

 

I make no guarantees that any of my solutions are correct, but they are detailed (often pedantically so) and could potentially be of some use. Good luck with analysis!

 

Thank you for the notes and the solutions. What's Reed book you are refering to?

 

EDIT:

As usual, I found the answer following your link (Fundamental Ideas of Analysis). Sorry for the useless post.