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/sci/ - Science & Math

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6967273 No.6967273 [Reply] [Original]

Rudin is considered 'the standard' when it comes to introductory Real Analysis. What are the 'classic' books for other areas of math, like differential geometry, multivariable analysis, abstract algebra etc?

>> No.6967285

It depends on what you're looking for. Some texts are good for self-study, some aren't. Some texts are just compilations of notes written in a neat fashion for experienced mathematicians to reference.

Baby Rudin really isn't that effective without a guide (i.e. teacher/professor). It's the standard (I'm guessing) because it is written nicely and has some clever proofs.

>> No.6967294

>>6967285
For Algebra, I think the classic textbook is Abstract Algebra by Herstein. Dummit and Foote is popular alternative, also.

For Differential Geometry,
Spivak's Comprehensive Introduction to Differential Geometry is the standard text (there are a few volumes).

I don't think any of the texts above are nice for self-study, however.

>> No.6967304

>>6967294
>>6967285
Oh okay. What about for self study?

>> No.6967306

>>6967294
>>6967304
I really liked Dummit & Foote for self study, actually.

>> No.6967309

>>6967285
What is the best self study book for differential geometry, abstract algebra, real analysis ?

>> No.6967310

>>6967273
>Differential Geometry after just reading baby rudin
enjoy your cancer m8

>> No.6967312

>>6967310
I'm doing Munkres' Analysis on Manifolds presently, was going to do Diff. Geometry after I finished it.

>>6967309
For Real Analysis I found Rudin pretty enjoyable for self study actually, but Ross' Elementary Analysis is an okay babied down Real Analysis book that's easily workable on one's own.

>> No.6967452

>>6967304
>>6967306
For Algebra, nothing beats Gallian (Contemporary Abstract Algebra) as an introduction. It is watered down compared to Dummit and Foote and Herstein, but this is desirable for undergraduates.

I'm not sure about a nice introductory differential geometry textbook. I just have been reading Spivak's for leisure because multiple people have recommended it to me. The math stackexchange is nice place to look for other recommendations if you think Spivak is too difficult.

>> No.6967491

>>6967452
>nothing beats Gallian

This is right. I have a many undergrad algebra texts... Gallian is the best. If you want more after that, go with Hungerford.

I've never really liked Spivak. For an intro course, I would suggest O'Neill Elementary Diff Geom.

>> No.6968550

Hogg and Craig for probability and math stats

>> No.6969034

>>6967273
*sniffs*
*pulls shirt collar*
*brushes hair*
*gestures*

>> No.6969347

>>6969034
My gott

>> No.6969482

>>6967491
Could you give some details on what you liked about O'Neill? I just finished a course using it and thought it was fairly difficult to use. No "big picture" was developed, exercises used results from exercises multiple chapters beforehand and even definitions were slipped into random paragraphs and couldn't be found in the glossary.

>> No.6969502

Differential Geometry - Introduction to Smooth Manifolds by Lee
Number Theory - Ireland & Rosen's book
Analytic Number Theory - Apostol
Algebraic Number Theory - Number Fields by Marcus
(Classical) Algebraic Geometry - Algebraic Curves by Fulton
Representation of Finite Groups - Serre's book
p-adic Numbers - Local Fields by Serre

>> No.6969508

Computational Complexity: Papadimitriou
Information Theory: Cover & Thomas

>> No.6971445

>>6967452
>>6967491
3rd for Gallian.

Brilliantly written. All the anecdotes and quotations and biographies really make this an enjoyable read.

>> No.6971465

I saved this frm hello-best guy

http://pastebin.com/z4ZyZpk0

>tfw he's not here anymore

>> No.6971723

>>6971465
>hello-best guy
Who could forget the /sci/ guy who actually knew something?

>> No.6971778

>>6967273
Dummit and Foote is stellar for abstract algebra. I as well recommend Bartle`s `Introduction to Real Analysis` for a good self-study book that you can read on your own (then you can move on to Rudin).