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Real Analysis

Anonymous Fri 22 Apr 15:59:19 2022 No.14418426 View Reply Original Report

Quoted By: >>14418430 >>14418432 >>14421754 >>14421823 >>14422941 >>14425146 >>14426447

Any decent real analysis books suitable for self study that don't assume previous exposure to calculus?

Anonymous

Anonymous Fri 22 Apr 2022 16:00:53 No.14418430 Report

Quoted By: >>14418944

>>14418426
I hope not.

Anonymous

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Anonymous Fri 22 Apr 2022 16:01:56 No.14418432 Report

Quoted By: >>14419875

>>14418426

Anonymous

Anonymous Fri 22 Apr 2022 19:44:27 No.14418944 Report

Quoted By: >>14418959

>>14418430
Why not?

Anonymous

Anonymous Fri 22 Apr 2022 19:50:45 No.14418959 Report

Quoted By: >>14419024 >>14421754

>>14418944
Just take calculus bro there are no shortcuts just learn it

Anonymous

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Anonymous Fri 22 Apr 2022 20:24:31 No.14419024 Report

Quoted By: >>14419337

>>14418959
Any books that approach Calculus in a more rigorous manner then?

Anonymous

Anonymous Fri 22 Apr 2022 22:16:25 No.14419337 Report

Quoted By: >>14421169

>>14419024
spivak

Anonymous

Anonymous Sat 23 Apr 2022 02:22:26 No.14419875 Report

Quoted By:

>>14418432
/thread

Anonymous

Anonymous Sat 23 Apr 2022 03:12:58 No.14420008 Report

Quoted By:

Terrence Tao's RA books are unironically the best RA textbook. You may or may not like his research, but his notes are based.

Anonymous

Anonymous Sat 23 Apr 2022 03:58:09 No.14420072 Report

Quoted By: >>14422395

real analysis was the class that dropped my self-esteem and made me realize I'm not cut out for upper level mathematics.

Anonymous

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Anonymous Sat 23 Apr 2022 07:36:58 No.14420327 Report

Quoted By: >>14420422 >>14421175 >>14421222 >>14423732 >>14426457

any opinions on this one?

Anonymous

Anonymous Sat 23 Apr 2022 08:44:09 No.14420422 Report

Quoted By:

>>14420327
You'll get wrecked

Anonymous

Anonymous Sat 23 Apr 2022 14:50:15 No.14421169 Report

Quoted By:

>>14419337
This

Anonymous

Anonymous Sat 23 Apr 2022 14:52:24 No.14421175 Report

Quoted By: >>14423632

>>14420327
If you really understand everything here, you could cram a few other concepts and be ready for graduate school.

Anonymous

Anonymous Sat 23 Apr 2022 15:11:51 No.14421222 Report

Quoted By:

>>14420327
Not for self-study. It's meant to be used in conjunction with Harvard's Honors Class in the subject.

Anonymous

Anonymous Sat 23 Apr 2022 18:23:29 No.14421754 Report

Quoted By: >>14421757 >>14421788

>>14418426
>>14418959
>there are no shortcuts
Hate to be this guy but "calculus" as in "dumbed down analysis" is only a thing in the english speaking world. In Europe, real analysis is the first thing, along linear algebra, that you learn in uni as a math student.
So if you want to skip calculus, search for some german analysis textbooks, some of them are translated to english.

Anonymous

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Anonymous Sat 23 Apr 2022 18:26:47 No.14421757 Report

Quoted By: >>14421840 >>14422427

>>14421754
Any german books you can recommend for self study?

Anonymous

Anonymous Sat 23 Apr 2022 18:39:19 No.14421788 Report

Quoted By: >>14421801

>>14421754
european high schoolers learn about cauchy sequences? yeah i totally buy this

Anonymous

Anonymous Sat 23 Apr 2022 18:45:45 No.14421801 Report

Quoted By:

>>14421788
Guess he was talking about university.
Americans still get Analysis-light in the form of calculus before eventually beginning Real Analysis. Do english speaking countries even do Real Analysis during a Bachelors degree?
In Germany you begin with Real Analysis the moment you step into university and start a math or math related undergraduate.

Anonymous

Anonymous Sat 23 Apr 2022 18:53:23 No.14421822 Report

Quoted By:

Rudin innit

Anonymous

Anonymous Sat 23 Apr 2022 18:53:54 No.14421823 Report

Quoted By:

>>14418426
Real Variables by Claude W. Burrill and John R. Knudsen

Anonymous

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Anonymous Sat 23 Apr 2022 19:06:39 No.14421840 Report

Quoted By:

>>14421757

Anonymous

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Anonymous Sat 23 Apr 2022 19:08:54 No.14421847 Report

Quoted By: >>14422421

for real

Anonymous

Anonymous Sat 23 Apr 2022 23:04:22 No.14422395 Report

Quoted By:

>>14420072
Same. I just failed my first real analysis exam yesterday.

Anonymous

Anonymous Sat 23 Apr 2022 23:12:31 No.14422421 Report

Quoted By:

>>14421847
burn is great

Bernd

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Bernd Sat 23 Apr 2022 23:14:33 No.14422427 Report

Quoted By:

>>14421757

Anonymous

Anonymous Sun 24 Apr 2022 00:47:06 No.14422671 Report

Quoted By: >>14423634 >>14423960

why are people saying "just learn calculus"? you can prove all of calculus with Real Analysis, starting from Real actually sounds more fun.

Anonymous

Anonymous Sun 24 Apr 2022 02:05:35 No.14422941 Report

Quoted By:

>>14418426
Just buy Mathematics for physicists by Altland, use that as a base for real analysis by Bartle, it'll be quick and easy.

Anonymous

Anonymous Sun 24 Apr 2022 08:50:36 No.14423632 Report

Quoted By:

>>14421175
I don't, I've just found its first chapters on diff calculus and topology pretty approachable and it looks relatively self-contained excluding chapter on differential equations

Anonymous

Anonymous Sun 24 Apr 2022 08:51:56 No.14423634 Report

Quoted By:

>>14422671
you need calculus to do computations and you need it for physics and engineering. math without science is WORTHLESS!

Anonymous

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Anonymous Sun 24 Apr 2022 08:58:28 No.14423640 Report

Quoted By: >>14423958 >>14424014 >>14425245

Is Rudin ok for self-study?

Anonymous

Anonymous Sun 24 Apr 2022 10:31:35 No.14423732 Report

Quoted By: >>14425131

>>14420327
>Shlomo Sternberg
I don’t even hate Jews but this sounds like a parody name lmao

Anonymous

Anonymous Sun 24 Apr 2022 13:08:55 No.14423958 Report

Quoted By:

>>14423640
Look for online lectures that use the book. I've rarely seen people make good progress just by reading the textbooks. Most successful self-taught people that I've seen use lectures along with the book.

Anonymous

Anonymous Sun 24 Apr 2022 13:11:42 No.14423960 Report

Quoted By:

>>14422671
You need to get used to higher levels of abstraction over time, otherwise you won't understand what you are doing or what's the point of the higher levels of generality.

Anonymous

Anonymous Sun 24 Apr 2022 13:34:31 No.14424014 Report

Quoted By:

>>14423640
Absolutely not.
It's horrendous in that regard and anyone telling you otherwise is memeing.

Anonymous

Anonymous Sun 24 Apr 2022 13:44:02 No.14424044 Report

Quoted By:

i would start out with this video as a calculus refresher
https://www.youtube.com/watch?v=KWN1RRSkUAc

Anonymous

Anonymous Sun 24 Apr 2022 20:40:29 No.14425131 Report

Quoted By:

>>14423732
you like dick in your ass, we get it

Anonymous

Anonymous Sun 24 Apr 2022 20:44:03 No.14425146 Report

Quoted By:

>>14418426
OP, I just thought about your question and remembered that "Understanding Analysis" by Stephen Abott could be good for you. It is considered a gentle introduction to real analysis, unlike Baby Rudin and other such books. It works completely (or mostly, I have no idea) on the context of the real line, which is what you would want (it would be just stupid to want a book that treats R^n and even more general metric spaces when you haven't even taken single variable calculus). I think that it is considered good for self-studying, but I am not sure. Check it out and see if you like it. I have no idea if it assumes knowledge of calculus already but the book is as easy as you will find them.

Anonymous

Anonymous Sun 24 Apr 2022 21:20:56 No.14425238 Report

Quoted By:

Kolmogorov and Fomin Theory of functions and Functional Analysis

Anonymous

Anonymous Sun 24 Apr 2022 21:23:25 No.14425245 Report

Quoted By:

>>14423640
Absolutely but maybe not as the only resource, ask for intermediate steps on the internet or look at lectures ideally based on the book. IMO you should power through it and learn to learn

Anonymous

Anonymous Mon 25 Apr 2022 07:49:06 No.14426447 Report

Quoted By:

>>14418426
No you lazy bum. Learn Calculus. Master Calculus. And then read Rudin. If you understand calculus well enough, analysis should come easily to you.

Anonymous

Anonymous Mon 25 Apr 2022 07:58:19 No.14426457 Report

Quoted By:

>>14420327
I read through roughly half of it last year despite its title it's not actually a calculus book, but an advanced book on analysis. It covers analysis in many variables in the more general setting of vector spaces, including infinite dimensional ones, if you haven't studied real analysis in $/mathbb{R^n}$ I'd forget it due to how absract it is. The ladder half covers manifolds with charts to vectors spaces (it sticks to finite dimensional ones though) and is a bit sloppy from what I read, and its chapter on meassure theory is nonstandard. Also the notation is really wierd.

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