Real analysis

If you just wanna study the stuff(no certification), there are some lecture videos posted on youtube by Haverford and other colleges. In terms of the preq, you should be familiar with the mathematical notations and some basic proof logics. Basically, the video will cover materials up to chap 6 in Rudin, which will be basic topology, sequence and series convergence, continuity, differentiation and Riemman-Stieltjes integral. Yet, I haven't seen any video covered uniform convergence, Weinstrass theorem and Lebesgue theory, which is from chap 7 - 11 in Rudin. So probably, you have to study those stuffs by yourself(those are the core materials of baby analysis).
 
Here is one offered online by UIUC through their NetMath program: Math 444: Elementary Real Analysis | NetMath

Looks like a standard first/intro course to real analysis. Little pricey, but you'll earn credit hours with UIUC (if that's something you care about) and while I haven't taken this course in particular, I did take their abstract linear algebra and thought the entire experience was wonderful.

If you're considering self-studying, I'd probably avoid Rudin (i.e., PMA) and instead consider the text by Abbott. My two cents!

Edit: The Math 444 course "is for students who do not plan graduate study (those students should take Math 447)", according to the site. While I'm almost sure the emphasis here is on students planning graduate studies in more pure math fields, if you're willing to wait it out a bit, they are adding Math 447 Real Variables (Spring 2019 syllabus linked) to the NetMath platform soon: New Courses Coming Soon | NetMath
 
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Peter M said:
Here is one offered online by UIUC through their NetMath program: Math 444: Elementary Real Analysis | NetMath

Looks like a standard first/intro course to real analysis. Little pricey, but you'll earn credit hours with UIUC (if that's something you care about) and while I haven't taken this course in particular, I did take their abstract linear algebra and thought the entire experience was wonderful.

If you're considering self-studying, I'd probably avoid Rudin and instead consider the text by Abbott. My two cents!

Edit: The Math 444 course "is for students who do not plan graduate study (those students should take Math 447)", according to the site. While I'm almost sure the emphasis here is on students planning graduate studies in more pure math fields, if you're willing to wait it out a bit, they are adding Math 447 Real Variables (Spring 2019 syllabus linked) to the NetMath platform soon: New Courses Coming Soon | NetMath
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Thanks, this looks very good. I'm thinking about possibly pursuing a PhD so this is an important class.
 
Peter M said:
Here is one offered online by UIUC through their NetMath program: Math 444: Elementary Real Analysis | NetMath

If you're considering self-studying, I'd probably avoid Rudin and instead consider the text by Abbott. My two cents!
Click to expand...

The UIUC course is using Bartle and Sherbert, which is perfectly all right. The book by Abbott is also fine. And the one by Ross. Anything except Rudin. Rudin belongs in the cemetery.
 
bigbadwolf said:
The UIUC course is using Bartle and Sherbert, which is perfectly all right. The book by Abbott is also fine. And the one by Ross. Anything except Rudin. Rudin belongs in the cemetery.
Click to expand...

Taking an undergrad real analysis course at the moment that is using Rudin and I couldn’t agree more lol! I bought Abbott to supplement. I’m sure Rudin’s text was first choice at some point in time (maybe?).
 
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bigbadwolf said:
The UIUC course is using Bartle and Sherbert, which is perfectly all right. The book by Abbott is also fine. And the one by Ross. Anything except Rudin. Rudin belongs in the cemetery.
Click to expand...
Rudin was the book our 1st-year maths undergrad class 1972 used. It was fine. But I think it was used as a filter..
Dedekind cuts!
 
bigbadwolf said:
The UIUC course is using Bartle and Sherbert, which is perfectly all right. The book by Abbott is also fine. And the one by Ross. Anything except Rudin. Rudin belongs in the cemetery.
Click to expand...
Rudin has several books.
 
2. Real and Complex Analysis (good on measure).
3. Functional Analysis

Looking back, I think the 'issue' (if that is so) is

1. Rudin's syntax uses metrics and metric spaces d(x,y) is really just x - y in one variable. So maybe premature optimization? The suitable place for d(x,y) is functional analysis. Like teaching a yellow-belt brown-belt stuff.
2. Not enough worked out examples, for maths undergrads less of an issue than say non-maths.

The wiki pages on real analysis topics are very good.
 
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When learning new stuff, I always find the notation the most difficult part. Stare at the symbols until you understand them.
 
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Peter M said:
Lol Cauchy sequences construction > Dedekind cuts IMO
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DC was a nightmare. The seats in the lecture hall were on the same level, so if you didn't get a front seat, no way to see those deltas and epsilons falling off at the bottom of the blackboard. Those students in row > 4 had no chance. I'm not kidding. Another filter :) 50 in year 1,. 6 in year 4..

The prof was very good and accessible .. one of William Feller's students at Princeton.
 
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