(y)I offer this comprehensive course
Thanks, this looks very good. I'm thinking about possibly pursuing a PhD so this is an important class.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
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.
Rudin was the book our 1st-year maths undergrad class 1972 used. It was fine. But I think it was used as a filter..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.
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..Lol Cauchy sequences construction > Dedekind cuts IMO