What Are the Best Supplementary Materials for a Beginner's Real Analysis Course?

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For those preparing for an introductory real analysis course, several supplementary materials are recommended. Velleman's proofs book is noted as a good resource, although some participants express skepticism about its effectiveness for real analysis, suggesting it may focus more on sequences and series. The Rudin book is heavily criticized, with claims that it is outdated and not suitable for beginners, especially for those unfamiliar with proofs. Instead, "Guide to Analysis" is suggested as a potentially better alternative. Additionally, watching online lectures from Harvey Mudd College is mentioned as a helpful resource. Participants emphasize the importance of understanding the foundational concepts of real analysis rather than getting bogged down in complex texts. Overall, the discussion highlights the need for accessible materials that align with the introductory nature of the course.
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I'm likely taking an introductory real analysis course in the fall, and I was wondering what supplementary material I should look into. I'm working my way through Velleman's proofs book, what else would you recommend as a supplement to a first course in RA?
 
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I've also watched a few videos of those Harvey Mudd lectures. How well are you following the Rudin book? Have you had a proofs course before?
 
autre said:
I'm likely taking an introductory real analysis course in the fall, and I was wondering what supplementary material I should look into. I'm working my way through Velleman's proofs book, what else would you recommend as a supplement to a first course in RA?

Velleman book is good. But, real analysis is just knowing how to set up the question. I doubt you will do any real analysis if you need to work through Vellemans book. You probably are doing more sequences and series. So you don't worry.

I only really did Real analysis in my second year and that was with complex analysis joined together.

I've also watched a few videos of those Harvey Mudd lectures. How well are you following the Rudin book? Have you had a proofs course before?

Don't even waste your time trying to read Rudin book. You probably won't need it as it's an introduction to real analysis course. Secondly, you would fail badly even to read the first chapter. Literally if you need to read a book on how to prove stuff then this isn't your book.

Personally I think Rudin book is god awful. It's old as hell and is pretty outdated. Guide to Analysis is probably better for you if you want to buy a book.
 
I doubt you will do any real analysis if you need to work through Vellemans book.

I'm only using Velleman to catch up to the students that might have taken proof-based math classes before.

Personally I think Rudin book is god awful. It's old as hell and is pretty outdated. Guide to Analysis is probably better for you if you want to buy a book.

Thanks for the advice. Who's the author of "Guide to Analysis"?
 
autre said:
I've also watched a few videos of those Harvey Mudd lectures. How well are you following the Rudin book? Have you had a proofs course before?

I am reading, making notes and try to prove any theorem he doesn't. I am almost done with the first two chapters. Didn't do many end of chapter problems though. I had proofs in other courses but not any proof heavy course.

simplicity123 said:
Don't even waste your time trying to read Rudin book. You probably won't need it as it's an introduction to real analysis course. Secondly, you would fail badly even to read the first chapter. Literally if you need to read a book on how to prove stuff then this isn't your book.

Personally I think Rudin book is god awful. It's old as hell and is pretty outdated. Guide to Analysis is probably better for you if you want to buy a book.

Are you sure you are thinking about the same book. I am talking about the blue cover Rubin not the green graduate analysis text. This one seems pretty standard for a first course in real analysis.
 
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Yesterday, 9/5/2025, when I was surfing, I found an article The Schwarzschild solution contains three problems, which can be easily solved - Journal of King Saud University - Science ABUNDANCE ESTIMATION IN AN ARID ENVIRONMENT https://jksus.org/the-schwarzschild-solution-contains-three-problems-which-can-be-easily-solved/ that has the derivation of a line element as a corrected version of the Schwarzschild solution to Einstein’s field equation. This article's date received is 2022-11-15...

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