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

In summary, the conversation discusses various supplementary materials for a first course in real analysis, including Velleman's proofs book, Rubin's Principles of Mathematical Analysis, and the Harvey Mudd lectures. The speakers also share their thoughts on the usefulness of the materials and offer alternative recommendations, with one speaker suggesting the Guide to Analysis as a better alternative to Rudin's book. The conversation also touches on the importance of having a background in proof-based math courses and the difficulty of Rudin's book for beginners.
  • #1
autre
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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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  • #3
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?
 
  • #4
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 It's old as hell and is pretty outdated.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.
 
  • #5
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"?
 
  • #6
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.
 

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

What is real analysis?

Real analysis is a branch of mathematics that deals with the study of real-valued functions, limits, continuity, derivatives, and integrals. It is considered to be the foundation of calculus and is used extensively in many areas of mathematics and science.

What are the prerequisites for studying real analysis?

The prerequisites for studying real analysis include a strong foundation in calculus, linear algebra, and basic proof-writing skills. It is also helpful to have some knowledge of set theory and abstract algebra.

What is the goal of preparation for real analysis?

The goal of preparation for real analysis is to develop a solid understanding of the fundamental concepts and techniques used in real analysis. This includes learning how to read and write mathematical proofs, understanding the concepts of limits and continuity, and building a strong intuition for the behavior of real-valued functions.

What are some useful resources for preparing for real analysis?

Some useful resources for preparing for real analysis include textbooks such as "Understanding Analysis" by Stephen Abbott and "Introduction to Real Analysis" by Robert G. Bartle and Donald R. Sherbert. Online resources such as lecture notes and practice problems from universities can also be helpful.

How can I best prepare for real analysis?

The best way to prepare for real analysis is to actively engage with the material. This includes reading and understanding proofs, practicing problem-solving, and seeking help from professors or tutors when needed. It is also important to stay organized and review material regularly to reinforce understanding and retention.

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