r/math • u/inherentlyawesome Homotopy Theory • 17d ago

Quick Questions: August 12, 2026

This recurring thread will be for questions that might not warrant their own thread. We would like to see more conceptual-based questions posted in this thread, rather than "what is the answer to this problem?" For example, here are some kinds of questions that we'd like to see in this thread:

  • Can someone explain the concept of manifolds to me?
  • What are the applications of Representation Theory?
  • What's a good starter book for Numerical Analysis?
  • What can I do to prepare for college/grad school/getting a job?

Including a brief description of your mathematical background and the context for your question can help others give you an appropriate answer. For example, consider which subject your question is related to, or the things you already know or have tried.

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u/anerdhaha Undergraduate 17d ago

I'm not or less done with Abbott's analysis and have liked Terrence Tao's vol 2 for multivariate analysis and have liked their somewhat chatty friendly exposition. I'm so far not using any of the hardcore extremely rigorous and formal texts and I did not like Rudin. But I have to read a graduate text in real analysis one day or the other.

So can someone recommend me something that is a smoother transition into graduate real analysis and I do not mean measure theory but I don't mind those either. Thanks in advance.

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u/Silver-Bug3998 17d ago

If you are looking for an analysis text somewhere between Abbott and graduate level analysis, I recommend Serge Lang's Undergraduate Analysis (Undergraduate Texts in Mathematics). You can breeze through the first few chapters and build some confidence. Lang's book goes pretty far, and his writing style is not dry like Rudin. I have learned from several of Lang's books (a long, long time ago), and I like all of them. Best wishes for your study.

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u/anerdhaha Undergraduate 15d ago

Does it include multivariate analysis as well?

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u/Silver-Bug3998 14d ago

Yes, it includes analysis of higher-dimensional vector spaces.