Introduction to analysis

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1. michaericalriboJan 2023
   In my experience, the best way to get better at math is to do a lot of it. Find some book that's "good enough" for some topic you're interested, and work many many problems from the book. You'll learn about the topic, but more importantly you'll learn problem solving skills. I recommend working the problem until you're sure the answer is right -- in grad school problem sets didn't have answers you could check, and full understanding was necessary to get the problem sets correct.

   For me, a watershed book was Introduction to Analysis by Rosenlicht [1]. Proof-based, very "mathy", small and compact (so to speak) but with a massive scope. A great introduction to a really important topic, and it'll put your brain through its paces.

   Again, I recommend working nearly every problem.

   [1] https://www.amazon.com/Introduction-Analysis-Dover-Books-Mat...

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2. ubasuNov 2010
   Here's my list:

   Basic

   1. Chapter Zero (Carol Schumacher) 2. Naive Set Theory (Paul Halmos)

   Linear Algebra

   1. Finite-Dimensional Vector Space (Paul Halmos) 2. Linear Algebra Done Right (Steven Axler)

   Real Analysis

   1. Real Mathematical Analysis (Charles Pugh) 2. Introduction to Analysis (Maxwell Rosenlicht)

   Algebra

   1. A first course in abstract algebra (John Fraleigh)

   These books are better for self-directed reading compared to some of the classics like Rudin or Herstein. These should keep you busy for a while.

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