# Tips for understanding and effectively studying mathematical analysis

Just like the aim of elementary linear algebra is to understand the relations of linear maps and to convert mappings (matrices) into Jordon canonical forms to simplify their relations to understand them better (at least this is my understanding of the subject), from what I've been learning, mathematical analysis is studied in order to rigorously establish the fundamentals of calculus.

However, while I may (or may not...) understand the objective of the discipline, I am finding significant trouble being able to solve any question (especially evident given my midterms this week), unless they are very basic. I believe this is due to my lack of 1) identifying the methodology to solve the given question, and 2) laying out a proof utilizing said methodology that is mathematically sound and sufficiently rigorous.

Unfortunately, the problem ultimately seems to reside with my lack of understanding. The book I am currently using for my course is Baby Rudin. The included proofs are extremely succinct, leaving a lot to fill between the lines, not helping my case at all.

Are there any supplementary books that I could be looking into to help me study analysis better? What would be some tips for approaching the subject matter, and tackling questions in analysis courses?

• Maybe this post will help a bit? – Adam Thompson Oct 24 '15 at 19:55
• @AdamThompson Thank you! I will definitely read the books listed. – user245273 Oct 24 '15 at 19:57
• I liked Jerrold E. Marsden, "Elementary classical analysis". I find Rudin much too succinct for my abilities. I need intuition. – copper.hat Oct 24 '15 at 19:57
• I survived Baby Rudin as did the late Jerry Marsden (who was in the year ahead of me and considered even then a star). Certainly get his book. A cheaper version you might like (cheap = free) can be found on our website classicalrealanalysis.com. This was meant to take better care of the students than Rudin ever meant to. But don't be discouraged: 50% of every class in the subject I ever taught were in a state of anxiety and frustration for a while. – B. S. Thomson Oct 25 '15 at 22:26

• After reading theorems, try to replicate the proofs, but not in the sense that you will memorize it line by line. Take your time and study why sentence $x$ or result $y$ is there, chances are those are very important.