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How to study from a Real Analysis textbook like this

  1. Oct 17, 2016 #1
    I am taking a class in RA, where we're using Bartle/Sherbert. Since I have studied few chapters from it in the summer before, I decided to take a look at a more rigorous book, like baby rudin, but since many have advised against that book, I turned to Pugh's real mathematical analysis, but I am confused a little bit about the book.
    Unlike every textbook that I have studied, this book presents the material in the chapter to give you the absolute minimum you need to solve the exercises or maybe less ( with very few examples, no problems /section) then at the end of the chapter it gives you a ton of exercises, but the problem is, these exercises are mostly theoretical, and almost non of the usual drill exercises that enforces the theory, and some of the problems in Pugh are sections in bartle/sherbert, like the monotone convergence property.
    So my questions are, how to study (effectively) from a textbook like this, and how to know which problems to solve? ( in chapter 2, about topology, there are 152 exercise at the end of the chapter, non of them is a routine calculation, then 15 prelim problems from UCBerkely, thus a total of 167 problems), and where to find routine problems that enforces the basic def/theorems ?
  2. jcsd
  3. Oct 17, 2016 #2


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    For self study and exercises to practice on, I have always been a fan of the Schaum's Outline series. They have one on real analysis. The problem of matching it's content to another book is something I have never attempted, but the content is fairly standard.
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