Context: I am an assistant professor at a small college in the US.

Next semester I am teaching real analysis for the first time, and we are using Steven R. Lay's book. (It also happens to be the same text that I used at my undergraduate institution.) I like to write my own homework assignments, and I sometimes draw on other texts for inspiration.

That brings me to my question: What are affordable and level-appropriate texts that I could use to supplement Lay's book? I have my analysis texts from graduate school, but I am aiming for something softer than Baby Rudin.

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    $\begingroup$ If I understand correctly, you're looking for a supplement to assist you as the instructor, instead of something along the lines of Alcock's How to Think About Analysis, which is a supplement for students taking a first real analysis course. $\endgroup$
    – J W
    Commented Jun 28, 2018 at 19:05
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    $\begingroup$ I would suggest going to a college library (maybe at a bigger school than yours) and just scanning the textbooks on the shelf. But try your library first (maybe it has something). A more specific suggestion is Schaum's Advanced Calculus. $\endgroup$
    – guest
    Commented Jun 28, 2018 at 19:35
  • $\begingroup$ @guest: Hey, that's my typical comment to something like this! Anyway, besides just going to a library (especially for slightly older texts, say from the 1950s through the 1980s that might be before most internet book recommendators' experiences and thus extremely under-represented in internet searches), try searches like this, where you include the name of an author of a well known text similar to what you want. I've mentioned quite a few middle-to-upper level undergraduate real analysis books in my posts (continued) $\endgroup$ Commented Jun 28, 2018 at 19:59
  • $\begingroup$ over the years, but I don't believe I've ever made a thorough bibliographic list of such books similar to many of the other bibliographies on more specialized topics I've posted over the years (probably because it would simply be too daunting of a task), but possibly some of the items I posted in my answer to Lesson plan to self-teach real analysis to student with comp-sci background could be of use. $\endgroup$ Commented Jun 28, 2018 at 20:04
  • $\begingroup$ Awesome, thank you for all the recommendations. I'll look into all of these suggestions. $\endgroup$ Commented Jun 30, 2018 at 1:41

2 Answers 2


Understanding Analysis by Stephen Abbott is a very gentle and solid introduction to undergraduate analysis. Good exercises, too.

  • $\begingroup$ Oh, but I do have a beef with the definitions in this book! Some of the quantifiers are implicit or ambiguous, which is a real shortcoming in an introduction to analysis. $\endgroup$ Commented May 10, 2019 at 17:08
  1. Bartle and Sherbert, Introduction to Real analysis, Wiley

  2. A. Kumar and S. Kumaresan, A Basic course in Real analysis, CRC Press

Both these books are at introductory level for Real analysis course. You will find exercises in the second book particularly useful in developing your own exercises.


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