I am teaching undergraduate real analysis for the first time in the fall. This means that I will need to choose a textbook soon: I am looking for advice in the comments. Here are the textbooks I am considering so far:
- Understanding Analysis by Stephen Abbott
- Elementary Analysis by Kenneth Ross
- Limits by Alan Beardon.
- Introduction to Real Analysis by William Trench, which has the distinct advantage that it is free
These texts seem to be at the correct level for my students—we have used Abbott and Ross here before. I think that Beardon is intriguing—he hammers on limits at the beginning of the text, and then shows that everything else (derivatives, integrals, etc.) is a mere consequence of the notion of a limit—but I cannot find any reviews online (save for one on Amazon).
Here are some textbooks that I am not considering:
Convince me if I am wrong to disregard these (keeping in mind that Ross/Abbott is definitely the right level). In particular, I would really like to use the fabled Calculus by Spivak, but it seems more like advanced calculus than real analysis.
While I am at it: I am teaching complex analysis in the spring of next year. So far, I am considering Churchill. I would love ideas for this text, too.