Posts Tagged ‘Textbooks’

Abbott wins

March 30, 2011

Recall that I am teaching real analysis next semester, and I asked for help in deciding which textbook to use. I started by considering texts by Abbott, Beardon, Ross, and Trench, but I started considering Strichartz due to Adam Glesser’s comment.

First, I have decided to dive head-first into the inverted/flipped classroom and screencasting pool in the fall. This just seems like it makes sense: the professor should be around the students when they are doing the harder work, not the easier (and more passive) work.

With this in mind, I wanted a textbook that would complement this system well. Here are my thoughts on each:

  1. Strichartz is too expensive. I did not spend much time considering it (sorry, Adam!) because of the price.
  2. Beardon is too technical and too expensive, although I like his attempt at integrating all of the ideas.
  3. Trench is the right price (it would be about $25 to print and bind a copy for a student), but there is too little exposition—t seemed like he basically hopped from theorem to theorem. Since I am going to have my students read the text (in addition to screencasts), I wanted a readable book.
  4. Ross is a reasonable price and reasonably readable, but I do not like his treatment of continuity (he defines it in terms of sequences of points).
  5. Abbott is left standing. It is a reasonable price (though not the cheapest), it is the most readable, and I like his motivating questions. I have heard complaints about the amount of typos, but I can fix this by making this part of my first homework assignment.

So Abbott wins. Thanks for your input.

Undergraduate Real Analysis

February 7, 2011

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:

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:

  • Rudin—too advanced
  • Pugh—too advanced
  • Spivak—too calculus-y, not analysis-y enough

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.