I'm about to teach a graduate level one-semester complex analysis course. The audience will be very good advanced undergraduate students and first year graduate students.

I don't want to use Lang or Ahlfors.

I was considering "Complex Analysis" by Elias Stein and Rami Shakarchi or possibly "Complex Analysis" by Eberhard Freitag and Rolf Busam. Does anyone have any experience teaching courses with those books, particularly for a one semester course with the audience I mentioned above?

Thanks, Alan

  • $\begingroup$ University students shouldn't use one book, even worse graduate students. $\endgroup$ – conditionalMethod Oct 14 '19 at 23:44
  • $\begingroup$ From a student perspective, during my undergrad I used Complex Variables and Applications, Brown and Churchill. While apparently being geared towards engineers, in my opinion it's a fantastic text to use as a secondary source at least. $\endgroup$ – Hendrix Oct 14 '19 at 23:48
  • $\begingroup$ @conditionalMethod Unfortunately most textbooks are expensive. It isn't unusual that a student cannot afford two textbooks on the same subject. $\endgroup$ – user1551 Oct 15 '19 at 4:39
  • $\begingroup$ My students will already know complex analysis at the level of Brown and Churchill. So, I'm aiming a little higher than than. $\endgroup$ – Alan C. Oct 15 '19 at 19:02
  • $\begingroup$ The first comment about students not using one book seems principally intended to demonstrate arrogance rather than intelligence. $\endgroup$ – Alan C. Oct 15 '19 at 19:04

Complex Made Simple by David C. Ullrich is excellent.

To quote from an MAA review:

This is an excellent book for a first-year graduate student doing a course in complex analysis. Instructors will like it as well, but students will enjoy and profit from Ullrich’s careful explanation of why the theorems work the way they do and also sometimes why seemingly nice ideas that promised to work do not (but often can be patched so that they do).

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  • $\begingroup$ Why the downvote? $\endgroup$ – lhf Oct 15 '19 at 0:42
  • $\begingroup$ Yeah I like this book. I took it in a graduate complex course. $\endgroup$ – AmerYR Oct 15 '19 at 0:51
  • $\begingroup$ @lhf it could be because you don’t seem to address the question asked in the body of the post (although I’m not disputing the relevance of a good recommendation and it would make a good comment), or maybe someone is trying to discourage answering a question of the form “help me pick a book to teach with” since it is probably off-topic. (Either way it was not me.) $\endgroup$ – rschwieb Oct 15 '19 at 2:18
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    $\begingroup$ I have downvoted this answer because I do not believe that it really answers the question. Yes, it provides a reference, but it does not give any indication as to why the cited text is a choice for a graduate level course, nor how it compares to the other texts cited. If you expand your answer into something a bit more useful, I would be happy to retract my vote. $\endgroup$ – Xander Henderson Oct 15 '19 at 11:34
  • $\begingroup$ David Ullrich, thank you for the suggestion. My library has a copy and I will definitely take a look at it. $\endgroup$ – Alan C. Oct 15 '19 at 18:55

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