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I am entering graduate school next year without any background in Complex Analysis. I have, however, taken 2 semesters of Real Analysis and a reader course in Measure Theory (using Bartle's Elements of Integration and Lebesgue Measure). I can, of course, brush up over the summer; however, I am more interested in reviewing material. That being said, would I perhaps be able to jump in to a course using the Alfhors text?

sac817
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  • you don't mention multivariable calculus or topology. The first you've probably done... – Will Jagy Oct 22 '13 at 02:04
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    I find Alfhors to be not so great as a first text in complex analysis, but a great second text. Perhaps you should look through Stein and Shakarchi for a bit to preview the material. – davidlowryduda Oct 22 '13 at 02:14
  • Indeed, I have taken Topology. We used the Munkres text. We covered the first four chapters and the basics of homotopy and the fundamental group. – sac817 Oct 22 '13 at 02:34

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When you start a course of complex analysis you want to be sure that you have a rock solid basis on complex numbers, de Moivre and solving basic complex equations. You also may want to practice Completing the Square on quadratic equations with complex coefficients. I found that preparation very useful when I did a course on complex vars. Another good thing to practice is complex numbers and locus, describing a set of complex numbers fulfilling some constraint in the form of an equation. Lastly you may look into complex transformations, like conform mapping and Möbius transformations. For the most part, the topics I mentioned do not involve complex calculus, but mastering these topics will be very useful when you take on a complex analysis course. It worked for me...Good luck

azimut
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imranfat
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