Amazon.com: Complex Analysis (Princeton Lectures in Analysis): Elias M. Stein, Rami Sha... - 0 views
-
In reviewing a textbook, one should consider the background of the book's audience. I believe that this text by Stein and Shakarchi on complex analysis is outstanding, and is appropriate for a student who has the background of a course in real analysis at the level of Rudin's "Principles of Mathematical Analysis".
-
The text has a number of strengths. Some of these are the following: 1. The choice of material and the order of presentation are superb. Just to give you a sample, within the first 100 pages, the authors cover Runge's Theorem, the Schwarz Reflection Principle, Riemann's Theorem on Removable Singularities, the Casorati-Weierstrass Theorem, Rouche's Theorem, and the homotopy version of Cauchy's Integral Theorem. The novice is thus treated to some beautiful mathematics very quickly.
-
3. The proofs are very clear and elegant. The main ideas are emphasized, and just enough details are given so that a diligent student with the background stated above will be able to grasp the arguments.
