Review of Visual Complex Analysis, by Tristan Needham
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Tristan Needham's Visual Complex Analysis will show you the field of complex analysis in a way you almost certainly have not seen before. Drawing on historical sources and adding his own insights, Needham develops the subject from the ground up, drawing attractive pictures at every step of the way. If you have time for a year course, full of fascinating detours, this is the perfect text; by picking and choosing, you could use it for a variety of shorter courses. I am tempted to hide the book from my own students, in order to appear the more clever for popping up with crisp historical anecdotes, great exercises, and pictures that explain things like that mysterious 2πi that crops up in integrals. Whether you use Visual Complex Analysis as a text, a resource, or entertaining summer reading, I highly recommend it for your bookshelf.