Very Good.
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Good things; the "tactical tips" are generally excellent and the material in the book is adequate and reasonably well paced for the 1st to 2nd year undergraduate. Wise choices with regards to topological abstraction are also made and worked in well to the text.
Occasionally important insights in proofs are omitted or worse genuine oversights are made (for instance, on p25 where the proof does not hold for all triplets in Cinfinity), there are also a few comical errors, e.g. p56 where even on the 2nd printing there is a glaring error in the very first definition of complex differentiable!
The author seems to take a dim view of alternative ways of constructing complex analysis which are genuinely quite interesting and worth exploring.
The downside of the book is the routineness of the exercises which are well below exam standard in a lot of places and sometimes is nothing more than a list of dull applications. The silly "Z mistake" things everywhere are also sort of insulting...
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Great text book
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This book has been the text book for the second year course I have been studying, "Complex Analysis", and I have found Priestley's book to be invaluable. Priestley's style is excellent, and the way she has organised the material is helpful, because she breaks certain topics down into a "basic" and "advanced" track, so you can get the feel for the topic before considering it in more detail.
Priestley also includes many worked examples, which again I found to be very helpful, because by working through the examples myself, I managed to consolidate what I had learned previously.
I would recommend this book to anyone who is an undergraduate studying complex analysis.
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Cuts to the chase
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Priestley moves quickly to the heart of the subject, with a sure touch as to what is really important, and what is a technical detail best saved for a second reading. Since the Bourbaki dangerous bend sign is used liberally for points that might confuse the reader precisely on the first reading, there is no harm and much good done by the rapid pace and focused attention.
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