Top critical review
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on 13 March 2015
Needham has achieved a unique treatment of complex analysis (CA) : making it visual and thereby attractive.
The challenge was enormous and is definitely met
Yet, there is a cost, to the reader : since it is next to impossible for an author to achieve, simultaneously, a thorough explanation of the figures i.e. the visual treatment of CA and to give a fundamental, classical treatment of the subject, the latter effort is left to the reader who has to fetch for other sources... So, be prepared, with a good load of pencils : my copy is annotated almost at each paragraph.
This obviously cannot be held against Needham who, right from the preface warns us.
Nevertheless, there are a few points that annoyed me :
- bad articulation of chapters/ sections/subsections and no mention of such info at the top of each 2 pages... making searches difficult.
- no table of symbols.
- no synthesis at the end of each chapter e.g. about what we have achieved and where we are heading to.
- poorly contrasted figures, which have to be penciled, if you can guess where the curves and lines are.
I intended to give the book 4 stars, before going through sections IV to VII of chapter 12 which are simply indigestible.
Actually, a good idea would be to follow, simultaneously, the two excellent video series by : Petra Bonfert-Taylor (Coursera) and Herbert Gross (Mit).
Finally, does this book replace a fundamental treatment ? Clearly not and there are many classical treatments around, culminating with Markushevich's "Theory of functions of a complex variable".