VisualComplexAnalysis 
by TristanNeedham
ISBN: 0198534469

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This book is amazing. It's driven by the idea that you should learn mathematics using geometric intuition and refer to rigorous proof only once you have a clear geometrical understanding of something. This idea is applied to the teaching of ComplexAnalysis, and the result is miraculous. The book has many successes, like its derivation of e^z and its clear explanation of Cauchy integration. The one area where it falls down a little is in the geometric description of complex differentiation, the 'amplitwist'. I found the concept unclear and and not always helpful. That aside, it's still well worth reading.

I'm not great at maths (MathIsHard) and have recurring problems with RealAnalysis, but this book gave me a genuine grasp of ComplexAnalysis, and filled my head with pretty pictures to boot.

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Absolutely a landmark in mathematics instruction. I thought the amplitwist was not as intuitive as the "right-hand rule" I was taught, but the mapping of a complex line to a curve on a sphere was mind-blowing. ComplexNumbersArePoints indeed. -- StevenNewton

It has 616 pages and its author recommends you also read ''Mathematics and its History'' [[ISBN 0387953361]- 568 pages], so allow plenty of time.

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CategoryBook CategoryMath