Visual Complex Analysis by Tristan Needham, 0198534469, Lowest Book Price Finder

Customer Reviews:

What a disappointment

I stood in the bookshop and read the reviews printed on the back cover and with mounting excitement the introduction. I bought the book and took it home. Imagine my disappointment when I actually started reading it. I got to page 18 before the combination of unexplained terms and unexplained steps brought me to a halt.

In my experience books like this which are not written as text books fall into two groups. There are those in which the author has truly translated the mathematics into English so as to make the topic accessible to those not already familiar with it (try Eli Maor), and there are those that require the reader to be familiar with the topic in order to be able to follow the explanations and are presumably written for the sake of the ego of the author. This book definitely falls into the latter category. Notice how all of the other reviewers talk of their previous knowledge of the subject.

Of course you may think me stupid but I have an engineering degree and an Msc in dynamics and I do not know any mathematics which I think of now as being conceptually difficult. And yet think how hard we had to work to learn some of it when we were at school and college. Things that we think of as simple and ordinary now were such a struggle to learn, and why? Because we didn't have the language. Well in order to gain any insight from this book you are already going to have to have the language because this author does not think of it as his job to give it to you. What a pity. What a missed opportunity. What a disappointment.

Part of the books that help crack complex analysis

Hi,

In a way you only see how good this book is when you read a number of other books on this topic? This is a book that works best when other books balance these two approaches, and by doing this it lets you see the whole 'landscape' of complex analysis.

If other books are rich in detailed questions, you slog along and break them down in small steps often without the `big picture' of where it fits in the wider scheme of things. With this book you see a vast sweeping panorama that allows the reader to gain insight with a geometrical approach in conceptualising areas.

The book starts in elemental terms in reflections and translations and complex algebra. Also a common feature is the book has outstanding illustrations and has helpful text to explain in more depth. I found the approach helped my geometrical interpretation of the links between complex numbers projected onto 'Riemann spheres' using 'MÃ¶bius transforms' through into 'Hyperbolic geometry' and the Calculus and on further to consider the properties of 3 combinations of two curved mirrors (reflections and translations again) on a Euclidian plane. The book also carries on to cover more general-purpose 'Laurent series' and beyond and how they can be applied in Complex Analysis.

Summary: I.M.H.O. It's a good buy as part of your bookshelf on this gripping topic. A Mathematics professor I knew once (who I will not name) -paraphrased-described the book to me as "the type of book you have at MSc level, without the intensive level of calculation. Its a lovely book to give you a `feel' of the topic".

Complex analysis as you never studied before

I discovered this book in passing through the bibliography of Penrose "A road to reality" , and suddenly my curiosity brought me to take a look at it (and i thank Sir Penrose for this...).
The subject is treated just as the title says, although not every aspects of complex analysis is covered (for which many standard textbooks do the right and better job).
Of particular interest to me was reading chapter 6 on non euclidean geometry, in which the author gives a concise and insightful description of the main ideas.
I think the book is particularly tailored, other than for mathematicians, for physicists who care of the beautiful links between geometric and algebraic aspects of modern maths.

Absorbing , reflective and highly interesting

This book is a jewel, if only there was a perfect Mathematics lecturer in the world s/he would bother explaining concepts like this fascinating book.

Absorbing, explanatory and fun to read the reader takes an active part.
There are 12 main chapters and each has exercises at the end. There are no solutions however, this book takes a visual insight into the world of complex numbers so the more you reflect the more your understanding grows.

There are plenty of well-illustrated and annotated diagrams. This book also has a few topics linked with Physics such as Riemann Mapping theorem, and Mobus transformation with Einstein's theory of relativity.

If you are serious about Mathematics and love logical and abstract thinking as well as visualising then this book is definitely worth a thorough look.

One of the best maths textbooks ever

Tristan Needham has written a wonderful synthesis of geometry, complex analysis and vector fields. Before I read this book I had "studied" complex analysis, but had never truly understood it. Now it all makes sense !

The scope of the book is very broad. It covers 2D and 3D geometry, Mobius transforms, non-Euclidean geometry, analytic functions, complex differentiation and integration, winding numbers, vector fields and harmonic functions. But it is the approach that makes this text so unusual and so accessible.

Needham believes that geometric arguments reveal underlying connections which algebraic proofs diguise. In his own words: "while it often takes more imagination and effort to find a picture than to do a calculation, the picture will always reward you by bringing you nearer to the Truth". Needham gloriously justifies his assertion in this text. Geometric proofs are used wherever possible, with the final conclusions translated back into algebraic terms. A variety of effective techniques are introduced for visualising the effect of Mobius transforms, analytic functions, complex differentiation etc.

One small word of warning - as Needham says himself in the Introduction, the arguments in this book are not formally rigorous. He bypasses the usual scaffolding of convergence and limits, and treats continuity as an intuitive concept. He uses phrases such as "the effect on an infinitesimal vector" which would cause a sharp intake of breath from a purist. This is not a problem, as long as you are happy to take it on trust that a formal framework can be provided if required. However, if you are studying for a conventional complex analysis exam, then you will need to fill in the formal structure from a more "standard" text once you know the landscape.

Definitely one of the best maths textbooks that I have ever read.

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