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The author discusses not only mathematics but also personalities. Many of the chapters in the book are organized around people, and good biographies of them, complete with photographs, appear throughout. The lives of these mathematicians are placed in historical context, and the author does a good job of conveying the fact that mathematical advances are often the product of false starts and mistaken ideas.

This book, like Worlds out of Nothing , is part of the Springer Undergraduate Mathematics Series and, we are told, derives from a series of lectures given by the author to British senior undergraduate students.

Consistent with these undergraduate origins, the author has employed a number of useful pedagogical devices. The earlier chapter 21 also touched on assessment issues.


  • Complex Analysis by John M. Howie.
  • Complex Analysis?
  • The Real and the Complex: A History of Analysis in the 19th Century.

Analogous chapters on writing 12, 21 and 31 appeared in Worlds. In addition to these chapters, Gray has, in an Appendix, included translations all but one done by himself of portions of important papers, including works by Fourier, Dirichlet, Riemann, and Schwarz.

Complex Analysis - Fundamental(Lecture1)

Notwithstanding these nice features, I doubt this book would prove very successful as a text for undergraduates on this side of the Pond. For one thing, there is the obvious difference between a British undergraduate mathematics education and an American one, and, in addition, the prerequisites for reading this book seem a bit daunting.

This is presumably because these two books are not really intended as histories of analysis, but instead as introductory courses in analysis from a historical perspective. Certainly, no good university library should be without it. We are also told in the preface that two other volumes on 19th century mathematics history on algebra and differential equations, respectively are planned, and I eagerly await their publication. Mark Hunacek mhunacek iastate.

Math eBooks from Springer, Oct-Dec | Washington University in St. Louis

See the table of contents in pdf format. Not only do Howie's selection of topics and their sequence correspond perfectly to what I believe to be the ideal approach to this gorgeous subject, the writing style is again wonderful. Consider the following sample: "Since we shall require Cauchy's Theorem and its consequences for contours that are neither convex nor polygonal, it becomes a duty on the author's part to present a proof of a more general case.

Whether there is a corresponding duty on the reader's part is left to individual conscience! There is no doubt, however, that useful skills follow from the mastery of substantial proofs. So many contemporary texts quickly embrace condescension and proceed mainly to annoy the reader.

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As regards technical points, the book is split into twelve chapters, each of which is split into a relatively small number of short and sweet sub-sections which can be easily used to build individual lectures. It's nigh on a perfect text-book in this way. There are also a number of wonderful ideological passages; see e. And here is problem 4.

Real Analysis

He said, "It's the principal logarithm Of -1 - i. So, clearly, I think this is a terrific book. I'm going to use it the first chance I get. Summing up: Highly recommended.

Real Complex Analysis

It covers all the topics likely to feature in a first course in complex analysis up to Laurent series, the residue theorem and conformal mappings. All this make the book ideal for self-study.

Summing Up: Highly recommended. JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser.

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Mathematics Analysis. Buy eBook. Buy Softcover. FAQ Policy. About this Textbook Complex analysis is one of the most attractive of all the core topics in an undergraduate mathematics course. Show all. From the reviews: Howie's book is a gem.