Fourier Analysis by T. W. K?rner

by T.W. Körner

The author has provided a shop window for some of the ideas, techniques and elegant results of Fourier analysis, and for their applications. These range from number theory, numerical analysis, control theory and statistics, to earth science, astronomy, and electrical engineering. Each application is placed in perspective with a short essay. The prerequisites are few (the reader with knowledge of second or third year undergraduate mathematics should have no difficulty following the text), and the style is lively and entertaining.

Genres: Mathematics, Textbooks, Science, Nonfiction

Paperback Bunko

First published January 1, 1988

About the author

Thomas William Körner (born 17 February 1946) is a British pure mathematician and the author of school books. He is titular Professor of Fourier Analysis in the University of Cambridge and a Fellow of Trinity Hall. He is the son of the philosopher Stephan Körner and of Edith Körner.

He studied at Trinity Hall, Cambridge, and wrote his PhD thesis Some Results on Kronecker, Dirichlet and Helson Sets there in 1971, studying under Nicholas Varopoulos. In 1972 he won the Salem Prize.

He has written three academic mathematics books aimed at undergraduates, and two books aimed at secondary school students, the popular 1996 title The Pleasures of Counting and Naive Decision Making (published 2008) on probability, statistics and game theory.

Reviews

[Mark Moon · Rating 5 out of 5]

I did not read this book from cover to cover, because that would not have been true to the spirit in which it was written. I had to read more than a few chapters before it clicked: this book is a buffet... no, a smorgasbord! The breadth of topics treated here is incredible, especially considering how well they are bound together by their common theme (as given in the title). Several distinct threads run through the book, in a way that makes jumping around from chapter to chapter easy and rewarding.

This is not the place to go for all the (gory) analytic details about exactly when and how various thing converge. The theory is investigated in detail just when it's interesting to do so (which means your enjoyment of this book will depend on the compatibility between your taste and the author's).

Applications-related topics that get their own chapter(s) include: Monte Carlo methods, mechanical linkages, the debate over the age of the Earth in the 19th century, the laying and operation of the first transatlantic cables, stability of control systems, statistical data analysis for fraud detection, estimating the diameters of distant stars, and coding theory.

[Chris · Rating 5 out of 5]

The proof aren't pretty, but it's my absolute favorite undergraduate level nighttime-reading math book. It's compulsively readable.