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I used to think math was no fun
'Cause I couldn't see how it was done
Now Euler's my hero
For I now see why zero
Equals e^{[pi] i}+1
--Paul Nahin, electrical engineer
In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Euler's Fabulous Formula shares the fascinating story of this groundbreaking formula--long regarded as the gold standard for mathematical beauty--and shows why it still lies at the heart of complex number theory.
This book is the sequel to Paul Nahin's An Imaginary Tale: The Story of I [the square root of -1], which chronicled the events leading up to the discovery of one of mathematics' most elusive numbers, the square root of minus one. Unlike the earlier book, which devoted a significant amount of space to the historical development of complex numbers, Dr. Euler begins with discussions of many sophisticated applications of complex numbers in pure and applied mathematics, and to electronic technology. The topics covered span a huge range, from a never-before-told tale of an encounter between the famous mathematician G. H. Hardy and the physicist Arthur Schuster, to a discussion of the theoretical basis for single-sideband AM radio, to the design of chase-and-escape problems.
The book is accessible to any reader with the equivalent of the first two years of college mathematics (calculus and differential equations), and it promises to inspire new applications for years to come. Or as Nahin writes in the book's preface: To mathematicians ten thousand years hence, "Euler's formula will still be beautiful and stunning and untarnished by time."
"Nahin's tale of the formula e^{[pi]} i+1=0, which links five of the most important numbers in mathematics, is remarkable. With a plethora of historical and anecdotal material and a knack for linking events and facts, he gives the reader a strong sense of what drove mathematicians like Euler."--Matthew Killeya, New Scientist
"What a treasure of a book this is! This is the fourth enthusiastic, informative, and delightful book Paul Nahin has written about the beauties of various areas of mathematics. . . . This book is a marvelous tribute to Euler's genius and those who built upon it and would make a great present for students of mathematics, physics, and engineering and their professors. Paul Nahin's name has been added to my list of those with whom I wouldn't mind being stranded on a desert island--not only would he be informative and entertaining, but he would probably be able to rig a signaling device from sea water and materials strewn along the beach."--Henry Ricardo, MAA Reviews
"The heart and soul of the book are the final three chapters on Fourier series, Fourier integrals, and related engineering. One can recommend them to all applied math students for their historical development and sensible content."--Robert E. O'Malley, Jr., SIAM Review
"It is very difficult to sum up the greatness of Euler. . . . This excellent book goes a long way to explaining the kind of mathematician he really was."--Mathematics Today
"The author conducts a fascinating tour through pure and applied mathematics, physics, and engineering, from the ethereal heights of number theory to the earthiness of constructing speech scramblers. . . . [T]his is a marvelous book that will illuminate the mathematical landscape of complex numbers and their many applications."--Henry Ricardo, Mathematics Teacher
"This is a book for mathematicians who enjoy historically motivated mathematical explanations on a high mathematical level."--Eberhard Knobloch, Mathematical Reviews
"It is a 'popular' book, written for a general reader with some mathematical background equivalent to a first-year undergraduate course in the UK."--Robin Wilson, London Mathematical Society Newsletter
Preface : "when did math become sexy?" | ||
1 | Complex numbers (an assortment of essays beyond the elementary involving complex numbers) | |
2 | Vector trips (some complex plane problems in which direction matters) | |
3 | The irrationality of [pi][superscript 2] ("higher" math at the sophomore level) | |
4 | Fourier series (named after Fourier but Euler was there first - but he was, alas, partially wrong!) | |
5 | Fourier integrals (what happens as the period of a periodic function becomes infinite, and other neat stuff) | |
6 | Electronics and [actual symbol not reproducible] (technological applications of complex numbers that Euler, who was a practical fellow himself, would have loved) | |
Euler : the man and the mathematical physicist |
Overview
In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to ...