Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills

Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills

by Paul J. Nahin
     
 

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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

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Overview

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."

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Editorial Reviews

Nature
Nahin includes gems from all over mathematics, ranging from engineering applications to beautiful pure-mathematical identities. Most of his topics lie just beyond the periphery of a typical mathematics course: they are facts, such as the irrationality of pi, that you may have heard of but never had explained in detail. It would be good to have more books like this.
New Scientist
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
MAA Reviews
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
SIAM Review
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.
Mathematics Today
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 Teacher
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
Mathematical Reviews
This is a book for mathematicians who enjoy historically motivated mathematical explanations on a high mathematical level.
— Eberhard Knobloch
London Mathematical Society Newsletter
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
New Scientist - Matthew Killeya
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.
MAA Reviews - Henry Ricardo
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.
SIAM Review - Robert E. O'Malley
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.
Mathematical Reviews - Eberhard Knobloch
This is a book for mathematicians who enjoy historically motivated mathematical explanations on a high mathematical level.
London Mathematical Society Newsletter - Robin Wilson
It is a 'popular' book, written for a general reader with some mathematical background equivalent to a first-year undergraduate course in the UK.
"Nature othy Gowers

Nahin includes gems from all over mathematics, ranging from engineering applications to beautiful pure-mathematical identities. Most of his topics lie just beyond the periphery of a typical mathematics course: they are facts, such as the irrationality of pi, that you may have heard of but never had explained in detail. It would be good to have more books like this.
From the Publisher

"Nahin includes gems from all over mathematics, ranging from engineering applications to beautiful pure-mathematical identities. Most of his topics lie just beyond the periphery of a typical mathematics course: they are facts, such as the irrationality of pi, that you may have heard of but never had explained in detail. It would be good to have more books like this."--Timothy Gowers,Nature

"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

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Product Details

ISBN-13:
9781400838479
Publisher:
Princeton University Press
Publication date:
04/25/2011
Sold by:
Barnes & Noble
Format:
NOOK Book
Pages:
416
Sales rank:
1,157,419
File size:
13 MB
Note:
This product may take a few minutes to download.

What People are saying about this

Des Higham
The range and variety of topics covered here is impressive. I found many little gems that I have never seen before in books of this type. Moreover, the writing is lively and enthusiastic and the book is highly readable.
Des Higham, University of Strathclyde, Glasgow
Peter Pesic
If you ever wondered about the beauties and powers of mathematics, this book is a treasure trove. Paul Nahin uses Euler's formula as the magic key to unlock a wealth of surprising consequences, ranging from number theory to electronics, presented clearly, carefully, and with verve.
Peter Pesic, St. John's College

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