

Dr. Euler's Fabulous Formula: 
In the mideighteenth century, Swissborn 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 formulalong regarded as the gold standard for mathematical beautyand 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 neverbeforetold tale of an encounter between the famous mathematician G. H. Hardy and the physicist Arthur Schuster, to a discussion of the theoretical basis for singlesideband AM radio, to the design of chaseandescape 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 includes gems from all over mathematics, ranging from engineering applications to beautiful puremathematical 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 islandnot 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 File created: 4/26/2015  
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