| ![An Imaginary Tale: The Story of i [the square root of minus one]](http://ecx.images-amazon.com/images/I/51EdpS4WaIL._SL160_.jpg)
 enlarge | Author: Paul J. Nahin
Publisher: Princeton University Press
Category: Book
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Rating:  44 reviews
Sales Rank: 58166
Media: Paperback
Pages: 288
Number Of Items: 1
Shipping Weight (lbs): 0.9
Dimensions (in): 9.1 x 6.1 x 0.8
ISBN: 0691127980
Dewey Decimal Number: 515.9
EAN: 9780691127989
Publication Date: January 15, 2007
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| Customer Reviews:
 A history of "i" for the mathematically initiated! May 26, 2002
Justin Bost (Salisbury, NC)
18 out of 20 found this review helpful
Nahin's text on the history of i is an exciting, comprehensive look into the origins of i and its elementary theoretical applications. It rightfully has been compared to Eli Maor's wonderful book "e: The Story of A Number", which deserves five stars in its own right. I do have to take issue with some of the other reviews posted here. For instance, a few have said that you have to have a "graduate math" background to fully appreciate this book?!? Who are they kidding? Nahin actually *sacrifices* mathematical rigor in order to improve his exposition. Anyone with a real mathematics background knows that complex analysis gets far more complicated than the basic material Nahin presents in his book. To get an idea, you can peruse Walter Rudin's fine text "Real and Complex Analysis".
To be fair, I agree with the reviewer who wrote that Nahin should not have omitted material on Klein groups, Julia and Mandelbrot sets. However, I can understand why he did. It is difficult to write on such subjects as groups and fractals to an audience intended to have a (motivated) high school or freshman calculus background. I read this book, understood it, and loved it, long before I had any idea what groups or fractals were. Nahin gives fair warning in the introduction to his book that it is not a "mathematical lightweight". I do think that a solid background in (single variable) calculus, including power series, is crucial to a true appreciation of the book. In particular, one must know these things to value the genius of Euler and others in the section on "Wizard Mathematics".
Nahin does tread lightly into other topics, such as differential equations and (advanced) algebra, but to say these are a prerequisite to reading the book is ridiculous. I think even if the reader has never encountered ideas such as the Fundamental Theorem of Algebra before, they serve to enrich, not detract from, the material. In any case, the reader should be pleased to see a leisurely treatment of something so blown out of proportion as FTA, as an understanding of it is basic to anything beyond calculus. Proofs of it are rich in variety, ranging from topology to geometry to complex variables (using the theorem of Liouville and properties of entire functions). One criticism that is entirely justified is the typographical errors that regrettably plague the book. In particular, the theorem of Green, relating double integrals to single contour integrals, a result that is surprising and illuminating. However, the careful reader can usually spot and correct such errors, and he or she should be delighted in their own astuteness, rather than blame the author.
He does a wonderful job explaining the conceptual basis of i, and I think this overrides any of the books minor flaws. The book does seem to end rather abruptly, however, and I hope that if the author chooses to revise his work, he will expand upon the material, in particular, a (brief?) treatment of the Residue Theorem, the crowning jewel of complex integration. Perhaps even a section on conformal mapping? I do realize though that this may place the book too far out of reach of his intended audience.
The bottom line: if you want a storybook, this is not for you. If you *really* like mathematics, and have a historical bent, this book will satisfy you. If second semester calculus is a painful memory, steer clear because this book has its share of series and integrals.
Clears up mysteries June 22, 2005
David A. Garcia (Albuquerque, NM)
13 out of 13 found this review helpful
This book gets five stars because I had a major "wow, now I get it" moment reading it (the elegant explanation of De Moivre's theorem). I also really appreciated the focus on the geometry and coordinate mapping of i.
Anyone that has previously worked with multiple integrals and elementary differential equations should have no trouble plodding through the math. It took me a lot of (rewarding) time to follow the harder parts, but I usually was able to unpack things enough to get the point.
Yes, there are a couple of misprints (more distracting than critical) and, perhaps, a bit too much electrical engineering for my taste (although maybe I simply haven't got enough EE background to benefit).
However, what matters most is that this author knows how to highlight the really important things. I cannot deduct any stars, the "wow" moment I had with De Moivre was just too good.
thumbs-up from an EE/physicist - not meant as a textbook September 22, 2003
Paul DeLong (Metuchen, NJ)
10 out of 10 found this review helpful
This was an incredible book. I'm an electrical engineer by degree and a physicist by hobby, so I'm pretty familiar with imaginary numbers. While a lot of the concepts were a review to me, the book also introduced me to a lot of new and fascinating territory. But besides the pure math, it also introduced me to a lot of the history and personalities behind it all. Putting it in perspective and historical context helps breathe new life into it.I must strongly disagree with the reviewers who said that the math was not rigorous enough, and that the presentation was lacking in personality (two opposite viewpoints). The style had way more personality than any textbook on mathematics. And anyone with a high-school math background can get through most of the book (not all of it - they may need to skip the bits involving calculus). And whoever says the presentation lacks rigor is missing the point entirely, because this is NOT a textbook and was never meant to be. The author never intended to scare away the casual reader with lenghty proofs - he wants to explain in accessible terms, not alienate.
This intriguing story of imaginary numbers was a joy to read December 3, 2002
Michael E. Wright (Silicon Valley, CA, USA, proud to be an American)
8 out of 8 found this review helpful
I loved reading this book. It is exactly what it states that it is, a story of imaginary numbers. A loving story. Imaginary numbers have a facinating history of very slow adoption through the centuries, a history that wonderfully facilitates a certain love and joy of mathematics and better understanding of our struggles as humans to improve ourselves and better understand the language of the physical universe: mathematics.
I did not find this book too tedious at all. Nothing run into the ground at all. If you encounter sections of this book with math too tedious for you, or if you are simply a more casual reader or don't have the time to go deeper, then do as I did, skip those sections. The vast majority of the book is text. The author is a mathematician, so he used mathematical examples, that is all. I assert that the only way to do justice to math history is to include some math.
Understanding imaginary numbers by the broader historical view offered in this book allowed me deeper insight and the ability to see deeper parallels with other areas of matahematics. Just as there were eons where people had no use for negative numbers, but where negative numbers were found convenient for arithmetic operations and so put into common everyday usage, so it goes for imaginary numbers.
One of the reviewers wrote that this book is an excellent introductory treatment of complex analysis. I believe that reviewer to be a mathematician. This book is a historical story telling, not at all a text book This book is great for a fun casual read by any curious person.
There was lots of new and insightful stuff in this book for me. Highly recommended. A fun read.
Exciting introduction to complex variables September 10, 2002
Jeffrey L. Cooper (North Central Massachusetts, USA)
12 out of 12 found this review helpful
This book will introduce you to complex numbers, complex variables, and complex functions and you _will_ be able to make the journey. You'll need a little familiarity with algebra but, like all these modern mathematical expositories, you can completely grasp the subject with diligence. The hard or clever parts are spelled out for you.Perhaps there are some typos but I wasn't hampered appreciably by them. Some beautiful and elegant mathematics is exposed very sensitively in this book and with a great appreciation for the chronology and history of the process. The demonstration bears out Hadamard's comment, "The shortest distance two points in the real plane oftens passes through the complex plane." This book really spurred on my interest in complex variables. The continued study of complex math can take you to some stunning and unexpected connections in mathematics. I encourage interested readers to consider this book as a starting place for that journey.
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