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The Mathematical Universe: An Alphabetical Journey Through the Great Proofs, Problems, and Personalities 1st Edition

4.4 out of 5 stars 49 customer reviews
ISBN-13: 978-0471176619
ISBN-10: 0471176613
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Editorial Reviews

From Booklist

Start with a for Arithmetic and wend your way to z, the symbol for complex numbers, and you will have completed Dunham's wonderfully informative tour of mathematics. Readers ought not turn away from this book because equations make them queazy and formulas leave them confused. Dunham writes for nonspecialists, and they will enjoy his piquant anecdotes and amusing asides even if they cannot follow all of his (simplified) derivations and illustrative problems. What president published an original proof of the Pythagorean theorem just four years before his election? What Nobel laureate unearthed a paradox that discredited his own logical system? What distinguished mathematician and scientist wrote almost a million words on alchemy? In providing the surprising answers to these and other questions, Dunham sheds light not only on the personalities--eccentric, vain, brilliant--of major mathematicians, but also on contemporary social issues, such as multiculturalism and gender equity. Readers who want to understand the cultural significance of mathematics would do well to begin with this book. Bryce Christensen --This text refers to the Digital edition.

About the Author

WILLIAM DUNHAM, Ph.D., is the Truman Koehler Professor of Mathematics at Muhlenberg College in Allentown, Pennsylvania. The author of the acclaimed Journey Through Genius, he was awarded the 1993 George Pólya Award of the Mathematical Association of America for excellence in expository writing about mathematics. He is also the recipient of grants from the National Endowment for the Humanities.
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Product Details

  • Paperback: 320 pages
  • Publisher: Wiley; 1 edition (February 18, 1997)
  • Language: English
  • ISBN-10: 0471176613
  • ISBN-13: 978-0471176619
  • Product Dimensions: 6.2 x 0.8 x 9.3 inches
  • Shipping Weight: 13.6 ounces (View shipping rates and policies)
  • Average Customer Review: 4.4 out of 5 stars  See all reviews (49 customer reviews)
  • Amazon Best Sellers Rank: #176,016 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

By Timothy Haugh VINE VOICE on November 11, 2000
Format: Paperback
I first read this book a number of years ago and recently read it again. I still think it is a magnificent overview of basic mathematics. In fact, it is one of the best overviews of basic mathematics that I have ever read. Dunham covers a wide range of topics and he does so in a very readable and understandable manner without giving up reasonable mathematical rigor. Someone with elementary algebra and geometry can follow all of Dunham's arguments and enjoy.
Of course, it is impossible to cover the entire range of mathematics in a book such as this but Dunham has chosen well. He sticks mainly to the fundementals of the major fields. In addition, his book reminds us that people with personalities have developed mathematics and that it's not a field created merely to strike fear into the hearts of schoolkids (and adults).
This book will always hold a special place for me: it was the catalyst for an epiphany. I had been teaching high school geometry for a few years when this book came out and I was very good at teaching the modern methods of proof and problem-solving. On the other hand, I didn't really like teaching constructions, because, though I could do them quite well, I didn't truly understand their place and function in geometry and its development. When I first read chapter "G" of this book ("Greek Geometry"), however, it was like a thousand puzzle pieces fell into place and I knew more than how to do constructions, I understood them and was able to teach them more effectively.
If you have any interest in mathematics at all, I recommend this book. It will not disappoint.
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Format: Paperback
In this follow-on to his excellent "Journey Through Genius", William Dunham once again breathes life into a variety of mathematical topics. Whereas "Journey" was arranged around 12 great mathematical theorems, this book is arranged around the 26 letters of the alphabet. Some chapters cover the work of individuals (e.g., "Euler", "Knighted Newton", "Lost Leibniz", and "Russell's Paradox"), while others describe important mathematical results (e.g., "Isoperimetric Problem", "Spherical Surface", and "Trisection"). Still others, such as "Mathematical Personality" and "Where are the Women?", address social aspects of the field.
As in the previous book, Dunham's descriptions are entertaining and enlightening. The main difference is that this book has broader coverage. As a result, it tends to omit more of the proofs, which I found disappointing, but perhaps that will make it of interest to a wider audience. For people with a deeper interest in mathematics, I recommend you read either "Journey Through Genius" or "Euler: The Master of Us All", another Dunham masterpiece that includes detailed proofs throughout.
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Format: Paperback
I have now read Dunhams 'Journey through Genius', 'Euler, the master of us all' and 'The Mathematical Universe'. These are three great books on Mathematics and choosing can become difficult. My personal favourite is 'Journey through Genius'.If you are mainly interested in magnificent proofs (real gems)with a historical account, then I would recommend 'Journey through Genius', for lots of nice eulerian proofs, then I recommend 'Euler, the master of us all' and if you want more a overview with some proofs and less depth, then buy 'The mathematical Universe'.
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I really enjoy this book, and I keep consulting it. But I really don't know whether what I'm learning from it is correct or not. Here's the problem: The two entries with which I have the most familiarity are just plain wrong.

The entry on the "Russell Paradox" reads like a hagiography of Bertrand Russell. It makes it appear that Russell ceased working on the Principia Mathematica because he could not find a solution to his paradox--whether a set, all of whose members are not members of themselves, contains itself. According to Dunham, his inability to find a satisfactory solution spelled the end of his quest for the development of a logical foundation for mathematics, which he communicated to Frege, who gave up on his attempts as well. This is pure fiction. The entire Principia Mathematica is based on Russell's theory of ramified types (the stipulation that a set cannot be a member of itself), which he confidently asserted as being the solution to the paradox throughout the work. What put an end to Russell and Whitehead's project, as well as Frege's, was Goedel's incompleteness theorem, totally ignored by Dunham.

Dunham's treatment of Venn diagrams is even worse because it is deprecating of John Venn and his work--and totally wrong. Dunham states that the diagrams that are named after him were Venn's only contribution to mathematics and then makes disparaging remarks about them, particularly that they lacked any originality. Here's the reality: John Venn was an extremely competent mathematician/logician whose many contributions included the furtherance of George Boole's innovations.
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