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On Quaternions and Octonions Hardcover – January 23, 2003

ISBN-13: 978-1568811345 ISBN-10: 1568811349 Edition: 1st

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Product Details

  • Hardcover: 159 pages
  • Publisher: A K Peters/CRC Press; 1st edition (January 23, 2003)
  • Language: English
  • ISBN-10: 1568811349
  • ISBN-13: 978-1568811345
  • Product Dimensions: 0.8 x 6.2 x 9.2 inches
  • Shipping Weight: 12.6 ounces (View shipping rates and policies)
  • Average Customer Review: 3.9 out of 5 stars  See all reviews (9 customer reviews)
  • Amazon Best Sellers Rank: #403,889 in Books (See Top 100 in Books)

Editorial Reviews

Review

"Conway and Smith’s book is a wonderful introduction to the normed division algebras … They develop these number systems from scratch, explore their connections to geometry, and even study number theory in quaternionic and octonionic versions of the integers. … a lucid and elegant introduction. … remarkably self-contained. It assumes no knowledge of number theory, string theory, Lie theory, or lower-case Gothic letters."
—John C. Baez, Bulletin of the American Mathematical Society, January 2005

"A resonant spike above background noise in one parameter as another parameter is varied is a frequent indicator…"
—Geoffrey Dixon, Mathematical Intelligencer, May 2004

"Those readers who are fascinated by the links between geometry and groups will find that this book gives them new insights."
—Hugh Williams, The Mathematical Gazette, July 2004

"This is a beautiful and fascinating book on the geometry and arithmetic of the quaternion algebra and the octonion algebra. … most intriguing to read: it is an excellent exposition of very attractive topics, and it contains several new and significant results."
—Theo Grundhöfer, Mathematical Reviews, 2003

Customer Reviews

3.9 out of 5 stars
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Most Helpful Customer Reviews

63 of 72 people found the following review helpful By Jim Curry on July 25, 2003
Format: Hardcover
Conway is an excellent mathematician and an extremely lucid author. No criticism should be given to any of his writings. In the case of quaternions (and octonians), a much better, more complete, and more powerful view is achieved by seeing them in the larger setting of geometric algebra. The geometric algebra gives direct access to all the results and all the geometry of these algebras, and does so in an intuitive and useful way. I suggest that the new book by Chris Doran and Anthony Lasenby called "Geometric Algebra for Physicists" is a better place, generally, to get acquainted with these issues deeply. It isn't a criticism of Conway. It's just an advantage of seeing things in the right context.
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1 of 1 people found the following review helpful By Dr Luke O'Connor Drury on May 12, 2014
Format: Hardcover Verified Purchase
A very beautiful little book with some interesting takes, especially the links to algebraic integers and groups. Some statements are quite elliptical and require a good background in mathematics to follow, but generally fascinating for those who like Conway's work.
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3 of 5 people found the following review helpful By Roger Bagula on September 27, 2009
Format: Hardcover
This books gives a window into the newer notation in group theory.
Sometimes things that are "obvious" to Conway and his co-arthor,
just aren't to the rest of us.
But in contrast to that he gives concrete examples
of new approaches that are beyond classical Coexter
and Cartan type approaches.
If you are looking for physics applications to quantum mechanics
for modern group theory,
you might want to try another book,
but if you want an idea of what a Moufang loop is or why
octonions are not associative, then you might like this book.
Some time in this century we may even get
a chance to understand Freudenthal's metasymplectic geometry?
This book for me is sort of a study guide to
what i should try to learn for the future?
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1 of 2 people found the following review helpful By Erich H. Cerny on October 19, 2013
Format: Kindle Edition Verified Purchase
Candid review by one of the masters of the subject. The text is accessible to undergraduate students, very concise and clearly written.
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1 of 2 people found the following review helpful By Ken Macrae on December 28, 2013
Format: Hardcover Verified Purchase
I love it. There are many fascinating, deep and unique tidbits from John Conway himself.
The style is simple and lucid, assuming you are a mathematician.
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