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On Quaternions and Octonions Hardcover – Jan 23 2003


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Product Details

  • Hardcover: 160 pages
  • Publisher: A K Peters/CRC Press; 1 edition (Jan. 23 2003)
  • Language: English
  • ISBN-10: 1568811349
  • ISBN-13: 978-1568811345
  • Product Dimensions: 1.9 x 15.9 x 23.5 cm
  • Shipping Weight: 358 g
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Bestsellers Rank: #634,201 in Books (See Top 100 in Books)

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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


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2 of 2 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 Sally on March 25 2003
Format: Hardcover
John Conway's books are always well written, and this could serve as a model for other mathematics authors. I don't need to know that much about quaternions and octonions, but I found myself working through most of the book and the beautiful mathematics it covers. The only thing that disappoints is the dreadful cover and the difficulty getting hold of a copy in a bookstore. But then I guess Amazon.com exists to help people get their hands on stuff they might never see in a bookstore.
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Format: Hardcover
On Quaternions And Octonions: Their Geometry, Arithmetic, And Symmetry is a collaboratively presented treatise by John H. Conway and Derek A. Smith on the geometry of the quaternion and octonion algebras. Examining 3- and 4-dimensional Euclidean spaces, enumerating the corresponding finite group of symmetries, analyzing the arithmetics of quaternions and octonions and much more, this impressive presentation sheds new light on the geometry of complex numbers and is a scholarly addition to Advanced Mathematics reference collections and reading lists.
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Most Helpful Customer Reviews on Amazon.com (beta)

Amazon.com: 9 reviews
63 of 72 people found the following review helpful
Good, but something is better July 25 2003
By Jim Curry - Published on Amazon.com
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.
1 of 1 people found the following review helpful
A beautiful book May 12 2014
By Dr Luke O'Connor Drury - Published on Amazon.com
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.
3 of 5 people found the following review helpful
People either love Conway or hate him? Sept. 27 2009
By Roger Bagula - Published on Amazon.com
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?
1 of 2 people found the following review helpful
For afficionados Dec 28 2013
By Ken Macrae - Published on Amazon.com
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.
1 of 2 people found the following review helpful
quaternions and octonions revisited Oct. 19 2013
By Erich H. Cerny - Published on Amazon.com
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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