Abstract Algebra and Famous Impossibilities (Universitext) | 
 enlarge | Authors: Arthur Jones, Sidney A. Morris, Kenneth R. Pearson
Publisher: Springer
Category: Book
List Price: $64.95
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Rating:  2 reviews
Sales Rank: 1421374
Media: Paperback
Edition: Corrected
Pages: 187
Number Of Items: 1
Shipping Weight (lbs): 0.8
Dimensions (in): 9.1 x 5.9 x 0.6
ISBN: 0387976612
Dewey Decimal Number: 512.02
EAN: 9780387976617
Publication Date: December 14, 1993
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Product Description
The famous problems of squaring the circle, doubling the cube, and trisecting the angle have captured the imagination of both professional and amateur mathematician for over two thousand years. These problems, however, have not yielded to purely geometrical methods. It was only the development of abstract algebra in the nineteenth century which enabled mathematicians to arrive at the surprising conclusion that these constructions are not possible. This text aims to develop the abstract algebra.
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| Customer Reviews:
The easiest introduction to field extensions I've read August 18, 2005
Neal J. King (Munich, Germany)
4 out of 4 found this review helpful
This is the easiest-to-read introduction to abstract algebra and, in particular, field extensions, that I have ever seen. It is easier to follow than Artin's famous little book, and has easy but useful problems to allow you to check your understanding.
This material is developed in order to explain the questions of how to prove that certain famously unsolved problems of geometry (a general Euclidean method for trisecting an arbitrary angle, constructing a square with the area of a given circle) are actually unsolvable. It also addresses the question of the transcendence of Euler's number (e).
The first problem is handled by understanding the abstract algebra of geometrical constructions; the second goes further into analysis as well; and I haven't finished reading the discussion on the third problem. Admittedly, the learning curve rises rather rapidly on the last two problems!
However, the book is worth reading even for the first problem alone, and as an introduction to abstract algebra.
Fabulous Book July 17, 2007
H. A. ShahAli (Tehran-IRAN)
0 out of 1 found this review helpful
This is the best book on the three famous math problems from antiquity
(squaring a circle, doubling a cube, and trisecting an angle) I have ever seen.
The authors do this job excellently in a lucid and live style.
I recommend highly this very nice and fabulous book to all math-lovers.
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