Abstract Algebra and Famous Impossibilities

Abstract Algebra and Famous Impossibilities
Author :
Publisher : Springer Science & Business Media
Total Pages : 191
Release :
ISBN-10 : 9781441985521
ISBN-13 : 1441985522
Rating : 4/5 (21 Downloads)

Book Synopsis Abstract Algebra and Famous Impossibilities by : Arthur Jones

Download or read book Abstract Algebra and Famous Impossibilities written by Arthur Jones and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: The famous problems of squaring the circle, doubling the cube and trisecting an angle captured the imagination of both professional and amateur mathematicians for over two thousand years. Despite the enormous effort and ingenious attempts by these men and women, the problems would not yield 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. In this book we develop enough abstract algebra to prove that these constructions are impossible. Our approach introduces all the relevant concepts about fields in a way which is more concrete than usual and which avoids the use of quotient structures (and even of the Euclidean algorithm for finding the greatest common divisor of two polynomials). Having the geometrical questions as a specific goal provides motivation for the introduction of the algebraic concepts and we have found that students respond very favourably. We have used this text to teach second-year students at La Trobe University over a period of many years, each time refining the material in the light of student performance.


Abstract Algebra and Famous Impossibilities Related Books

Abstract Algebra and Famous Impossibilities
Language: en
Pages: 191
Authors: Arthur Jones
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

The famous problems of squaring the circle, doubling the cube and trisecting an angle captured the imagination of both professional and amateur mathematicians f
Abstract Algebra and Famous Impossibilities
Language: en
Pages: 204
Authors: Springer
Categories:
Type: BOOK - Published: 2012-10-01 - Publisher:

DOWNLOAD EBOOK

Abstract Algebra and Famous Impossibilities
Language: en
Pages: 233
Authors: Sidney A. Morris
Categories: Mathematics
Type: BOOK - Published: 2022-11-26 - Publisher: Springer Nature

DOWNLOAD EBOOK

This textbook develops the abstract algebra necessary to prove the impossibility of four famous mathematical feats: squaring the circle, trisecting the angle, d
A Book of Abstract Algebra
Language: en
Pages: 402
Authors: Charles C Pinter
Categories: Mathematics
Type: BOOK - Published: 2010-01-14 - Publisher: Courier Corporation

DOWNLOAD EBOOK

Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatm
A History of Abstract Algebra
Language: en
Pages: 175
Authors: Israel Kleiner
Categories: Mathematics
Type: BOOK - Published: 2007-10-02 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

This book explores the history of abstract algebra. It shows how abstract algebra has arisen in attempting to solve some of these classical problems, providing