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Download full pdf book Abstract Algebra and Famous Impossibilities by Arthur Jones available in full 189 pages, and make sure to check out other latest books Mathematics related to Abstract Algebra and Famous Impossibilities below.Abstract Algebra and Famous Impossibilities
By Arthur Jones ISBN Code: : 9781441985521
 Publisher : Springer Science & Business Media
 Pages : 189
 Category : Mathematics
 Reads : 800
 Book Compatibility : Pdf, ePub, Mobi, Kindle
 Pdf : abstractalgebraandfamousimpossibilities.pdf
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 secondyear students at La Trobe University over a period of many years, each time refining the material in the light of student performance.
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