Exploratory Galois Theory

Exploratory Galois Theory

by John Swallow
     
 

ISBN-10: 0521836506

ISBN-13: 9780521836500

Pub. Date: 09/15/2004

Publisher: Cambridge University Press

Combining a concrete perspective with an exploration-based approach, Exploratory Galois Theory develops Galois theory at an entirely undergraduate level. The text grounds the presentation in the concept of algebraic numbers with complex approximations and assumes of its readers only a first course in abstract algebra. The author organizes the theory around natural…  See more details below

Overview

Combining a concrete perspective with an exploration-based approach, Exploratory Galois Theory develops Galois theory at an entirely undergraduate level. The text grounds the presentation in the concept of algebraic numbers with complex approximations and assumes of its readers only a first course in abstract algebra. The author organizes the theory around natural questions about algebraic numbers, and exercises with hints and proof sketches encourage students' participation in the development. For readers with Maple or Mathematica, the text introduces tools for hands-on experimentation with finite extensions of the rational numbers, enabling a familiarity never before available to students of the subject. Exploratory Galois Theory includes classical applications, from ruler-and-compass constructions to solvability by radicals, and also outlines the generalization from subfields of the complex numbers to arbitrary fields. The text is appropriate for traditional lecture courses, for seminars, or for self-paced independent study by undergraduates and graduate students.

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Product Details

ISBN-13:
9780521836500
Publisher:
Cambridge University Press
Publication date:
09/15/2004
Pages:
208
Product dimensions:
6.97(w) x 9.96(h) x 0.87(d)

Related Subjects

Table of Contents

1Preliminaries5
2Algebraic numbers, field extensions, and minimal polynomials22
3Working with algebraic numbers, field extensions, and minimal polynomials39
4Multiply generated fields63
5The Galois correspondence103
6Some classical topics152
AppSubgroups of symmetric groups197

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