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Exploratory Galois Theory~tqw~ darksiderg

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Exploratory Galois Theory
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Type.................: Ebook
Part Size............: 1,197,810 bytes




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Posted by............: ~tqw~

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Release Notes
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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.

Table of Contents

1 Preliminaries 5
2 Algebraic numbers, field extensions, and minimal polynomials 22
3 Working with algebraic numbers, field extensions, and minimal
polynomials 39
4 Multiply generated fields 63
5 The Galois correspondence 103
6 Some classical topics 152
App Subgroups of symmetric groups 197

Product Details

* ISBN: 0521544998
* ISBN-13: 9780521544993
* Format: Paperback, 220pp
* Publisher: Cambridge University Press
* Pub. Date: September 2004

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