Download e-book for kindle: Exploratory Galois Theory by John Swallow

By John Swallow

ISBN-10: 0521544998

ISBN-13: 9780521544993

ISBN-10: 0521836506

ISBN-13: 9780521836500

Combining a concrete point of view with an exploration-based procedure, Exploratory Galois thought develops Galois idea at a completely undergraduate point. The textual content grounds the presentation within the idea of algebraic numbers with complicated approximations and assumes of its readers just a first path in summary algebra. the writer organizes the speculation round traditional questions about algebraic numbers, and workouts with tricks and facts sketches motivate scholars' participation within the improvement. For readers with Maple or Mathematica, the textual content introduces instruments for hands-on experimentation with finite extensions of the rational numbers, permitting a familiarity by no means earlier than on hand to scholars of the topic. Exploratory Galois conception contains classical purposes, from ruler-and-compass buildings to solvability by means of radicals, and likewise outlines the generalization from subfields of the complicated numbers to arbitrary fields. The textual content is acceptable for standard lecture classes, for seminars, or for self-paced self reliant examine via undergraduates and graduate students.

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