Exploratory Galois Theory by John Swallow

By John Swallow

Combining a concrete standpoint with an exploration-based method, Exploratory Galois idea develops Galois idea at a completely undergraduate point. The textual content grounds the presentation within the inspiration of algebraic numbers with complicated approximations and assumes of its readers just a first direction in summary algebra. the writer organizes the speculation round ordinary questions on algebraic numbers, and routines with tricks and facts sketches inspire 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 prior to on hand to scholars of the topic. Exploratory Galois concept contains classical functions, from ruler-and-compass structures to solvability by means of radicals, and in addition outlines the generalization from subfields of the advanced 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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