Combining a concrete perspective with an exploration-based approach, this analysis develops Galois theory at an entirely undergraduate level. The text grounds the presentation in the concept of algebraic numbers with complex approximations and only requires knowledge of a first course in abstract algebra. It introduces tools for hands-on experimentation with finite extensions of the rational numbers for readers with Maple or Mathematica. Please visit the author's website at: http://www.davidson.edu/academic/math/swallow/john.htm
John Swallow is John T. Kimbrough Associate Professor of Mathematics at Davidson College. He holds a doctorate from Yale University for his work in Galois theory. He is the author or co-author of a dozen articles, including an essay in The American Scholar. His work has been supported by the National Science Foundation, the National Security Agency, and the Associated Colleges of the South.
1. Preliminaries; 2. Algebraic numbers, field extensions, and minimal polynomials; 3. Working with algebraic numbers, field extensions, and minimal polynomials; 4. Multiply-generated fields; 5. The Galois correspondence; 6. Some classical topics; Historical note.