Groups, Fields, and Galois: Part 1

Group theory is recognized as one of the great unifying mathematical disciplines, with far-reaching applications in virtually all scientific (and many non-scientific) fields.  This course, the first of a two-quarter sequence that concludes in Winter 2027 with a course on fields and Galois Theory, is geared toward developing the tools of group theory needed to establish the Abel-Ruffini theorem on the insolvability by radicals of the general polynomial of degree five or greater.  Results established along this journey will also be applied toward addressing the three classical ruler and compass construction problems of antiquity: trisecting the angle, duplication of the cube, and squaring the circle, as well as Gauss' surprising characterization of constructible regular polygons.