Groups, Fields, and Galois: Part 2

In no branch of mathematics is there such an elegant fusion of classical and modern ideas as in Galois Theory. Its basic tenets were delineated by the 20-year-old Evariste Galois in a letter written the night before he was killed in a pistol duel in 1832. There he unraveled the mystery concerning the conditions under which a polynomial equation could be "solved by radicals." This course offers an introductory, rigorous, and quick-paced development of the mathematics leading up to Galois' characterization of equation solvability. Topics to be discussed include field extensions (algebraic and transcendental), algebraic closures, symmetric functions, Galois groups, solvability by radicals and insolvability of the quintic, and the three classical construction problems of antiquity: angle trisection, cube duplication, and circle squaring, as well as Gauss' surprising characterization of constructible regular polygons.