Math 1540 Lectures

Week 1:
Thur: Intro, review of groups, fields, vector spaces

Week 2:
Tues: (5.1) Field extensions and algebraic numbers
Thur: (5.1) Main proof about algebraic numbers and field extensions

Week 3:
Tues: (5.2) Transcendence of e, Liouville Numbers
Thur: (5.3) Existence of Splitting Fields

Week 4:
Tues: (5.3) Uniqueness of Splitting Fields
Thur: (7.1) Classification of Finite Fields

Week 5:
Tues: no class
Thur: (5.4) Ruler and Compass constructions

Week 6:
Tues: (5.5) Simple roots, construction of regular 17-gon
Thur: (5.6) Statement of Galois Theorem, beginning of proof

Week 7:
Tues: (5.6) proof continued
Thur: (5.6) end of proof.

Week 8:
Tues: (5.7,5.8) overview of solvability
Thur: (5.7,5.8) solvability proof

Week 9:
Tues: (5.7,5.8) end of solvability proof
Thur: intro to projective geometry

Week 10: Spring Break

Week 11: Tues: more projective geometry
Thurs: grid theorem

Week 12:
Tues: grid theorem + elliptic curves
Thur: Weierstrass Elliptic curve group law

Week 13:
Tues: Weierstrass Elliptic curve group law
Thur: general elliptic curves