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