Math 154


time/place: Tu-Th 1:00-2:40 Barus&Holley Room 161
instuctor: Prof. Rich Schwartz
my office hours: F10-12

course summary: This is a course mainly on the theory of fields, especially Galois Theory. There will also be a component on elliptic curves, and possibly a bit about error-correcting codes.

text: Topics in Algebra (2nd ed.) by I.N. Herstein
I'll also photocopy a few chapters out rational points on elliptic curves by J. Silverman and J. Tate

grading: Your grade is based on 3 components:

homework: 30%

midterm: 30%

final exam: 40%

homework: I will assign homework each Tuesday
and collect it the following Tuesday. No late HW.
Click here for the assignments.
list of topics:

• quick review of polynomial rings
• field extensions and algebraic numbers
• fundamental theorem of algebra
• splitting fields
• constructible numbers
• The Galois Isomorphism Theorem
• solvability by radicals
• finite fields
• transcendence of e and Pi; Lindemann's Theorem
• projective geometry; homogeneous polynomials.
• group law for elliptic curves over Q
• topology of elliptic curves over C
• A primer on complex analysis
• Weierstrass uniformization
• Lenstra's elliptic curve factoring algorithm
• linear error-correcting codes and finite fields
• Golay's (24,12) code and the Miracle Octad Generator

notes

• algebraic integers
• Liouville numbers
• constructing the regular 17-gon
• approximating pi
• notes on solvability
• transcendence of e
• transcendence of pi & Lindemann's Theorem
• projective curves
• A case of the Cayley-Bacharach Theorem
• A primer on Complex Analysis
• Weierstrass uniformization I
• Weierstrass uniformization II
• error correcting codes