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