Material covered:
- Monday, January 3: introduction to rings (section 10.1).
- Wednesday, January 5: polynomials (section 10.2).
- Friday, January 7: discussed sample portfolio problem.
- Monday, January 10: ring homomorphisms (section 10.3).
- Wednesday, January 12: ideals (section 10.3).
- Friday, January 14: polynomials, quotient rings (sections
10.3, 10.4).
- Wednesday, January 19: discussed problem 10 in section 10.3.
- Friday, January 21: quotient rings, adjoining elements
(sections 10.4, 10.5).
- Monday, January 24: adjoining elements, started discussing
integral domains (sections 10.5, 10.6).
- Wednesday, January 26: discussed homework, fraction fields
(section 10.6).
- Friday, January 28: maximal ideals, irreducible polynomials
(section 10.7).
- Monday, January 31: peer-critiquing of portfolio problems.
- Wednesday, February 2: midterm.
- Friday, February 4: the Nullstellensatz and algebraic
geometry (sections 10.7, 10.8).
- Monday, February 7: introduction to factorizations (section
11.1, more or less).
- Wednesday, February 9: UFDs, PIDs, Euclidean domains
(section 11.2).
- Friday, February 11: proof that Euclidean domain implies
PID, and that PID implies UFD (section 11.2).
- Monday, February 14: started the proof that if R is a UFD,
so is R[x] (section 11.3).
- Wednesday, February 16: finished the proof.
- Friday, February 18: criteria for irreducibility of integer
polynomials (section 11.4), started discussing primes in
Z[i] (section 11.5).
- Wednesday, February 23: more on Z[i].
- Friday, February 25: discussion.
- Monday, February 28: started discussing factorization of
ideals in rings of integers in quadratic number fields
(sections 10.6, 10.7, 10.8).
- Wednesday, March 2: ideals vs. lattices, lemmas aimed at
proving factorization of ideals.
- Friday, March 4: finished the proof of ideal factorization.
- Monday, March 7: Worked on an example: for which primes
p is there an integer solution to
x2 + 5y2 = p?
- Wednesday, March 9: finished this example and discussed the
ideal class group.
- Friday, March 11: review.
Back to Math 403A home page.
John Palmieri Padelford C-538 (206) 543-1785
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