Lectures and Homework :

Lectures						Homework
Dates				Sections	Topics	Problems	HW due date
January
	Week 1	11	M	Ch. 2.	Field theory review.
		13	W		Rings of algebraic integers.
		15	F
	Week 2	20	W		Trace, norm, units.
		22	F		Discriminants.	Homework 1.	2/3.
	Week 3	25	M		Integral bases.
		27	W		Integral basis computations.
		29	F
February
	Week 4	1	M		Integral bases for cyclotomic extensions.
		3	W		Ring theory review.	Homework 2.	2/12.
		5	F		Dedekind rings.
	Week 5	8	M		The ring of integers of a number field is a Dedekind ring.
		10	W		A Dedekind ring admits unique factorization into prime ideals.
		12	F		Fractional ideals and the ideal class group.	Homework 3.	2/22.
	Week 6	15	M		Ideal arithmetic.
		17	W		Ideal norm.
		19	F		Prime splitting in number fields.
	Week 7	22	M		Ramification and inertia.
		24	W		The "efg Theorem".
		26	F		Kummer's Theorem.	Homework 4.	3/15.
March
	Week 8	1	M		Splitting in quadratic and cyclotomic extensions.
		3	W		The second case of Fermat's Last Theorem for regular prime exponent.
		5	F		Bernoulli numbers and regular primes.
	Week 9	15	M		Finiteness of the class number.
		17	W		Introduction to the geometry of numbers.
		19	F
	Week 10	22	M		Minkowski's Convex Body Theorem.
		24	W		The Minkowski Bound and computation of class numbers.	Homework 5.	4/5.
		26	F		Units in real quadratic nummber fields.
	Week 11	29	M		Lattices in logarithmic space.
		31	W		Conclusion of proof of Dirichlet's Unit Theorem.
April
		2	F		The Decomposition and Inertia Groups.
	Week 12	5	M
		7	W		The Artin Symbol.	Homework 6.	4/30.
		9	F		Artin symbol in quadratic and cyclotomic fields.
	Week 13	12	M		Infinite primes; absolute values.
		14	W		Hilbert Class Field, modular j-invariant, complex multiplication.
		16	F		Congruence subgroups, generalized ideal class groups, the Artin Map, and Artin Reciprocity.
	Week 14	19	M		Ray class fields, conductors, cyclotomic fields.
		21	W		The Kronecker-Weber Theorem and Quadratic Reciprocity.
		23	F		Dedekind zeta-function, analytic class number formula, Dirichlet density.
	Week 15	26	M		Chebotarev Density Theorem, zeros of irreducible cubics mod p, weight one modular forms.
	Finals week	30	F		Final Exam, 2 - 5.	Cumulative.