Math 250B Syllabus

Week of	Mon	Wed	Fri	Topics
8/23	X	X	Sets	Introduction: Sets, correspondences, operations
8/30	I.1, 2	I.3	I.4	Groups, monoids, subgroups, cyclic groups,
9/06	Holiday	I..5	I.6	Cyclic groups, Group actions. Semi-direct products, p-groups and p-subgroups,
9/13	I.6	I.5	I.7, I.8	Sylow subgroups. Symmetric groups. Simple groups. The alternating group. Primitive actions
9/20	Midterm		I.8	A_n is simple. Abelian groups.
9/27	I.8	I.11	I.11,I.12	Finitely generated abelian groups. Freeness. Categories.
10/04	II.1,2	II.3	II.4	Rings, Commutative rings. Monoid rings. Equations
10/11	II.5	III.1, 2	III.3, 4	Localization. Factorization. Modules, Hom, Direct products and sums, free modules,
10/18	III.5,6	III 7	III.10	Vector spaces, . Modules over PID's. Limits
10/25	IV.1	IV.2	IV.4	Polynomials. Unique factorization. Gauss content, Eisentsein criterion
11/01	V.1	V.2		Algebraic Equations and maximal ideals. Field extensions. Algebraic closure.
11/08	V.3	V.4	V.5	Splitting fields. Separable extensions. Finite fields
11/15	V.6	Midterm	VI.2	Galois extensions. Examples. The Midterm will cover up through and including V.2
11/22	VI.3		Holiday	Roots of unity. Characters, norm and trace
11/29	VI.6	VI.7	Holiday	Cyclic extensions. Solvable extensions. Roots
11/29	VI.9			Galois theory a la Grothendieck

The above schedule is just a rough guide and subject to change as the course progresses.