Math 250B Syllabus
Week of | Mon | Wed | Fri | Topics |
1/18 | Holiday | Categories. Presheaves. Yoneda's theorem. Limits | ||
1/25 | Modules over a ring. Kernels, cokernels, images,coimages, Abelian categories. Complexes. | |||
2/01 | Homomorphisms and Extensions. Injectives and projectives. Tensor products. | |||
2/08 | Flatness. Base change, induction, adjointness. | |||
2/15 | Holiday | Semisimplicity. | ||
2/22 | Commutative rings. Localization. The spectrum of a ring. Finite type and finite presentation. Nakayama's lemma. | |||
3/01 | The category of rings. Algebras, ideals, and equations. Finite and integral ring extensions. | |||
3/08 | Galois theory for rings. Noetherian rings. | |||
3/15 | Primary decomposition. Algebras over a field. Noether normalization. Nullstellensatz. | |||
3/22 | Spring Break | |||
3/29 | Differentials and deformations. | |||
4/05 | Filtered and graded rings. | |||
4/12 | Grobner bases. Completion. | |||
4/19 | Dimensioin theory. | |||
4/26 | Homological theory. Regular local rings Depth. | |||
5/03 | Reading Week |
The above schedule is just a rough guide and subject to change as the course progresses.