Math 60210 Basic Algebra 1 (Fall 2014)
Graduate Algebra
| Date | Topics | Source |
| Wed, Aug 27 | Basic definitions and examples of groups, cyclic groups and orders | Lecture 1 |
| Wed, Aug 29 | Subgroups, symmetric groups, dihedral groups, cycle decompositions | Lecture 2 |
| Mon, Sep 1 | Subgroups, homomorphisms, sign of a permutation | Lecture 3 |
| Wed, Sep 3 | Group quotients, normal subgroups. | Lecture 4 |
| Fri, Sep 5 | Normal subgroups, isomorphism theorems. | Lecture 5 |
| Mon, Sep 8 | Automorphisms, semidirect products | Lecture 6 |
| Wed, Sep 10 | Free groups, presentations, abelian groups | Lecture 7 |
| Wed, Sep 12 | Abelian groups, group actions | Lecture 8 |
| Wed, Sep 15 | Group actions, the class equation | Lecture 9 |
| Wed, Sep 17 | Class equation, Sylow theorems | Lecture 10 |
| Fri, Sep 19 | Proof of Sylow theorems, applications | Lecture 11 |
| Mon, Sep 22 | The Sylow theorems and semidirect products | Lecture 12 |
| Wed, Sep 24 | Semidirect products, groups of order 12 and 30 | Lecture 13 |
| Fri, Sep 26 | Groups of order 30 and 60 | Lecture 14 |
| Mon, Sep 29 | Groups of order 60, simple groups, A5 | Lecture 15 |
| Wed, Oct 01 | Simplicity of An, duals of groups. | Lecture 16 |
| Fri, Oct 03 | Duals, solvable groups. | Lecture 17 |
| Mon, Oct 06 | Solvable and nilpotent groups, direct limits. | Lecture 18 |
| Wed, Oct 08 | Direct and inverse limits. | Lecture 19 |
| Fri, Oct 10 | Direct and inverse limits. | Lecture 20 |
| Mon, Oct 13 | Inverse limits, duals. | Lecture 21 |
| Wed, Oct 15 | Profinite groups. | Lecture 22 |
| Fri, Oct 17 | Profinite groups and Pontryagin duals. | Lecture 23 |
| Mon, Oct 27 | Pontryagin duals, basics of rings. | Lecture 24 |
| Wed, Oct 29 | Ring homomorphisms, ideals, isomorphism theorems. | Lecture 25 |
| Fri, Oct 31 | Isomorphism theorems, Chinese Remainder Theorem, prime and maximal ideals, radicals | Lecture 26 |
| Mon, Nov 03 | Nilradical, radical of an ideal | Lecture 27 |
| Wed, Nov 05 | Jacobson radical. Pullbacks and pushforwards of ideals. | Lecture 28 |
| Fri, Nov 07 | Rings of fractions and localization. | Lecture 29 |
| Mon, Nov 10 | Euclidean domains, PIDs, UFDs | Lecture 30 |
| Wed, Nov 12 | UFDs, sums of squares | Lecture 31 |
| Fri, Nov 14 | Modules, isomorphism theorems, Noetherian modules | Lecture 32 |
| Mon, Nov 17 | Noetherian rings and modules | Lecture 33 |
| Wed, Nov 19 | The Hilbert basis theorem, modules over PIDs | Lecture 34 |
| Fri, Nov 21 | Free modules over PIDs | Lecture 35 |
| Mon, Nov 24 | Finitely generated modules over PIDs, Nakayama's lemma, Hom modules | Lecture 36 |
| Mon, Dec 01 | Projective and injective modules, localization of modules | Lecture 37 |
| Wed, Dec 03 | Exact functors and tensor products | Lecture 38 |
| Fri, Dec 05 | Tensor products and flatness | Lecture 39 |
| Mon, Dec 08 | Flatness: pushforwards and pullbacks, localization | Lecture 40 |
| Wed, Dec 10 | Flatness over PIDs | Lecture 41 |
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