| Jan 20 | AK 1-3: Rings, prime ideals, radical ideals |
| Jan 22 | AK 4: Modules |
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| Jan 25 | AK 5: Exact sequences |
| Jan 27 | AK 6: Direct limits |
| Jan 29 | AK 7: Filtered direct limits |
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| Feb 1 | AK 8: Tensor products |
| Feb 3 | AK 9: Flatness |
| Feb 5 | AK 10: Cayley-Hamilton theorem |
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| Feb 8 | Finish AK 10 |
| Feb 10 | AK 11: Localization of rings |
| Feb 12 | AK 12: Localization of modules |
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| Feb 15 | AK 14: Krull-Cohen-Seidenberg theory |
| Feb 17 | AK 15: Noether normalization |
| Feb 19 | Finish AK 15 |
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| Feb 22 | AK 16: Chain conditions |
| Feb 24 | AK 17: Associated primes |
| Feb 26 | AK 18: Primary decomposition |
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| Feb 29 | Finish AK 18 |
| Mar 2 | AK 19: Length |
| Mar 4 | Finish AK 19 |
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| Mar 7 | AK 20: Hilbert functions |
| Mar 9 | Finish AK 20 |
| Mar 11 | AK 21: Dimension |
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| Mar 14 | Lang V.1-V.2: Finite and algebraic extensions; algebraic closure |
| Mar 16 | Lang V.3: Splitting fields and normal extensions |
| Mar 18 | Lang V.4: Separable extensions |
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| Spring break |
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| Mar 28 | Finish V.4 |
| Mar 30 | Lang V.5: Finite fields |
| Apr 1 | Lang VI.1: Galois extensions |
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| Apr 4 | Finish VI.1 |
| Apr 6 | Lang VI.2: Examples |
| Apr 8 | Lang VI.3: Roots of unity |
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| Apr 11 | Lang V.6: Inseparable extensions; VI.4: Linear independence of characters |
| Apr 13 | Lang VI.5: Norm and trace |
| Apr 15 | Finish VI.5; Lang VI.6: Cyclic extensions |
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| Apr 18 | Lang VI.7: Solvable and radical extensions |
| Apr 20 | Finish VI.7 |
| Apr 22 | Lang XV.8: Alternating forms |
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| Apr 25 | Lang XV.9: Pfaffians |
| Apr 27 | Lang XIX.1: Exterior algebras |
| Apr 29 | Finish XIX.1 |
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| May 2 | Inverse limits; Lang Exercise VI.43: Profinite topology |
| May 4 | Lang VI.14: Infinite Galois extensions |
| May 6 | Next steps: overview of more advanced algebraic topics |