Math 80220 Topics in Algebra (Spring 2018)
Algebraic Number Theory
Lecture notes
| Day | Lecture | Topics | Sage code |
| Wed 01/17 | 1 | Euclidean domains and unique factorization | sage |
| Fri 01/19 | 2 | Finish ED and UFD | sage |
| Mon 01/22 | 3 | Number fields and rings of integers | sage |
| Wed 01/24 | 4 | Trace, norm, rings of integers | sage |
| Fri 01/26 | 5 | Integral bases | |
| Mon 01/29 | 6 | Factorization in rings of integers and fractional ideals | sage |
| Wed 01/31 | 7 | Fractional ideals have inverses | |
| Fri 02/02 | 8 | Unique factorization into prime ideals | |
| Mon 02/05 | 9 | Chinese Remainder Theorem, ideals are generated by 2 elements | sage |
| Wed 02/07 | 10 | Norms of ideals | |
| Fri 02/09 | 11 | Finiteness of the class group | |
| Mon 02/12 | 12 | Minkowski bounds | sage |
| Wed 02/14 | 13 | Dirichlet unit theorem part 1: units form a finitely generated abelian group | |
| Fri 02/16 | 14 | Dirichlet unit theorem part 2: computation of the rank of units | |
| Mon 02/19 | 15 | S-integers and S-units | |
| Wed 02/21 | 16 | p-adic completions | |
| Fri 02/23 | 17 | Adeles | |
| Mon 02/26 | 18 | Cocompact lattices in adeles and ideles | |
| Wed 02/28 | 19 | ||
| Fri 03/02 | 20 | ||
| Mon 03/05 | 21 | ||
| Wed 03/07 | 22 | ||
| Fri 03/09 | 23 | ||
| 3/10 - 3/18 | Spring break | ||
| Mon 03/19 | 24 | ||
| Wed 03/21 | 25 | ||
| Fri 03/23 | 26 | ||
| Mon 03/26 | 27 | ||
| Wed 03/28 | 28 | ||
| 3/30 - 4/2 | Easter | ||
| Wed 04/04 | 29 | ||
| Fri 04/06 | 30 | ||
| Mon 04/09 | 31 | ||
| Wed 04/11 | 32 | ||
| Fri 04/13 | 33 | ||
| Mon 04/16 | 34 | ||
| Wed 04/18 | 35 | ||
| Fri 04/20 | 36 | ||
| Mon 04/23 | 37 | ||
| Wed 04/25 | 38 | ||
| Fri 04/27 | 39 | ||
| Mon 04/30 | 40 | ||
| Wed 05/02 | 41 | ||
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