## 2018-03-13

### Abstract Algebra (Fall 2017) by James Cook at Liberty University

source: James Cook     2017年8月29日
These Lectures are from the Fall 2017 offering of Math 421 at Liberty University in Lynchburg Virginia, USA. I intend to follow Nicholson's "Introduction to Abstract Algebra" fourth edition. Students who take this course have experience with proofs and have already studied some abstraction in linear algebra, consequently this course is a bit more aggressive than some algebra courses where abstract algebra appears as a lower-level course. In brief, we cover monoids, groups, subgroups, cyclic groups, permutations, homomorphism, cosets, normal subgroups, factor groups, direct products, isomorphisms, lattice of subgroups, Sylow theorems, group actions, orbit stabilizer theorem, rings, integral domains, fields, polynomials, ideals, prime ideals, maximal ideals, PIDs, euclidean domains, UFDs, factorization. Essentially Chapters 0,1,2,3,4,5 and 8 of Nicholoson.

42:40 course intro, sets, maps, equivalence relations: 8-28-17
56:36 extra help with sets, maps and equivalence: 8-29-17
53:17 Integers and modular arithmetic: 8-30-17 (race day)
59:51 extra help with maps and modular arithmetic: 8-30-17
53:45 modular arithmetic, permutations, 9-1-17
55:43 monoids, associativity and inverse properties, 9-4-17 (party day)
54:59 extra help with permutations and map problem, 9-5-17
54:35 extra help with cayley tables, permutations: 9-7-17
51:29 groups, generators and relations, direct product, 9-8-17
10 53:46 subgroups, lattice diagrams, cyclic part 1, 9-11-17
11 58:44 couple subgroup examples, help with cyclics : 9-12-17
12 52:06 cyclic groups, 9-13-17
14 47:09 cyclic group end, isomorphism begin : 9-15-17
15 51:49 isomorphism theorems, automorphisms 9-20-17
16 56:10 help session, illustrating Cayley, forgot proofs, 9-21-17
17 50:48 preparing for Test 1, 9-2-17
18 50:39 cosets and Lagrange's Theorem, 9-27-17
19 42:48 post-mortem for Test 1, 9-28-17
20 50:06 applications of Lagrange's Theorem, 9-29-17
21 51:04 normal subgroups, 10-2-17
22 52:17 normal subgroup proofs, normal subgroups Dn, 10-3-27
23 51:22 the factor group construction (aka quotient group), 10-4-17
24 51:37 1st Isomorphism Theorem, 10-9-17
25 51:49 help session on order of elements in factor groups 10-10-17
26 52:01 isomorphism theorems, product theorems, 10-11-17
27 37:13 help session, silent movie time oh noes, 10-12-17
28 51:14 Cauchy's Theorem and Class Equation, 10-13-17
29 50:32 group actions part 1, 10-16-17
30 50:55 symmetry vs. motion, problem on normalizers, 10-17-17
31 49:48 Sylow Theorems, 10-18-17
32 46:34 help session, isomorphism, comment on core, 10-19-17
33 49:20 groups of units and RSA badly explained, 10-20-17
34 51:14 rings defined and basic examples, properties, 10-23-17
35 51:06 help session, fixer and Sylow examples, 10-24-17
36 49:57 subrings and algebra isomorphisms, 10-25-17
37 52:42 help session, solution to Missions discuss, 10-26-17
38 52:01 ring theorems, field of quotients, 10-27-17
39 35:41 review for Test 2, 10-30-17
40 39:45 help session, 10-31-17
41 43:11 help session, group mystery project, ring endomorphisms 11-2-17
42 50:50 factor rings, 11-3-17
43 53:16 prime and maximal ideals, simple rings, 11-6-17
44 50:14 ideal of matrix ring, 11-8-17
45 48:03 almost helpful session, 11-9-17
46 52:26 ring homomorphisms, 11-10-17
47 50:47 decomposing rings, polynomial foundations, 11-13-17
48 54:17 help session, post mortem of Test 2, 11-14-17
49 18:51 comments on Nicholson 4.1 (polynomials) , 11-15-17
50 51:46 irreducibility up to Eisenstein, 11-15-17
51 52:06 help session, polynomials and irreducibility, 11-16-17
52 52:53 associates, irreducibles, primes 11-17-17
53 52:14 irreducible polynomial generates maximal ideal, 11-27-17
54 35:48 help session rings, factor rings, select hwks, 11-28-17
55 51:13 ED implies PID implies UFD, some number theory, 11-29-17
56 53:27 help session, rings, big classification picture, 11-30-17
57 50:29 quaternions and 4 square identity, Kronecker Thm, 12-1-17
58 47:33 review for Test 3, 12-4-17
59 59:51 questions for Test 3, 12-5-17, part 1
60 2:31 questions for Test 3, 12-5-17, part 2
61 48:03 representations of groups, quarks, Test 3 p.m. 12-11-17