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source: James Cook 2016年8月30日

These are my lectures for Math 421 in Fall 2016. Our text is Contemporary Abstract Algebra by Joseph Gallian, 5th ed. I have a bunch of homeworks, tests and some solutions posted at: http://www.supermath.info/AbstractAlgebra.html

L1: a bit of history, definition of group, 8-29-2016 52:52 Incidentally, I meant to say "quintic" at the 10:30 or so time. That said, Galois theory has application to polynomials of any order.

L2, subgroups and modular examples, 8-31-16 51:16

practice problems, chapter 2 and 3 Gallian, 9-1-16 44:26

L3, center, centralizer, symmetries, dihedral groups, 9-2-16 54:44

L4, divisibility, gcd, euclid's extended algorithm, 9-5-16 52:23

practice problems 9-6-16, chapter 2 and 3 Gallian 41:46

L5, modular arithmetic foundations, 9-7-16 52:18

practice problems 9-8-16, chapter 3 Gallian 46:49

L6, cyclic groups part 1, 9-9-16 51:34

L7, cyclic groups part 2, 9-12-16 50:58

practice problems 9-13-16, chapter 4 Gallian 54:35

L8, permutations and cycle notation, 9-14-16 49:34

practice problems 9-15-16, chapter 5 Gallian 42:36

L9, even and odd permutations, 9-16-16 51:00

L10, homomorphism and isomorphism, 9-23-16 52:16

L11, properties of isomorphisms, 9-26-16 51:29

help session, 9-27-16 45:52

L12, cosets and Lagrange's Theorem, 9-28-16 4:37

L12, cosets part 2, 9-28-16 41:16

help session, 9-29-16 47:10

L13, how to divide or multiply groups, 9-30-16 48:28

L14, towards first isomorphism theorem, 10-3-16 52:24

L15, first isomorphism theorem and select applications, 10-5-16 53:08

help session on 10-4-16 46:53

L16, external and internal direct products, 10-10-16 51:41

L17, a little number theory, 10-12-16 52:46

L18, group action, 10-14-16 45:36

L19, orbit stabilizer theorem, 10-17-16 51:06

help session, solutions to Lecture 10,11 and 12 problems, 10-18-16 55:54

L20, Cauchy's Theorem, Sylow mention , 10-19-16 45:22

help session on 10-20-16 48:06

L21, Isomorphism Theorems, mention of finite simple group classification , 10-21-16 39:41

L22, First Isomorphism Theorem and Linear Algebra, Boolean group , 10-24-16 49:08

help session, 10-25-16 39:33

help session, 10-27-16 45:03

L23, rings and integral domains, 10-31-16 51:20

help session, 11-1-16 50:45

L24, ideals and factor rings, 11-2-16 51:01

L25, ring homomorphism, 11-4-16 52:21

L26, polynomials , 11-7-16 52:00

L27, F[x] is a PID, polynomial factoring I, 11-9-16 50:34

help session, 11-10-16, part 1 59:51

help session, 11-10-16, part 2 12:10

L28, factorization and divisibility, 11-11-16 51:44

L29, irreducible and prime, EDs, PIDs, UFDs, 11-14-16 52:48

help session, 11-15-16 56:03

L30, extension fields , 11-16-16 50:29

L32, extension fields and a word on algebraic closure, 11-28-16 52:49

help session, 11-29-16 52:20

L33: applications of algebra to number theory part 1, 11-30-16 50:00

help session, 12-1-16 34:39

L35, a discussion of algebraic integers, postmortem on Test 3, 12-2-16 maybe. 52:09

L34, review for final 47:52

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