MATH 423: Abstract Algebra
**Math 423 Resource Homepage**

The videos below were originally part of the lecture series for Math 421 given in the Fall 2018 Semester. Math 423 is different in emphasis and that distinction is more clearly seen in the selection of problems for the eight weekly homework assignments. There are problems in those assignments which are based on watching and processing the videos linked on this page. In addition, it may be useful to note the Lecture Notes which are periodically referenced in the videos below can be found at:

2018 Abstract Algebra Notes

Please also be aware, there is additional content in the playlist:

2018 Abstract Algebra Playlist

Math 423 students are not expected to watch all the videos in the above playlist. There are a handful of topics which have been omitted and the help session videos sometimes discuss homework which was particular to Math 421 of 2018.

__Homework for Math 423__

Week 1 Homework: preliminaries and groups

Week 2 Homework: subgroups and isomorphism

Week 3 Homework: cyclic groups, dihedral groups and more

Week 4 Homework: group homomorphisms and generalized cycle notation

Week 5 Homework: quotient and product groups

Week 6 Homework: rings

Week 7 Homework: factor rings and ideals

Week 8 Homework: fields

__Problems from Gallian's 9th Edition__

Sometimes the ebook doesn't work. No need to fret, behold pdf scans of the part that matters:
problems from Chapters 1,2,3,4

problems from Chapters 5,6,7,8

problems from Chapters 9, 10

problems from Chapters 12, 13, 14, 15

problems from Chapters 16, 17, 18

problems from Chapters 20, 21

__Videos for Week 1__

Video 1: properties of integers, Euclidean algorithm

Video 2: modular arithmetic

Video 3: permutations and cycle notation

Video 4: historical motivation of group construction, definitions of group, ring and field.

__Videos for Week 2__

Video 5: Examples of groups; additive ring Zn, groups of units in Zn, matrix groups

Video 6: isomorphism, order preserved for elements, n-th roots of unity discussed

Video 7: subgroups and isomorphism, cyclic subgroups map nicely, equation mapping theorem

__Videos for Week 3__

Video 8: dihedral groups, includes background on symmetries in Euclidean space and Perm(S), generators and relations

Video 9: order in Dn, G1 x G2, cyclic groups

Video 10: cyclic groups

Video 11: theory of cyclic groups, subgroups and generators

__Videos for Week 4__

Video 12: group homomorphism theory

Video 13: Cayley's Theorem

__Videos for Week 5__

Video 14: cosets and Lagrange’s Theorem

Video 15: normal subgroups and quotient groups

Video 16: direct products inside and out

Video 17: units of Zn and encryption

Video 18: isomorphism theorem

__Videos for Week 6__

Video 21: rings and integral domain

Video 22: ideals and factor rings

Video 23: prime and maximal ideals

Video 24: ring homomorphism and the field of fractions construction

__Videos for Week 7__

Video 25: formal construction of polynomials

Video 26: factorization of polynomials

Video 27: divisibility in Integral Domains I

Video 28: divisibility in Integral Domains IIa

Video 28: divisibility in Integral Domains IIb

__Videos for Week 8__

Video 29: extension fields

Video 30: algebraic extensions

Last Modified: 7-14-23