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