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