Course Website

Homepage

Syllabus

Textbook

Abstract Algebra, by Dummit and Foote, Third Edition, 2004

Lecture Notes

Download PDF

Week 1
1/24	Divides, Equivalence Relations
1/26	Well-ordering of Z
Week 2
1/29	Division Algorithm, gcd
1/31	Euclidean Algorithm
2/2	Equivalence Class, Z/nZ, Group
Week 3
2/5	Group, Well-definedness, Z/nZ
2/7	(Z/nZ)*, Properties of Group
2/9	Order, Symmetric Group
Week 4
2/12	Symmetric Group, Cycle
2/14	Homomorphism, Isomorphism
2/16	Order, Homomorphism, Subgroup
Week 5
2/19	Dihedral Groups, Subgroup
2/21	Cyclic Group, lcm, Order of g^a
2/23	Cyclic Subgroup, Generating Set of a Group
Week 6
2/26	Finitely Generated Group
2/28	Coset, Normal Subgroup
3/2	Exam 1
Week 7
3/5	Quotient Group, Index, Lagrange’s Theorem
3/7	Corollaries of Lagrange’s Theorem
3/9	The First & Second Isomorphism Theorems
Week 8
3/12	The Third Isomorphism Theorem
3/14	Transposition, Sign of Permutation
3/16	Homework 6, The Correspondence Theorem
Week 9
3/19	Sign of Permutation, Alternating Group
3/21	Subgroups of A_4, Group Action, Orbit, Stabilizer
3/23	Orbit, Stabilizer, Cayley’s Theorem
Week 10
4/2	Conjugacy Class, The Class Equation
4/4	Cauchy’s Theorem, Recognizing Direct Products
4/6	Homework 8, Properties of Finite Abelian Group
Week 11
4/9	Fundamental Theorem of Finite Abelian Groups
4/11	Definition of Ring
4/13	Exam 2
Week 12
4/16	Properties of Ring, Zero-Divisor, Unit
4/18	Field, Product Ring, Integral Domain
4/20	Product Ring, Finite Domain and Field, Subring
Week 13
4/23	Polynomial Ring, Ideal, Principal Ideal
4/25	Examples of Ideals, Quotient Ring
4/27	Isomorphism Theorems for Rings
Week 14
4/30	Generating Ideal, Maximal Ideal, Prime Ideal
5/2	Prime Ideal, Euclidean Domain
5/4	Review, Galois Theory