MATH 369: Introduction to Abstract Algebra

Fall 2025


Preparing a course schedule is typically an exercise in fiction-writing. However, we hope to roughly follow this schedule:

Date Lecture Assigned Reading Additional Topics
Week 1
8/25 Course Introduction; Review of Divisibility and Modular Arithmetic Notes Chapters 1.1-1.4 (review) Proof Writing Tips
8/27 Functions; Equivalence Relations Notes Chapters 2.1-2.2
Week 2
9/1 No Class - Labor Day
9/3 Permutations and Cycle Notation Chapter 2.3
Week 3
9/8 Definition of a Group Notes Chapter 3.1 Building Groups: From Magmas to Groups
9/10 Group Examples and Properties Notes Chapter 3.1
Week 4
9/15 Subgroups Notes Chapter 3.2
9/17 Constructing Examples Chapter 3.3
Week 5
9/22 Isomorphisms Notes Chapter 3.4
9/24 Cyclic Groups Chapter 3.5
Week 6
9/29 Permutation Groups Notes Chapter 3.6
10/1 Homomorphisms Notes Chapter 3.7
Week 7
10/6 Midterm 1
10/8 Homomorphisms (continued) Notes Chapter 3.7
Week 8
10/13 Cosets, Normal Subgroups, and Factor Groups Notes | Notes Chapter 3.8
10/15 Cosets, Normal Subgroups, and Factor Groups (continued) Notes Chapter 3.8
Week 9
10/20 Cosets, Normal Subgroups, and Factor Groups (continued) Notes Chapter 3.8
10/22 Fields; Roots of Polynomials Notes Chapter 4.1
Week 10
10/27 Factors Notes | Notes Chapter 4.2
10/29 Existence of Roots Notes | Notes Chapter 4.3
Week 11
11/3 Existence of Roots (continued) Notes Chapter 4.3
11/5 Polynomials over Q, R, and C Notes Chapter 4.4
Week 12
11/10 Extension Fields; Applications to Finite Fields Notes | Notes Chapter 4.4
11/12 Commutative Rings; Integral Domains Notes Chapter 5.1
Week 13
11/17 Commutative Rings; Integral Domains (continued) Notes Chapter 5.1
11/19 Midterm Exam 2
Week 14
11/24 Ring Homomorphisms Notes | Notes Chapter 5.2
11/26 No Class - Thanksgiving Break
Week 15
12/1 Ideals and Factor Rings Notes Chapter 5.3
12/3 Ideals and Factor Rings (continued) Notes Chapter 5.3
Week 16
12/8 Quotient Fields Notes Chapter 5.4
12/15 Final Exam - 8:00--10:00am