MATH 5821 - Topics in Abstract Algebra
Fall 2026 Syllabus, Section 01, CRN 40512,
Credit hours: 4
Course Meeting Times
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Instructor
Thomas Madsen
Email: tlmadsen@ysu.edu
Course Description
Course Readings
| Group | Title | Author | ISBN |
|---|---|---|---|
| Required | Course notes | Thomas Madsen |
As primary text for this course we will use some notes. If you would like to buy a physical textbook, I recommend the 8th edition of Joseph Gallian’s Contemporary Abstract Algebra. There is a newer edition, but the 8th edition is fine. You don’t need to buy this book, but it might be helpful for some things.
The course readings are subject to change in the event of extenuating circumstances, research developments, current events, and/or to ensure better learning.
Assignments/Assessments
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Tentative Schedule - This is a rough guide for our plan. We may include more topics as there is interest/opportunity/time
| Week of | Proposed Topic | Due/To Prepare for Class |
|---|---|---|
| 8/24 | Review of things from Linear Algebra and Discrete Mathematics. Introduction to group theory. | Study your notes, Homework may be due, prepare for quiz/exam. |
| 8/31 | Basic group theory (definition, examples, properties) | Study your notes, Homework may be due, prepare for quiz/exam. |
| 9/7 | Basic group theory (definition, examples, properties) Subgroups |
Study your notes, Homework may be due, prepare for quiz/exam. |
| 9/14 | Subgroups Cyclic Groups |
Study your notes, Homework may be due, prepare for quiz/exam. |
| 9/21 | Permutation groups | Study your notes, Homework may be due, prepare for quiz/exam. Exam 1 |
| 9/28 | Permutation groups, dihedral groups | Study your notes, Homework may be due, prepare for quiz/exam. |
| 10/5 | Homomorphisms | Study your notes, Homework may be due, prepare for quiz/exam. |
| 10/12 | Isomorphisms Group actions |
Study your notes, Homework may be due, prepare for quiz/exam. |
| 10/19 | Group actions Cosets and Lagrange's Theorem |
Study your notes, Homework may be due, prepare for quiz/exam. |
| 10/26 | Cosets and Lagrange's Theorem | Study your notes, Homework may be due, prepare for quiz/exam. Exam 2 |
| 11/2 | Normal subgroups and factor groups | Study your notes, Homework may be due, prepare for quiz/exam. |
| 11/9 | The Fundamental Theorem for Finite Abelian Groups | Study your notes, Homework may be due, prepare for quiz/exam. |
| 11/16 | Rings and fields | Study your notes, Homework may be due, prepare for quiz/exam. |
| 11/23 | Rings and fields | Study your notes, Homework may be due, prepare for quiz/exam. Exam 3 |
| 11/30 | Catch-up and review | Study your notes, Homework may be due, prepare for quiz/exam. |
| 12/7 | Final Exam | Final Exam |
The course schedule, policies, procedures, and assignments in this course are subject to change in the event of extenuating circumstances, by mutual agreement, and/or to ensure better learning.