MATH 5310/6310: Introduction to Abstract Algebra I
Office Hours: 10:00-11:00 Wednesdays and Thursdays in Office 1150, Stem+Ag Complex, Building A
Essential Information
The central location for all course-related information (schedule, homework, syllabus, etc) is Canvas. All solutions to quizzes, tests, and worksheets will be posted to Canvas. The times and dates for all examples are listed below in the table.
When you have a question, of course feel free to email me but also please consider posting it to Piazza (which you can do anonymously!) so that everyone can benefit from the discussion. It is incredibly likely that someone else is struggling with a similar issue.
I will be lecturing off of my own notes, which you can see below. These notes were compiled from a few sources, the most closely of which is Dummit and Foote’s book Abstract Algebra, 3rd edition. As an experiment, I’ve also had AI take these notes and attempt to make them into a searchable and navigable web of ideas format, which you can visit below. If you’d like to offer anonymous feedback to me, click the button below.
Some Important Dates and Times
| Date | Event |
|---|---|
| Monday, August 17th | First day of classes |
| Friday, August 21st | Last day to add courses |
| Friday, September 4th | Quiz 1 |
| Monday, September 7th | Labor day - No classes |
| Friday, September 18th | Test 1 |
| October 8-9th | Fall break - No classes |
| Friday, October 16th | Quiz 2 |
| Friday, November 13th | Test 2 |
| Friday, November 20th | Last day to withdraw with a grade of ‘W’ |
| November 23-27th | Thanksgiving break - No classes |
| Wednesday, December 2nd | Quiz 3 |
| Friday, December 4th | Last day of classes |
| Friday, December 12th, 1:30-3:30 PM | Final Exam |
| Monday, December 14th, 9:30 PM | Final grades are submitted |
Rough Class Schedule
| Date | Topics |
|---|---|
| Week 1: August 17-21 | 1.1 Definitions and first examples; 1.2 Basic algebra in a group |
| Week 2: August 24-28 | 1.3 A first gallery of examples; 1.4 Subgroups: first pass |
| Week 3: August 31-September 4 | 1.5 Symmetric groups; 1.6 Dihedral groups; Quiz 1 |
| Week 4: September 7-11 | Labor Day; 1.7 Homomorphisms and isomorphisms: first pass; 1.8 Group actions: first pass |
| Week 5: September 14-18 | Review and catch-up; Test 1 |
| Week 6: September 21-25 | 2.1 Definitions and examples; 2.2 Generators and relations |
| Week 7: September 28-October 2 | 2.3 Cyclic groups in detail; 3.1 Cosets and Lagrange’s theorem |
| Week 8: October 5-9 | 3.1 Cosets and Lagrange’s theorem; 3.2 Normal subgroups; Fall break |
| Week 9: October 12-16 | 3.3 Quotient groups; review and catch-up; Quiz 2 |
| Week 10: October 19-23 | 3.4 Isomorphism theorems; 3.5 Composition series and the Holder program |
| Week 11: October 26-30 | 4.1 Orbits and stabilizers |
| Week 12: November 2-6 | 4.2 The class equation; 4.3 Other group actions with applications |
| Week 13: November 9-13 | Review and catch-up; Test 2 |
| Week 14: November 16-20 | 5.1 Definitions and examples; 5.2 Subrepresentations and irreducibility |
| Week 15: November 23-27 | 🦃 Thanksgiving Break! 🦃 |
| Week 16: November 30-December 4 | 5.3 Schur’s lemma and Maschke’s theorem; 5.4 Characters; Quiz 3; wrap-up and review |
Class Policies
Exercises, Assessment, and Grading
Gradescope
All assignments will be given on gradescope, which you can access via the menu on Canvas. You will be responsible for uploading pictures or pdfs of your homework to gradescope. You may do this however you wish, but it appears easiest to use the gradescope app. You can use it to scan pages of your homework and then assign those pages to the particular questions that are being graded.
Grading
Course grades will be computing using the following weights:
| Category | Percent |
|---|---|
| Homework | 20% |
| Quizzes | 10% |
| Test 1 | 20% |
| Test 2 | 20% |
| Final Exam | 30% |
Grade cutoffs will be never stricter than 90% for an A- grade, 80% for a B-, 70% for a C-, and 60% for a D-. Some exams may have grade cutoffs set more generously depending on their difficulty.
To encourage eventual mastery, the final exam may be used to improve a student’s exam average. If a student performs better on the cumulative final exam than on one or both tests, then the final exam score may replace the lowest test score.
Homework
Among the notes are various exercises, which are collated into worksheets. These exercises are separated by subsection. I will assign problems from these worksheets. Of these problems assigned, I will check all for completion, and some selected problems for correctness and clarity. Students should expect that any assigned problem may be selected for detailed feedback.
All homework will be visible on gradescope and announced in class. There will be a 24 hour grace period after the due date to allow for any last minute submission issues. After the grace period, no late submissions will be allowed.
Quizzes
There will be three in-class quizzes and their dates are listed above. No make-up quizzes will be given; however, the lowest quiz score will be dropped.
Exams
There will be two in-class exams and their dates are listed above. These exams will be focused on material covered since the last exam, but will rely on ideas and methods learned earlier in the semester. A test can only be made-up if there is a university approved excuse. Exam must be made up within one week. It is the student’s responsibility to make arrangements for any work and/or notes missed due to an absence.
There will also be a final exam covering all material.
Graduate Credit
Students enrolled for graduate credit will attend the same lectures, complete the same core homework, take the same quizzes, and take the same tests and final exam as students enrolled for undergraduate credit. The mathematical content of the course will be the same for all students. Graduate-credit students will, however, be held to a higher standard of mathematical understanding. In practice, this distinction will appear in two ways:
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First, tests may include extra-credit parts for undergraduate students that are required for students enrolled for graduate credit. Instead of acting as extra credit, these will factor into their grade. These parts will generally ask for a more conceptual argument, a generalization of a theorem from class, a counterexample showing the necessity of a hypothesis, or a synthesis of multiple ideas from the course.
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Second, students enrolled for graduate credit will complete a short paper exploring some additional suggested topics in the course. This paper will be factored into their homework grade. This may also be turned into an extra credit students for other non-graduate students.
Academic Honesty
All portions of the Auburn University student academic honesty code will apply to this class. All academic honesty violations or alleged violations of the SGA Code of Laws will be reported to the Office of the Provost, which will then refer the case to the Academic Honesty Committee. Tiger Cards will be checked for all exams.
Disabilities
Students who need accommodations are asked to electronically submit their approved accommodations through AU Access and to arrange a meeting with their TA during office hours the first week of classes, or as soon as possible if accommodations are needed immediately. If you have not established accommodations through the Office of Accessibility, but need accommodations, make an appointment with the Office of Accessibility, 1228 Haley Center, 844-2096.
Resources
If the notes above are not doing it for you, there are other places to look. In particular, these notes were created largely by looking at:
- Dummit and Foote, which is the closest to the standard algebra textbook.
- Notes by Eloisa Grifo, a commutative algebraist at University of Nebraska.
- An infinitely large napkin by Evan Chen, which is mostly an intuitive introduction.
These were used in addition to my own notes I took while learning algebra. Here are some other random resources:
- 3Blue1Brown has a few videos about group theory, which may be fun to take a look at.
- Fields medalist Richard Borcherds has an underappreciated youtube channel in which he teaches many standard graduate courses, including essentially this one. A few good additions, assuming this is abstract/graduate algebra:
- Keith Conrad’s expository papers - excellent short notes on specific topics: quotient groups, Sylow theorems, irreducibility tests, finite fields, Galois theory, etc.
- J.S. Milne’s course notes - concise graduate-level notes, especially useful for Group Theory and Fields and Galois Theory.
- MIT OCW 18.703 Modern Algebra - has lecture notes, problem sets, and exams; good for extra practice.
- Aluffi, Algebra: Chapter 0 - a more modern/category-flavored graduate text; good for students who want a different viewpoint from Dummit and Foote.
- SageMath and GAP - useful for experimenting with groups, permutations, finite fields, and examples.