Math 101 Graduate Algebra:
Linear and Multilinear Algebra


Term: Fall 2025

Emmy Noether
Lecture
Inst : Prof. Asher Auel
asher * auel AT dartmouth * edu
Time : Tue Thu 2:25 - 4:15 pm
X-hour Wed 5:30 - 6:20 pm
Loct : Kemeny 307
Office : Kemeny 339
Phone : None
Office
hours : 		Fri 1:00 - 2:00 pm
or by appointment
 Course syllabus page.
X-Hour Course
Lecturer : Ben Singer
Category Theory Course : Fri 3:30 - 4:20 pm in Kemeny 343
Course Notes : TBA

Description of course: This graduate course in abstract algebra treats the subject of linear and multilinear algebra from an abstract point of view, setting up the theory of modules. Topics include tensor products, symmetric and exterior powers, universal properties, category theory, homological algebra, and module theory. Applications include the representation theory of finite groups and commutative algebra.

Expected background: Prior experience with undergraduate abstract algebra is required.

Grading: Your grade will be based on class participation, homework, and a final exam.


Group work, honestly: Working with other people on mathematics is highly encouraged and fun. You may work with anyone on your homework problems. If done right, you'll learn the material better and more efficiently working in groups. The golden rule is:
Work with anyone on solving your homework problems,
but write up your final draft by yourself.
Writing up the final draft is as important a process as figuring out the problems on scratch paper with your friends. If you work with people on a particular assignment, you must list your collaborators on the top of the first page. This makes the process fun, transparent, and honest.

External resources: Mathematical writing is very idiosyncratic; if your proofs are copied, it is easy to tell. You will not learn (nor adhere to the Honor Principle) by copying solutions from others, from external sources such as internet forums, or from generative artificial intelligence (GAI) output.

Concerning internet forums (e.g., math.stackexchange), you are free to look at them and use any understanding you've gained from them in your course work, subject to the above rules. Just be warned that these on-line sources often contain incorrect or circuitous solutions, misleading discussions, use of techniques outside of the scope of the course material that may be detrimental to your learning process. Even the time that it takes to repeatedly search for solutions could be better spent learning the material on your own or composing a question via email to your instructor.

Concerning GAI (e.g., ChatGPT), you are free to experiment with asking questions, but be warned that these systems are still trained on sources such as internet forums, hence content summaries and problem solutions can still have the same issues as discussed above. Older GAI generations were easily susceptible to proving false statements. Newer generations are much better with simple problems, but can run into trouble with precision and unspecified hypotheses with more advanced material. Therefore, you should be careful with using these tools as learning resources on their own as the course progresses.

Attendance: You are expected to attend class, including required X-hour sessions, in person unless you have made alternative arrangements due to illness or personal reasons. For the health of our classroom community, please follow Dartmouth's recommendations for respiratory viruses.

Accommodations: Students requesting disability-related accommodations and services for this course are required to register with Student Accessibility Services and to request that an accommodation email be sent to me in advance of the need for an accommodation. Then, students should follow-up with me to determine relevant details such as what role SAS or its Testing Center may play in accommodation implementation. This process works best for everyone when completed as early in the term as possible. If students have questions about whether they are eligible for accommodations or have concerns about the implementation of their accommodations, they should contact the SAS office. All inquiries and discussions will remain confidential.

Religious Observance: Dartmouth has a deep commitment to support students' religious observances and faith practices. Some students may wish to take part in religious observances that occur during the academic term. If you have a religious observance that conflicts with your participation in the course, please meet with the instructor as soon as possible — before the end of the second week of the term at the latest — to discuss appropriate course adjustments.