This is a graduate course in abstract algebra. The catalog description is:
Isomorphism theorems for groups. Group actions. Composition series. Jordan-Holder theorem. Solvable and nilpotent groups. Field extensions. Algebraic and transcendental extensions. Algebraic closures. Fundamental theorem of Galois theory, and applications. Modules over commutative rings. Structure of finitely generated modules over a principal ideal domain. Applications to finite Abelian groups and matrix canonical forms.
with more details in the official departmental syllabus. This corresponds roughly to Chapters 1-8 and 10-14 of the textbook.
Prerequisites: Undergraduate linear and abstract algebra (basics of groups, rings, fields, vectors spaces, etc.), for example as covered in Math 416 and Math 417.
Required text: Dummit and Foote, Abstract Algebra, 3rd Edition, 944 pages, Wiley 2003. The Grainger Engineering Library has a copy on reserve for in-library use.
Suplemental text: Charles Rezk, Lecture Notes for Math 500, Fall 2022: Part 1 (Groups), Part 2 (Rings and modules), Part 3 (Fields and Galois theory).
Overall grading: Your course grade will be based on homework (40%), two in-class midterm exams (15% each), and a comprehensive final exam (30%). You can view all of your scores in the online gradebook.
Weekly homework: These will typically be due on Friday. They are to be turned in on paper at the start of the class period. If you are unable to attend due to illness or quarantine, you can email me a PDF single file with a scan of your HW; if using your phone/tablet, please use an app designed for this purpose, such as Abobe Scan (iOS, Android). Late homework will not be accepted; however, your lowest two homework grades will be dropped, so you are effectively allowed two infinitely late assignments. Collaboration on homework is permitted, nay encouraged! However, you must write up your solutions individually and understand them completely.
In-class midterms: These two 50 minute exams will be held in our usual classroom on the following Wednesdays: September 27 and Nov 1 (weeks 6 and 11, respectively).
Final exam: The final exam will be Thursday, December 14 at 8am.
Missed exams: There will typically be no make-up exams. Rather, in the event of a valid illness, accident, or family crisis, you can be excused from an exam so that it does not count toward your overall average. I reserve final judgment as to whether an exam will be excused. All such requests should be made in advance if possible, but in any event no more than one week after the exam date.
Cheating: Cheating is taken very seriously as it takes unfair advantage of the other students in the class. Penalties for cheating on exams, in particular, are very high, typically resulting in a 0 on the exam or an F in the class.
Disabilities: Students with disabilities who require reasonable accommodations should see me as soon as possible. In particular, any accommodation on exams must be requested at least a week in advance and will require a letter from DRES.
Includes scans of my lecture notes and the homework assignments. Here [DF] refers to the text by Dummit and Foote, and [R1], [R2], and [R3] refers to the three parts of Rezk's notes.