Instructor
Professor Shelly Harvey
Herman Brown 446
shelly at rice dot edu

Course Information
Class meets: TR 10:50am-11:50am in HB 427 (the first two weeks will be on Zoom, see Canvas for the link)
Office Hours: TBA
Webpage: http://math.rice.edu/~shelly/564s22/
All homework and reading assignments can be found on Canvas
Teaching Assistant: TBA

Textbook
Abstract Algebra, by David Dummit and Richard Foote (3rd edition) (required)
A secondary text for the course will be \emph{Introduction to Commutative Algebra}, by Michael Atiyah and Ian Macdonald. Other sources might include individual chapters from books, which I will make available to the class.

Course description
The core of the course consists of Chapters 13--18 of Dummit and Foote.
• Fields and their extensions: Galois Theory. Time permitting, we will cover infinite Galois Theory and rewrite the fundamental theorem of Galois Theory as an equivalence of categories.
• Algebras: Division algebras over fields (including Frobenius' and Wedderburn's Theorems). Symmetric and exterior algebras, including their use in the construction of differential forms on $\mathbb{R}^3$.
• Homological algebra: tools for (non)commutative algebra. Direct and Inverse limits. Projective, injective, flat modules. Ext and Tor. Derived functors.
• Introduction to Representation theory: group algebras, character theory. Maschke's Theorem, Frobenius reciprocity.
• Noncommutative algebra: Chain conditions, (semi-)simplicity, Artin-Wedderburn Theorem.
• Commutative Algebra and affine algebraic geometry: Advanced ideal theory. Prime spectrum of a ring; the Zariski topology. Coordinate rings of affine algebraic varieties. Noether normalization and Hilbert's Nullstellensatz. Primary decomposition of ideals and its geometric interpretation. Localization, Integral extensions and the Cohen-Seidenberg Theorems.
• Time permiting: rings of low dimension: Artinian rings and Dedekind domains.

Your grade in the class will be based on the following weights:
 Homework: 45% Midterm: 20% Final Exam: 35%

Homework and Exams
Homeworks will be assigned every Thursday and will be due the following Thursday by 11:59pm on Gradescope; they will be posted on Canvas. You should turn your assignment in on Gradescope. Homework solutions must be legible. You must show all of your work for full credit. Late homework will receive at most 1/2 credit. The students in Math 564 will be required to do more homework problems than the students in Math 464. The homework is not pledged and you can collaborate with other students in the class. In fact, you are very much encouraged to do so. However, you are not allowed to look up solutions in any written form; in particular, you are not allowed to look up solutions online. Students caught violating this rule will be reported to the Honor Council. You should write up your solutions individually.

Exams
There will be one midterm (the date to be determined) and a final exam. Both exams will be take home exams. Good mathematical exposition will be counted on both exams. The exams are pledged.

Attendance Policy
Attendance is not required. However, you are responsible for all the material and announcements covered in lecture.

Disability Support
If you have a documented disability that may affect academic performance, you should: (1) make sure this documentation is on file with Disability Resource Center (Allen Center, Room 111 / adarice@rice.edu / x5841) to determine the accommodations you need; and (2) get in touch with me to during the first two weeks of class to discuss your accommodation needs. All such discussions will remain as confidential as possible.

Statement of Conduct
The Department of Mathematics supports an inclusive learning environment where diversity and individual differences are understood, respected, and recognized as a source of strength. Racism, discrimination, harassment, and bullying will not be tolerated. We expect all participants in mathematics courses (students and faculty alike) to treat each other with courtesy and respect, and to adhere to the mathematics department standards of collegiality, respect, and sensitivity: mathweb.rice.edu/department-statement-collegiality-respect-and-sensitivity as well as the Rice Student Code of Conduct. If you think you have experienced or witnessed unprofessional or antagonistic behavior, then the matter should be brought to the attention of the instructor and/or department chair. The Ombudsperson is also available as an intermediate, informal option, and contacting them will not necessarily trigger a formal inquiry. See the above website for details on how to contact the Ombudsperson.