Instructor 
Professor Shelly Harvey
Herman Brown 446
shelly at rice dot edu 
Course Information 
Class meets: TR 10:50am11:50am 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
Syllabus: download syllabus (pdf)


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 1318 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, ArtinWedderburn 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 CohenSeidenberg Theorems.
 Time permiting: rings of low dimension: Artinian rings and Dedekind domains.

Grades 
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/departmentstatementcollegialityrespectandsensitivity
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.

Title IX Responsible Employee Notification

Rice University cares about your wellbeing and
safety. Rice encourages any student who has experienced an incident of harassment, pregnancy
discrimination or gender discrimination or relationship, sexual, or other forms interpersonal violence
to seek support through The SAFE Office. Students should be aware when seeking support on
campus that most employees, including myself, as the instructor/TA, are required by Title IX to
disclose all incidents of nonconsensual interpersonal behaviors to Title IX professionals on campus
who can act to support that student and meet their needs. For more information, please visit
safe.rice.edu or email titleixsupport@rice.edu. 