Math 252 Course Webpage
Commutative Algebra
Spring 2010, Duke University
General information |
Course description |
Homework assignments |
Grading policies |
Other texts |
Links
Lecture: Tuesday and Thursday, 14:50 – 16:05, Physics Building 227
Contact information for the Instructor
Name: Prof. Ezra Miller (you should call me "Ezra")
Address: Mathematics Department,
Duke University, Box 90320,
Durham, NC 27708-0320
Office: Physics 209
Phone: (919) 660-2846
Email: ezra
math.duke.edu
Webpage:
http://math.duke.edu/~ezra
Course webpage: you're already looking at it...
but it's http://math.duke.edu/~ezra/251/252.html
Office hours: Wednesday, 13:00 &ndash 15:00, Physics 209
Course content: Commutative algebra, by David Eisenbud,
roughly Chapters 2 &ndash 15
- Noetherian rings, ideals, and modules
- affine and projective algebraic varieties
- gradings and Hilbert series
- Gröbner bases
- localization
- primary decomposition
- integral dependence and normalization
- Nullstellensatz
- flatness
- dimension theory
- completion
- resolutions and syzygies
Prerequisite: Math 251
- Tentative due dates for the five homework assignments this
semester are listed in the table below.
- All assignments, including the midterms and the final exam,
will be take-home.
- All solutions you turn in, including exams and homework,
must be typewritten. Communicating your ideas is an
integral part of being a mathematician. It is essential that
you learn this skill in graduate school. In addition to the
usual PDF files, I will provide the LaTeX source files for each
of the homework assignments as well as each of the midterms and
the final exam; you should feel free to use (or not) these as
LaTeX templates for your solutions, by simply filling in your
responses in those files. I will be happy to answer any
questions you might have about LaTeX, although you might want
to ask your classmates first.
- Turn in your printed homework solutions to me in class, and
send electronic versions to me and the grader. Send at
least your .tex file (we may comment on your TeX usage); if you
include your .pdf file as well then it can serve as verification
that your system produces the same thing as ours do. Do not
email your midterm or final exam solutions to the grader;
email them only to me.
- Print your typed solutions double-sided. This will save
paper and lighten the stack of papers that I or the grader will
have to carry around.
- I encourage collaboration on homework, as long as each
person understands the solutions, writes them up using their
own words, and indicates—on the homework page—who
their collaborators were.
- In contrast, no collaboration or consultation of human or
electronic sources is allowed for any of the three exams,
although they will be open-book and open-library.
- You must cite sources in your solutions. If you rely on
so-and-so's theorem, then you must state the theorem and tell
me where you found it. Be specific: "the term order lemma" is
not precise; in contrast, "Lemma 15.2 on page 328 of the
textbook" is. Theorems are often known by many names, so I'm
likely not to recognize many theorems by names you might attach.
Unless otherwise specified, all problems are from Eisenbud's textbook,
Commutative Algebra. Check here two weeks before each
homework is due, or one and a half weeks before each exam is due,
for the specifics of the assignments. If an assignment hasn't been
posted, and you think it should have been, please do email me.
Sometimes I encounter problems (such as, for example, the department's
servers going down) while posting assignments; other times, I might
simply have forgotten to copy the assignment into the appropriate
directory, or to set the permissions properly.