Math 251 Course Webpage
Groups, Rings, and Fields
Fall 2009, Duke University
General information |
Course description |
Homework assignments |
Grading policies |
Other texts |
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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/251/251.html
Office hours: Tuesday and Thursday, 13:30 &ndash 14:30, Physics 209
Course content: Algebra, by Serge Lang, Chapters II &ndash VI, XIV
- Rings
- Modules (including canonical forms for linear transformations)
- Polynomials
- Field extensions
- Galois theory
Prerequisite: Math 201, or equivalent.
- 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.
- Please 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 primality lemma" is
not precise; in contrast, "Lemma 7.4 in Chapter III 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 Serge Lang's textbook,
Algebra (the revised third edition). 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.