Math 428, Honors Algebraic Geometry, Fall, 2006
My information:
Thomas Nevins
357 Altgeld Hall
217.265.6762
nevins@uiuc.edu
Office hours: Mondays, 2-3 and Tuesdays, 1-2
Group problem session: Thursdays, 5 to 6 p.m., 143 Altgeld Hall.
Syllabus in PDF
Text: Fulton, Algebraic Curves. Note: Fulton's book is out of print.
I have the permission of the author (who holds the copyright) to make photocopies for the students in this course. These will be made available at the
beginning of the semester free of charge.
Midterm #1: Monday, October 2, in class. Here is the exam, here are the solutions.
Midterm #2: Monday, November 13, in class
Final Exam: Monday, December 11, 8--11 a.m.
Course Summary
Algebraic geometry is a beautiful classical subject: at its heart, it is the
study of solutions of polynomial equations. In recent decades, it has played
an increasingly central role both in the most recent trends in pure
mathematics and in a number of areas in physics and engineering.
The goals of this course are:
- to introduce students to this jewel of mathematics,
- to give them a solid foundation in the subject, and
- to make contact with some of its most exciting applications in string
theory, computer algebra, coding, cryptography...
A tentative list of topics:
Affine and projective algebraic varieties, with a special emphasis on
affine and projective curves. Curves of low degree, the group law
on a nonsingular plane cubic. Morphisms and rational maps. Singularities of
curves. Interactions with string theory, computer algebra, coding and
cryptography.
Homework:
- Homework #1, due Friday, August 25.
- Homework #2, due Friday, September 1 (turn in
*'ed problems).
- Homework #3, due Friday, September 8.
- Homework #4, due Friday, September 15 (turn it in).
- Homework #5, due Monday, September 25, has two parts: this and that (to be posted a little later). Turn in all solutions.
- Homework #6, due Monday, October 2: study for the midterm! I handed out a
fairly large number of problems on Wednesday; all the ones that don't involve projective space would make good practice problems.
- Homework #7, due Monday, October 9: rework and turn in all problems from
the midterm for which you got less than full credit (please don't look at the solutions unless you are really stuck!). Also, do problems (B),
(alpha), (beta), (I), and (III) from the Week 6 notes.
- Homework #8, due Monday, October 16.
- Homework #9, due Monday, October 23.
- Homework #10, due Monday, October 30: this is a catch-up week; do the problems from previous homeworks that you didn't get to!
- Homework #11, due Monday, November 6.
- Homework #12, due Wednesday, November 29: write up corrections to your exam.
- Homework #13, due Monday, December 4: do problems 2-39, 2-40, 5-19, 5-21 from Fulton, to be handed in. Also, do problems 5-23 and 5-24 from Fulton, not to be handed in.
Notes:
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