- Instructor: Yongwei Yao, Office: 1851 East Hall. Office phone: (734)763-2423.
- Class: 1:00-2:00pm at 3088 East Hall, Monday, Wednesday and Friday.
- Office hours: 1:00--3:00pm Tuesday and Thursday at 1851 EH. Or by appointment. Or by e-mail.
- Prerequisite: Math 614. For example, Hochster's Math 614 in Fall 2003.
- Syllabus: See Winter 2005 Course Descriptions. Or see the class hand-out as dvi file, ps file, or pdf file.
- UM academic calendar, Winter 2005.

**Homework assignments:**
There are 4 homework assignments, each containing about 5 problems.

- Homework Set #1: dvi file, ps file, or pdf file. Solutions: dvi file, ps file, or pdf file.
- Homework Set #2: dvi file, ps file, or pdf file. Solutions: dvi file, ps file, or pdf file.
- Homework Set #3: dvi file, ps file, or pdf file. Solutions: dvi file, ps file, or pdf file.
- Homework Set #4: dvi file, ps file, or pdf file. Solutions: dvi file, ps file, or pdf file.

**Helpful sources:** The following sources, among others, should be
helpful:

- M. Hochster's Math 715 lecture notes (Fall 2002, Winter 2003), available online.
- M. Hochster and C. Huneke,
Tight closure, invariant theory, and the Briancon-Skoda theorem,
Jour. of Amer. Math. Soc.
**3**(1990), no. 1, 31--116. Available online at JSTOR. - C. Huneke, Tight closure and its applications, CMBS regional Conference Series in Mathematics, no. 88.

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