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Course Announcement - Fall 2004

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Math 249: Combinatorial Commutative Algebra

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Instructor: Bernd Sturmfels

**Office hours:** Tuesdays, 9:45-11:00am
and Fridays, 10:30-11:30am

**Contact:** bernd at math, 925 Evans, 642 4687

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Time and Place: Tuesdays and Thursdays, 8:00-9:30am, 81 Evans Hall

** Prerequisites:** Math 250B or equivalent background in
commutative algebra, some exposure to combinatorics and geometry.

Students who have already taken a previous version of Math 249
may register for this course as
** Math 274, Section 3, CCN 55160**.

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Course Work
**(required for registered students,
encouraged for others): **
Seven exercises and a term paper

** Exercises:**
Please turn in ** one exercise
every Tuesday**, starting on September 7 and ending on October 19.
Choose from the book.

** Term paper:**
Write a term paper on a topic of your choice related
to Combinatorial Commutative Algebra. Colloborations
welcome.

** Important Deadlines** for your paper:
** Proposal due October 21, **
** First Draft due November 23, **
** Final Version due December 9.**

The chosen topics for the term papers
and the finished products will be posted on this webpage
(unless you voice objections).

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Text: Ezra Miller and Bernd Sturmfels,
Combinatorial Commutative Algebra, Springer, 2004.

To read this book click
**here**,
or purchase the ** Reader** for Math 249 ** at Copy Central**,
Hearst Ave.

This book will be published by Springer Verlag
(Graduate Texts in Mathematics).
Please e-mail errors and typos to me.

** Syllabus:**
The book has the following ** 18 chapters**.
A rough plan to discuss a different chapter each week,

so we may cover about two-thirds of the book.
Your input on the selection and order is welcome.

**
**

1. Squarefree Monomial Ideals

2. Borel-fixed Monomial Ideals

3. Three-dimensional Staircases

4. Cellular Resolutions

5. Alexander Duality

6. Generic Monomial Ideals

7. Semigroup Algebras

8. Multigraded Polynomial Rings

9. Syzygies of Lattice Ideals

10. Toric Varieties

11. Irreducible and Injective Resolutions

12. Ehrhart Polynomials

13. Local Cohomology

14. Plücker Coordinates

15. Matrix Schubert Varieties

16. Antidiagonal Initial Ideals

17. Minors in Matrix Products

18. Hilbert Schemes of Points