** Tuesday and Thursday 8:30 - 9:45 am in SAS 1220 **

**Instructor:** Cynthia Vinzant (3260 SAS, email)

**Offce Hours:** Monday, Wednesday 1 - 2pm or by appointment

** Textbook:** B. Hassett, *Introduction to Algebraic Geometry*, Cambridge University Press (errata)

**Syllabus**

** Exam:** There will be an in class midterm on Tuesday, October 4th. Solutions

** Final Project:**
Students will complete a project on a topic related to algebraic geometry,
consisting of a poster presentation on Dec. 13 and a final paper due the same day. Further
details and suggested topics are here.

**Topics:**

Jane Coons: Stanley-Reisner Rings

Katherine Harris: Elliptic Curve Cryptosystems

Samantha Kirk: Twenty-seven lines on a cubic surface

Brittany Riggs: The Combinatorial Nullstellensatz

Michael Ruddy: Bertini's Theorem

Xingjian Yu: Algebra in Computer Vision

** Homework**

Here are guidelines for
writing up your homework (prepared by Seth Sullivant).

Homework 1 (.pdf .tex) due Thursday, September 1

Homework 2 (.pdf .tex) due Thursday, September 8

Homework 3 (.pdf .tex) due Thursday, September 15

Homework 4 (.pdf .tex) due Thursday, September 22

Homework 5 (.pdf .tex) due Thursday, September 29

Homework 6 (.pdf .tex) due Thursday, October 20

Homework 7 (.pdf .tex) due Thursday, October 27

Homework 8 (.pdf .tex) due Thursday, Novemeber 3

Homework 9 (.pdf .tex) due Thursday, Novemeber 10

Homework 10 (.pdf .tex) due Thursday, Novemeber 17

** Software **

Macaulay2 (Examples from class)

Maple

Singular (try online)

Mathematica

** Extra resources and reading **

Ideals,
Varieties, and Algorithms, by Cox, Little, and O'Shea

What is a
Grobner Basis?, by Bernd Sturmfels