Jack Huizenga Office: 404 SEO Tel: 3124133749 email: huizenga@math.uic.edu URL: math.uic.edu/~huizenga 

Brief course description: The course will be an introduction to the theory of affine and projective varieties over an algebraically closed field. We will cover topics such as regular and rational functions, morphisms, dimension, degree, smoothness and singularities. Emphasis will be placed on important concrete examples of varieties. 
Prerequisites: Algebra at the level of a first year graduate course will be assumed. Basic familiarity with commutative rings and modules is essential. Some especially relevant points from commutative algebra will be developed as needed in the course. Familiarity with differential geometry and/or topology will be helpful, but is not required. 
Homework: Weekly homework assignments will be posted on the webpage each Wednesday, and they are due in class the following Wednesday. Please write your solutions clearly and carefully. Use of LaTeX is encouraged. If you have to miss class, you can turn in your assignment early to my box in SEO 304. Late homework will not be accepted. 
Collaboration: You are encouraged to work on problems together; however, the writeup must be your own and should reflect your own understanding of the problem. Please write the names of any students you collaborated with on your assignment. 
Grading: Your grade will be based entirely on the homework. 
Homework assignments : 