**Instructor: ** Adam S. Sikora
115 Math Bldg

** Email: ** asikora at buffalo dot edu

** Class meets:** TuTh 11:10-12:25, Math Bldg 122

**Prerequisite:** Abstract Algebra Course (Familiarity with the notion of a ring, ideal, field). Point set topology.

At the most basic level, Algebraic Geometry studies algebraic sets and algebras of functions on them. More conceptually, it establishes a powerful duality between geometry and commutative algebra, which is central to these and related areas (including number theory and non-commutative geometry). Algebraic Geometry has applications to many branches of mathematics (eg. analysis, combinatorics) and to physics.

**Textbook:** J. Milne, "Algebraic Geometry", online textbook online.

** Supplemental Textbooks:** (All of them more elementary than the textbook above, especially the first two.)

- "An Invitation to Algebraic Geometry" by Smith, Kahanpaa, Kekalainen and Traves.
- Cox, Little, and O'Shea, "Ideal, varieties and algorithms"
- I. Shafarevich, "Basic Algebraic Geometry I"

**Homework:** As with all math, it is impossible to learn algebraic geometry in a passive way. For that reason some homework will be assigned, collected and graded.