MATH 385 | Algebraic Geometry

In linear algebra, students learn about systems of linear equations and their solutions, which correspond to lines, planes, and other linear spaces. In Algebraic Geometry, students build on their understanding of linear algebra, learning about systems of polynomial equations and the geometric objects called algebraic varieties to which they correspond. Examples of algebraic varieties include circles, hyperbolas, cones, and their higher dimensional generalizations. Students develop their strengths in abstract mathematics by learning theorems about rings and ideals, the algebraic tools used to study algebraic varieties. Students learn algorithms to solve problems related to ideals and varieties. Topics may include the Hilbert Basis Theorem, Buchberger’s Algorithm, and Hilbert’s Nullstellensatz.