MAT 493 Rings and Varieties
When abstract algebra and geometry are fused together, they form a branch of mathematics called algebraic geometry. This fusion comes by uniting certain geometric objects, called varieties, with their algebraic counterparts, called rings. In this course we will study this two-way interplay: How are the algebraic properties of a ring reflected as geometric properties of its corresponding variety? And how does the geometry of a variety influence the structure of its corresponding ring?
This course will blend theory with practice; examples, computations, and algorithms will be given as much emphasis as abstract principles and concepts.