MATH 378
Algebraic Geometry Fall 2014
Division III Quantitative/Formal Reasoning
This is not the current course catalog

Algebraic Geometry has been at the heart of mathematics for at least two hundred years. While starting with a humble study of circles, it has influenced a tremendous amount of modern mathematics, ranging from number theory to robotics. Algebraic Geometry uses tools from almost all areas of mathematics; key for this course will be abstract algebra and multivariable calculus. We will study conics, cubics (books are written about the geometry of cubics; the depth of ideas involved with these curves is amazing) and higher degree curves. In particular, we will study Bezout’s Theorem and Riemann-Roch for curves. Simultaneously with learning about curves, we will also cover the more abstract ideas behind affine and projective varieties. Emphasis will be placed on both “big picture” concepts and the underlying technical details.