Wednesday, January 28, 2004: Class Begins at 10:00 in Room 401 Clapp. The textbook for the course is Elementary Geometry of Algebraic Curves by C.G. Gibson, paperback, Cambridge University Press. ISBN: 0 521 64641 3. Course description: This course is an introduction to the study of algebraic geometry. Algebraic geometry is the study of polynomials or more precisely the zero sets of polynomials. The field is a very old one but in the mid-1900's Andre Weil and Oscar Zariski worked together to set the field on a new foundation. To quote Zariski: "I began to feel distinctly unhappy about the rigor of the original proofs (without losing in the least my admiration for the imaginative geometric spirit that permeated these proofs); I became convinced that the whole structure must be done over again by purely algebraic methods." Since the work of Zariski and Weil the field of algebraic geometry has become more and more prominent until today when it is important to almost every area of mathematics. We will cover topics that include: projective space, homogeneous coordinates, plane curves, Bezout’s theorem, elliptic curves, affine and projective varieties, the Zariski topology, coordinate rings, and functions on varieties.
The textbook for the course is Elementary Geometry of Algebraic Curves by C.G. Gibson, paperback, Cambridge University Press. ISBN: 0 521 64641 3.
This course is an introduction to the study of algebraic geometry. Algebraic geometry is the study of polynomials or more precisely the zero sets of polynomials. The field is a very old one but in the mid-1900's Andre Weil and Oscar Zariski worked together to set the field on a new foundation. To quote Zariski: "I began to feel distinctly unhappy about the rigor of the original proofs (without losing in the least my admiration for the imaginative geometric spirit that permeated these proofs); I became convinced that the whole structure must be done over again by purely algebraic methods." Since the work of Zariski and Weil the field of algebraic geometry has become more and more prominent until today when it is important to almost every area of mathematics. We will cover topics that include: projective space, homogeneous coordinates, plane curves, Bezout’s theorem, elliptic curves, affine and projective varieties, the Zariski topology, coordinate rings, and functions on varieties.