MATH 473 : Ideals, Varieties and Algorithms
Introduction to Algebraic Geometry
Fall 2010 , METU
metu.edu.tr)
Office: 216.
Description: This is an introductory class in Algebraic Geometry.
This is the area of mathematics that deals with
geometric spaces defined by polynomial equations in several variables.
We study the systems of polynomial equations,
and ask questions such as: Does the system have finitely many solutions,
if so how can one find them? And if there are infinitely many solutions,
how can they be described and manipulated?
The solutions of a system of polynomial equations
form a geometric object called a variety; the corresponding algebraic object is called an ideal
in the polynomial ring k[x1,...,xn].
There is a close relationship between these ideals and the varieties which reveal the intimate link
between algebra and geometry.
Until recently, these topics involved a lot of abstract mathematics and were only taught in
graduate school. With today's technology, and recent algorithms for manipulating systems of polynomial equations,
it is possible to do some substantial mathematics,
including Hilbert Basis Theorem, Elimination Theory, and The Nullstellensatz,
and introduce these computational techniques to the undergraduates.
Text: Ideals, Varieties and Algorithms by Cox, Little, O'Shea,
3rd Edition, UTM, Springer-Verlag, 2007.
Prerequisites: Basic abstract algebra knowledge obtained through Math 367 is required.
Homework: Homework will be posted to the web once in two
weeks.
Please staple your homework
whenever it consists of more than a single page.
Exams: There will
be two midterm examinations and a final examination.
Grades: Grades will be assigned on
the following basis:
Homework 15%, Midterms 25% each,
Final 35%.
Web page: The course web page is http://www.metu.edu.tr/~mkalafat/metu473/.
Links: