| MATH 437 |
CRN 7678, 15 Points (2009 2/3) |
| Coordinator: |
AProf Peter Donelan
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| Recommended: |
MATH 311 |
| Recommended Reading: |
Adams and Loustaunau, An Introduction to Groebner Bases.Cox and Sturmfels, Applications of Computational Algebraic Geometry. |
| Textbook: |
Cox, Little and O'Shea, Ideals, Varieties and Algorithms. |
| Description: |
This is a course in algebraic geometry with special emphasis on algorithms and applications. Many problems in mathematics and applications require finding solutions of sets of multivariate polynomials with coefficients in some field k (e.g. finite fields, rational, reals, complex numbers). This is an algebraic problem concerning rings of polynomials and their ideals. It also has a geometric aspect in that the set of solutions may be visualised as some curve, surface or hypersurface in a space (affine or projective). Such sets are called varieties. There is a rich interaction between the geometric and algebraic objects.
In particular we explore computational methods such as Gröbner bases and resultants. The associated algorithms are implemented in computer algebra systems such as Maple which we make use of. We will study the theory of Gröbner bases and you will undertake investigation of an application such as graph colouring, robot kinematics, integer programming, coding theory etc.
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