Togliatti Quintic visualized by
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Nait Merzouk
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Math 548 Advertisement
MATH 548 (Geometry, Algebra, and Algorithms) is being offered for the first time in Spring 2018.
The course is an introduction to algebraic geometry - the study of systems of polynomial equations - with a hands-on computational emphasis. Students will learn about Gröbner bases and Buchberger's algorithm, which are a nonlinear generalization of Gaussian elimination from linear algebra. A key application is a practical method for solving polynomial equations; indeed, versions of the algorithms studied in the course are used in most computer algebra software.
For those considering graduate school in mathematics, this course is an introduction to algebraic geometry, commutative algebra, and symbolic algebra. Additionally, the course is excellent training for mathematics REU opportunities as computer algebra is a common feature of many of these programs. Students with more applied interests will be well-positioned to learn applications to image processing, robotics, genetics, and the new field of algebraic statistics.
The official prequisites are Math 300 and Math 544 since some comfort with proof and linear algebra is assumed. However, for strong students, Math 374 may be an adequate substitute for Math 300, while Math 344 or 526 may be a replacement for Math 544. Computer algebra systems will be used during the course, but no programming experience is required.
The textbook used will be:
Ideals, Varieties, and Algorithms, Fourth Edition.
David A. Cox, John Little, Donal O'Shea.
The official description in the bulletin is as follows:
MATH 548 - Geometry, Algebra, and Algorithms
Credits: 3
Polynomials and affine space, Gröbner bases, elimination theory, varieties, and computer algebra systems.
Prerequisites: Math 300 and Math 544 or consent of the Undergraduate Director.