Math 8803-LEY - Computational Algebraic Geometry - Spring 2014
- Place and time:
Skiles 270, 1:35 pm - 2:55 pm, Tue and Thu
- Instructor: Anton Leykin
- Office: Skiles 250
- Email: firstname.lastname@example.org
- Office hours: see webpage
The course is an introduction to computational methods of algebraic geometry that are frequently used in applications.
- There is no required textbook for this course. It is recommended to have one of the following two books for reference on basic notions:
(both are available for free in electronic form through the GT library)
- Cox, Little, O'Shea. Using algebraic geometry.
- Cox, Little, O’Shea. Ideals, Varieties, and Algorithms: an introduction to computational algebraic geometry and commutative algebra.
For additional reading on numerical algebraic geometry use
- Sommese, Wampler. The numerical solution of systems of polynomials arising in engineering and science.
- Below is an imcomplete list of keywords.
- Basic notions: ideal, variety, ideal-variety correspondence, Hilbert Nullstellensatz, projective space, Newton's method, approximate zero.
- Symbolic computation: resultant, monomial order, initial ideal, Groebner basis, elimination theory.
- Numerical algebraic geometry: polynomial homotopy continuation, Bertini's theorem, condition metric, endgame, deflation, regeneration, witness set, numerical irreducible decomposition, monodromy breakup, joins and intersections.
- There will be optional homework assignments. In addition, one may choose to study an advanced topic (or a problem) related to the course and make a short presentation at the end of the semester.