Math 4803: Algebraic Computation and its Applications


Instructor: Anton Leykin
  • Contact:
  • Skiles 109
  • Office hours: Mon 4pm, Tue/Thu 2pm, or by appointment
When and where:

11:05 am - 11:55 am, MWF, Clough Undergraduate Commons 102


This course is an introduction to techniques of algebraic computation that found applications in a variety of areas both in and outside mathematics. It delves into nonlinear algebra, whose basic problem is solving systems of polynomial equations in one and many variables.

Core topics:
  • Solving (systems of) polynomial equations
  • Polynomial homotopy continuation
  • Ideals in polynomial rings
  • Elimination theory and Groebner bases
  • Polynomial models arising in applications
  • Parts of Cox, Little, O'Shea, "Ideals, Varieties, and Algorithms" (electronic copy is available for free from the library)
  • Instructor's notes
Student activities:
  • Homework: problem sets (exercises from the textbook) assigned weekly.
  • In-class group work: problems solved and discussed in class in small groups.
  • Team projects: short projects assigned to small groups. A set of potential projects will be introduced in the lectures and then student opinion will be surveyed (interest, perceived difficulty, immediate questions). The teams will be formed based on the feedback.
  • There will be no exams. The last team project may be due the week before the finals.
  • Free software: Macaulay2 (recommended), CoCoA, Singular, Sage.
  • Commercial software: Mathematica, Maple.