Instructor: Anton Leykin
When and where:
- Contact: email@example.com
- Skiles 109
- Office hours: Mon 4pm, Tue/Thu 2pm, or by appointment
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.
- 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
- 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.