Nonlinear Algebra

3 Credits · Level: Graduate, Undergraduate

This course is about nonlinear algebra, which is as applicable and powerful as linear algebra. It has applications in areas as diverse as optimization, cryptography, computer graphics and statistics. Nonlinear algebra deals with systems of polynomial equations of various degrees (known as "ideals") and their solution sets (known as "algebraic varieties"). We will learn how to use computational algorithms to investigate and connect these objects. Topics covered will include basics of algebraic structures, generating sets for ideals known as Grobner bases (similar to bases of vector spaces), and algorithms to compute such bases (Buchberger's algorithm). This course will involve the use of computer algebra systems like SageMath or Macaulay2. These are powerful free software systems that are capable of algebraic computations, among many other things. No previous programming experience is assumed.