Spring 2012
Carnegie Mellon University
This course explores the relationship between algebra and computation, focusing on algorithms used for symbolic computation and modern algebra concepts. Subjects covered include proving combinatorial identities, Gröbner bases, symbolic integration, and experimental mathematics. Prerequisites suggest this is a mid-level course.
The goal of this course is to investigate the relationship between algebra and computation. The course is designed to expose students (sophomore/junior cs and math majors) to algorithms used for symbolic computation, as well as to the concepts from modern algebra which are applied to the development of these algorithms. This course provides a hands-on introduction to many of the most important ideas used in symbolic mathematical computation, which involves sproving combinatorial identities, solving system of polynomial equations, analytic integration, and solving linear difference equations.
The appropriate use of computer algebra systems (Mathematica) to support the teaching and learning of mathematics, and in related assessments, is incorporated throughout the course. This includes the use of Mathematica to assist in the development of mathematical ideas and concepts, as well as a tool for analysis, problem-solving and modelling work.
The course covers the following topics:
Learning Outcomes:
Optional Textbook: