Mathematics 415 - Topics in Mathematics

The topic will vary from year to year.  The topic for fall 2014 is computational algebraic geometry.

The study of geometric objects by means of their defining equations dates back to the introduction of coordinates by Descartes in 1637.

This course will introduce algorithmic methods for manipulating and understanding algebraic equations and will develop a dictionary between algebra and geometry.  We will also explore the structure of ideals in polynomial rings and the resulting quotient rings.  The course will end with student presentations on applications of algebraic geometry to robotics, geometric theorem proving, invariant theory, graph theory, and sudoku.  Three class hours per week plus a weekly one-hour computer lab. 

Requisite:  MATH 350.  Limited to 16 students.  Fall semester.  Professor Cox.