Other topics may include representation theory, module theory, and more, depending on the instructor. Offered in 2000-2001 and then alternate years in Spring Semester. Euclidean, similarity and affine transformations are explored analytically and generalized to obtain results in plane projective geometry. Dynamic geometry software and hands-on labs are used to explore both the transformations and properties of these geometries. This course covers basic enumeration, including generating functions, recursion, inclusion-exclusion, Polya theory, etc.
Students also explore topics in graph theory and constructive combinatorics, time permitting.
Offered in 1999-2000 and then alternate years in Fall Semester. 370 Mathematical Logic Mathematical logic uses mathematical methods to analyze reasoning and to examine what mathematics can and cannot do. It also provides the underlying paradigm on which intelligent computer systems are based. Initially, students study the language and rules of inference of predicate logic and investigate the relationships between provability and truth and between a mathematical theory and its models. Later, they explore applications of logic to computer science.