200
Begins with a close study of portions of Euclid's Elements, including complete coverage of the first book. The historical impact of his axiomatic approach and its ultimate refinement in Hilbert's axioms will be explored. This course will cover some of the history of the attempts to prove the Parallel Postulate, leading up to the discovery of non-Euclidian geometries in the 19th century. The two main models of non-Euclidean geometries (elliptic and hyperbolic) will be described and some of their properties investigated. Finally, the history of geometry since the discovery of non-Euclidean geometries (e.g. Kline's Erlanger Program) will be briefly covered.
One year of high school geometry or MTH 134
Surveys proof techniques, recursion, induction, modeling, and algorithmic thinking. Other topics covered include set theory, discrete number systems, combinatorics, graph theory, Boolean algebra, and a variety of applications. There is an emphasis on oral and written communication of mathematical ideas, cooperative learning, and the proofs of mathematical conjectures.
Considers solid analytic geometry, vectors, partial differentiation, and multiple integration. Students will use graphing calculators and will complete computer symbolic algebra (e.g. MAPLE) experiments.
Presents ordinary differential equations and their applications with an emphasis on techniques of solution including numerical methods.
Examines the mathematics behind two fascinating and inter-related topics, fractals and chaos. Chaos and fractals are components of dynamics, a subject that studies how systems change over time. Through computer experimentation and simulations, students will experience how new mathematics is developed. Topics covered include fractals: feedback and the iterator; classical fractals and self-similarity; length, area, and dimension; fractals with a random component; recursive structures including L-systems; attractors; deterministic chaos; fixed points, stable and unstable; and the period-doubling route to chaos.