Mathematics Education

This course is an introduction to mathematical reasoning as exemplified in the proof methodology inherent to formal mathematics. It includes a formal study of logic and the different methods of proof, and then uses examples from various branches of mathematics to illustrate these ideas. Fields from which examples are taken include, but are not limited to, set theory, cardinality, relations and order, functions, and elementary group theory. This course gives students an opportunity to practice their argumentative writing in a space where there are clear right and wrong answers.

This course introduces students to mathematics from a historical perspective. Topics include number theory, algebra, geometry, and calculus. Studying the history of mathematics helps students develop a deeper understanding of mathematics by learning how it developed over time and in various places. It encourages creative and flexible thinking by allowing students to see historical evidence of different and perfectly valid ways to view concepts and carry out computations.

This course introduces students to the fine art of problem-solving. It focuses on using computers, models, and examples to investigate problems, rather than formal, rigid processes to uncover a solution. Topics include, but are not limited to, number theory, probability, mathematical modeling, graph theory, fractals, real analysis, and open math problems.