Using math competitions such as the Putnam Exam as a springboard, in this class we follow the dictum of the Ross Program and “think deeply of simple things”. The two main goals of this course are to prepare students for competitive math competitions, and to get a sense of the mathematical landscape encompassing elementary number theory, combinatorics, graph theory, and group theory (among others). While elementary frequently is not synonymous with easy, we will see many beautiful proofs and “a-ha” moments in the course of our investigations. Students will be encouraged to explore these topics at levels compatible with their backgrounds.
The Class: Type: lecture
Requirements/Evaluation: evaluation will be based primarily on homework, classwork, and exams
Prerequisites: MATH 250 or permission of instructor
Enrollment Preference: members or alternates of the Putnam team, Mathematics, Physics or Computer Science majors
Department Notes: http://web.williams.edu/Mathematics/sjmiller/public_html/331/
Distributions: Division III; Quantative/Formal Reasoning;