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Course Description

Summary

Using concepts from combinatorial mathematics and computer science, this course is an introduction to the nature and process of doing mathematics; playing around with patterns, making conjectures, and then stating and proving theorems. The course revolves around a large collection of open-ended problems, concerning topics from graph theory, game theory, set theory, combinatorics, algorithms, geometry, logic, probability, and coding theory, and students can choose to focus on problems in which they have the most interest. Student work is compiled in a journal, and students will share conjectures and proofs with each other throughout the course. Specific proof techniques, such as induction and contradiction, will also be addressed.