MATH 4040

Patterns, Proofs, and Problems

Course Description

Course information provided by the 2026-2027 Catalog.

Basic problem-solving techniques and strategies for contest problems. Contest problems differ from standard mathematical instruction in that they are "contextless": the problem does not tell you which field it is in and sometimes goes to great lengths to disguise it. Understanding how to solve contest problems has applications to research, where knowing how to work with unknown concepts, how to attack a problem fluidly from the perspective of multiple fields, and different tricks for simplifying problems is extremely useful. This course will cover topics that appear in standard competitions (e.g., the Putnam exam), including combinatorics, number theory, geometry, and calculus. It will also teach strategies for understanding and attacking problems, more advanced proof techniques, and effective proof writing.

Prerequisites MATH 2210 or MATH 2230 or MATH 2310 or MATH 2940; MATH 2220 or MATH 2240 or MATH 1920; or equivalents.

Distribution Requirements (SMR-AS)

Last 4 Terms Offered 2025FA

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