Problem-Solving Club
Department of Mathematics · The University of Texas at San Antonio
Mathematics is not a spectator sport.
George Pólya
Wednesdays, 5:00–7:00 p.m., Main Building (MB) 0.414.
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We meet to figure out problems together that require reasoning and ingenuity. There is no lecture, and the main prerequisite is intellectual curiosity. Bring paper — we provide the chalk.
The club is open to every UTSA student, regardless of major or undergraduate / graduate standing. Undergraduates are eligible to compete in the Putnam Mathematical Competition, an annual North American contest held in early December. The next one is on Saturday 5 December 2026 and registration is open now.
How a meeting goes
Handouts of suggested problems are distributed. Students and faculty mentors try things out in groups; early mistakes are the norm; they often pave the way to a solution. Many problems are chosen so that the first step is very accessible but the last step teaches a valuable lesson.
Recent problem sets
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Optimization: Squares, Constraints, and Symmetry
Completing squares, dot products and symmetry find exact maxima and minima without multivariable calculus. Five warm-ups lead to three Putnam problems, ending with the largest circle that fits inside a four-dimensional cube (Putnam 2008 B3).
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Calculus: Look Before You Integrate
Reflection, reciprocal changes of variables, and geometry reveal the structure of definite integrals. Five warm-ups lead to competition problems, including an integral of an unknown function from Putnam 2016 A3.
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Invariants
Find the quantity that never changes, then use it to show something is forced or outright impossible: a chocolate bar whose game is decided before anyone moves, chameleons that can never agree on a colour, a knight that cannot cross the board, and the fifteen puzzle.