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Undergraduate Problem Seminar

Arizona State University, Fall 2025

When: Tuesdays and Thursdays 1:30pm–2:45pm

Where: WXLR A306

Instructor: Zilin Jiang ([email protected])

Please reserve email only for individual, non-technical matters; use the office hours for technical questions related to lectures and assignments.

Office hours: Tuesdays and Thursdays 2:45pm–4pm in WXLR A839.

Course description​

This seminar is designed for undergraduate students who enjoy tackling challenging and creative mathematical problems, with a particular focus on preparation for the William Lowell Putnam Mathematical Competition—a prestigious annual contest for undergraduates in the United States and Canada. All students officially registered in the course are required to participate in the Putnam Competition, which will be held on December 6, 2025, 8:00 AM–4:00 PM.

While the course centers around competition-style mathematics, its deeper purpose is to cultivate strong problem-solving skills—skills that are essential not just in mathematics, but in all fields where creative and analytical thinking is valued. Through carefully selected problems, students will explore elegant techniques and discover connections to more advanced areas of mathematics, gaining insight that extends far beyond the scope of contests alone.

The problems discussed will primarily be drawn from past competitions, and class sessions will be driven by collaborative problem-solving and guided discussions. The goal is to provide an engaging and intellectually stimulating environment that encourages mathematical exploration and builds a bridge to higher-level thinking.

Although the course permits variable credit enrollment, all students must register for 3 credits to ensure a consistent and coherent learning experience across the cohort.

Enrollment requirements​

Prerequisites: No prerequisites other than the usual demand for suitable mathematical maturity.

Grade policies​

A+ ≥ 97%; A ≥ 94%; A- ≥ 90%;
B+ ≥ 87%; B ≥ 84%; B- ≥ 80%;
C+ ≥ 76%; C ≥ 70%; D- ≥ 60%; E otherwise.

Absence policies​

  1. In general, no late submission of assignments will be accepted unless there is a genuine emergency backed up by official documents (such as a physician's note attesting the same).
  2. Attendance of all lectures is expected as it helps you learn well. However, I will not take attendance for lectures at all.

Textbook​

There is no required textbook for the course. However, students are encouraged to consult Putnam and Beyond by Razvan Gelca and Titu Andreescu, which complements the themes and techniques covered in the seminar. Purchasing the book is optional but recommended for those seeking additional practice and insight.

Grading breakdown​

  1. Handwritten Solutions: 50%
  2. Presentations: 50%

Weekly assignments​

  1. Problem sets will be posted every Thursday for discussion in the following week's classes.
  2. In weeks with two meetings, six problems will be assigned (three per class).
  3. In weeks with one meeting, three problems will be assigned.

Class presentations​

  1. Students will be randomly selected to present solutions in class.
  2. Each student will receive two pass tokens for the semester, which can be used to skip a presentation when selected (no explanation required). After both are used, students must present if selected.
  3. Students should be ready to present on any day they have submitted a solution.

Additional notes​

  1. Putnam Competition Requirement: All registered students must participate in the William Lowell Putnam Mathematical Competition on December 6, 2025, 8:00 AM–4:00 PM. Failure to participate will result in a failing grade.
  2. There are no midterms or final exam. Grades are based entirely on consistent participation and the quality of written and oral work.