18.A34 Mathematical Problem Solving (Putnam Seminar)

Fall 2022, MIT (Link to the most current version of the course)

Class meetings: Mondays and Wednesdays 1–2pm, room 2-132

Instructor: Prof. Yufei Zhao

Undergraduate Assistants (UA): Dain Kim and Tomasz Slusarczyk

Emails and Slack:

Course description and policies

William Lowell Putnam Mathematics Competition: The Putnam Competition is an annual mathematics contest for undergraduates in the USA and Canada. This year it will be held Saturday, December 3, 2022.

All registered students will be required to participate in the Putnam competition. Students should self-register on the official Putnam website.

Seminar participants are selected through the First-year Advising Selection process. Unfortunately I cannot add additional students. See below for policies on lecture attendance.

Class format

Class attendance is required for registered students. Please notify me in advance if you cannot make it to class. Too many unexcused absences is cause for concern and may lead to a non-passing grade.

Non-registered MIT students are welcome to attend the lectures but not the discussion sessions and may not turn in homework.


Pass/Fail. Based on homework and participation. Homework will be graded on correctness and presentation. Illegible or sloppy write-ups are unacceptable.

Students needing support should consider reaching out to Student Support Services (S3) or Student Disability Services.

Schedule and due dates

Lectures are open to all MIT students.
All other sessions are restricted to official seminar participants.

W 9/7 Class introduction

M 9/12 Discussion & Presentations. Due: Probability & SS1

W 9/14 Lecture by Yufei Zhao

M 9/19 Discussion & Presentations. Due: Hidden independence and uniformity & SS2

W 9/21 Lecture by Ashwin Sah

M 9/26 Discussion & Presentations. Due: Analysis (notes) & SS3

W 9/28 Lecture by Carl Schildkraut

M 10/3 Discussion & Presentations. Due: Combinatorial configuration & SS4

W 10/5 Lecture by Daniel Zhu

M 10/10 No class & Indigenous Peoples Day

W 10/12 Discussion & Presentations. Due: Generating functions & SS5

M 10/17 Discussion & Presentations. Due: Congruences and divisibility & SS6

W 10/19 Lecture by Dain Kim

M 10/24 Discussion & Presentations. Due: Polynomials & SS7

W 10/26 Lecture by Mihir Singhal

M 10/31 Discussion & Presentations. Due: Abstract algebra & SS8

W 11/2 Lecture by Tomasz Slusarczyk

M 11/7 Discussion & Presentations. Due: Inequalities (notes) & SS9

W 11/9 Lecture by Allen Liu

M 11/14 Discussion & Presentations. Due: Linear algebra & SS10

W 11/16 Lecture by Edward Wan

M 11/21 Discussion & Presentations. Due: Sums and integrals & SS11

W 11/23 Discussion & Presentations (on any previously assigned problems)

M 11/28 Discussion & Presentations: Putnam 2020

W 11/30 Discussion & Presentations: Putnam 2021

Saturday 12/3 Putnam Competition

M 12/5 Discussion & Presentations: Putnam 2022

W 12/7 Discussion & Presentations: Putnam 2022

M 12/12 Discussion & Presentations: Putnam 2022

W 12/14 Discussion & Presentations: Putnam 2022

For past Putnam problems see the Putnam Archive


Each problem set contains a long list of problems. You are encouraged to try many problems, but please only hand in your three best solutions (do not submit more than three):

If you wish to get a head start on later problem sets, you can check out the material from previous semesters (see links at the bottom). This year’s problem sets will likely be mostly the same, although there could be minor changes and re-numbering.


Homework # # solutions required to be typed in LaTeX
1 — 2 ≥ 0
3 — 5 ≥ 1
6 — 8 ≥ 2
9 — 11 3

Late policy


Acknowledging collaborators and sources

It is required to acknowledge your sources (even if you worked independently)

Intentional violations of the above policies may be considered academic dishonesty/misconduct.

Additional resources

You may find the following optional resources helpful for additional preparation. Some resources may be available electronically from MIT Library.

Previous Putnam problems and solutions

Additional books helpful for preparation