Ma 17 - Fall 2025
Ma 17: How to solve it (Fall 2025)
Instructor Lingfu Zhang (lingfuz@caltech) Office Linde Hall 358
TA Minghao Pan (mpan2@caltech)
Class time 7PM to 9PM or 10PM, on Tuesdays
Class location Hameetman Auditorium, Cahill Center
Problem session 7PM to 8PM, on some Thursdays
Problem session location Hameetman Auditorium, Cahill Center
Course description
The William Lowell Putnam Mathematics Competition by the Mathematical Association of America (MAA) is the most prestigious annual contest for college students. While the problems only employ machinery from the standard undergraduate curriculum, the ability to solve them requires a great deal of ingenuity. This can be developed through systematic training, and this class aims to assist the interested students in the preparation for the Putnam exam. Beyond the competition, problem-solving is an essential skill in many disciplines, so at the same time we will use the contest as an excuse to develop this ability through challenging and fun problems. Our aim is to use the competition problems to provide a tour through many interesting topics, and to expose a bridge to higher mathematics.
The 86th Putnam Competition will take place on Saturday, December 6th, 2025. Register (link for Caltech students) now if you think that there is a chance you will participate.
For more information about the Putnam competition, see the official website of MAA and Handout 0.
Grading and Collaboration
You are expected to attend classes and problem sessions, and submit problem sets (through Canvas). You should hand in carefully written solutions to exactly three problems for each assignment. Problem sets will usually contain more problems, and you are encouraged to work on more than three for your own enjoyment, but they will not be graded.
Your main goal in this class should be to develop the largely individual skill of problem-solving. Therefore, collaboration on homework before you have solved at least three problems on your own is discouraged, though not strictly forbidden. You should make a serious effort to work through each problem independently before turning to classmates, the internet, or tools like ChatGPT.
Final Grade Pass/Fail. Based on 15% participation + 40% problem sets + 45% mock Putnam.
Late policy Late problem sets will not be accepted.
The key resource
The Putnam Archive by Kiran Kedlaya. This page contains all the problems and solutions of previous Putnam exams.
Schedule (subject to change)
Sep 30 Introduction and general information of this course (Handout 0). General problem-solving strategies: induction, pigeonhole principle, proof by contradiction (Handout 1).
Oct 7 Extremal elements, elementary number theory (Handout 2).
Problem Session on Oct 9 (7PM to 8PM) Discussion of PSet 1.
Oct 14 (7PM to 10PM) Mock Putnam 1 (Mock 1).
Problem Session on Oct 16 Discussion of PSet 2.
Oct 21 Discussion of Mock Putnam 1 (Handout 3).
Oct 28 Probability and expectation (Handout 4).
Nov 4 (7PM to 10PM) Mock Putnam 2.
Nov 11 Discussion of Mock Putnam 2.
Nov 18 (7PM to 10PM) Mock Putnam 3.
Nov 25 Discussion of Mock Putnam 3.
Dec 2 TBD
Problem sets
Submissions should be made through Canvas.
PSet 1 due by the end of Oct 8.
PSet 2 due by the end of Oct 15.
PSet 3 due by the end of Oct 29.
PSet 4 to be released on Oct 29, due by the end of Nov 12.
PSet 5 to be released on Nov 12, due by the end of Nov 19.
PSet 6 to be released on Nov 26, due by the end of Dec 3.