Competitions and Prizes

For 2024: Interested students should submit their proposals to the DUS by the deadline to be announced. The proposal should describe an independent reading or research project which the student will undertake with the approval and guidance of a faculty member.

We are working with the prizes office to see if we could award the prize earlier in the Spring, so as to help everyone make summer plans in advance. If we succeed, proposals for the next Lewis prize will be collected in January 2024. 

Please note that reading projects must be on topic(s) that are currently not taught in Yale classes. (There can be some small overlap - but we are not permitted to have an official reading project on the contents of Math 380, for example.) The same rule applies to Math 470 during the semester, and YSS independent research course during the summer. 

Your proposal should include:

• Your name, and name of the faculty member who agreed to advise your project. 
• Typically, a Lewis project would mean two months of full-time work. It could be a little shorter and more intensive, or a bit longer and less intensive. Please provide information about your plan in the proposal. 
• A description of the project that you plan to work on. (There is some flexibility, to follow the project where it leads you in real time, but the proposal should describe the topic(s) and initial plan.)
• Information about relevant text(s), paper(s), or other references. 

You must consult with your project adviser about the details of your proposal, especially the timeline (to make sure it fits their schedule) and the contents of your project. The adviser’s approval is an essential component of our selection process. 

Technical note: If your project receives funding from other sources, including funding to cover expenses, then it will only be eligible for a Lewis prize amount that brings up the existing funding to $6,000. For example, if you receive a 1,000 travel and accommodations funding and 2,000 stipend from elsewhere, then winning the Lewis prize will award 3,000. 

The 2023 Barge exam will take place on Sunday, April 30 from 1pm to 4pm. 

Signup for the test is through an online form. The deadline to sign up is April 24. 

If you have been granted testing accommodations through the SAS, please forward the official SAS notification for this semester to math.dus@yale.edu by April 24. 

The exam is similar in style to competitions for high school students such as the International math olympiad, or contests for undergraduate students such as the Putnam exam. (Both sites provide sample problems and solutions.)

Recommended mathematical background includes familiarity with mathematical proofs, calculus, some knowledge of probability. All solutions must be fully justified. 

A few sample questions from past years:

1. Fix a real number x. Define a sequence by a₀ = 1, and a_n = (1+x^(2^n)) a_n-1 for all n > 1. For what values of x does this sequence converge? When it converges, what is the limit?

2. Let p be a prime and k a positive integer with k < p. How many k-element subsets {a₁, …, a_k} of {1, …, p} are there such that a₁ + … + a_k is divisible by p? 

3. Determine all (if any) integers a, b, c satisfying the following equation:

a^2c + b^4c = 2011

4. Suppose you have an equilateral triangle with vertices ABC. Let P be a point in your triangle, with |PA|=5, |PB|=4, and |PC|=3. Determine the area of the triangle with vertices PBC. 

5. Let a and b be natural numbers. For each natural number n, let p_n be the greatest prime factor of an + b. Prove that there is a number M such that p_n < M for infinitely many values of n. 

The day of the 2023 contest is yet to be announced. Typically, it is on the first Sunday in December.

If you are interested in participating, you will need to register on the above site, after registration opens for students (probably in October). 

This year’s problem solving seminar will run on Mondays 7 - 9pm, starting on September 25. It is an enjoyable way to learn some problem solving skills and techniques useful in mathematics competitions (and many other places), collaborate with friends, and think about math puzzles. It is also great practice for this year’s Putnam exam. 

Dr. Andrew Yarmola, and math majors William Ning, Ayush Tibrewal, and Grant Zhang have planned a program that will be accessible and useful for students with all levels of math contest experience (including no experience at all - don’t hesitate to sign up and see what it’s like!) 

To read more about the seminar, and to sign up, click on the following form, prepared by the organizers.