Program Overview

Virtual Math Research Circle

The Virtual Math Research Circle is a program that brings motivated high-school students together with university mentors to pursue authentic, publishable mathematics.

Overview

The program works by providing students with research proposals and mentors to guide them through the research process. The program is designed to give students hands-on experience with mathematical research and to provide them with the opportunity to work with experienced mentors.

Session · Jun 28, 2021 Jul 16, 2021

The program session ran from June 28, 2021, to July 16, 2021, and included several research projects.

Research Proposals

The following research proposals were available during the session:

• Dictionary Probabilities: This project involved exploring the probability of choosing a random three-letter word from a dictionary that is a palindrome, begins with the letter A, or has other characteristics.
• Flint Hills Series: This project involved investigating the convergence of the Flint Hill series, which is given by n=11n2sin(n)2.
• Probabilities on the Integers: This project involved examining the probabilities of getting integers from different number sets when choosing an integer randomly from the entire integers.
• Probability and Geometric Series: This project involved developing an algorithm to use a fair coin to select from three mutually disjoint events with equal probability, and then extending this result to the case of n pairwise disjoint events.
• Squaring the Square: This project involved exploring the problem of filling an n×n square with multiple non-overlapping squares, all with integer side lengths.
• Stacks and Queues for Graphs: This project involved exploring the question of whether the stack number of a graph is bounded by the queue number.

Research Areas

The program covered several research areas, including:

• Probability Theory
• Number Theory
• Combinatorics
• Graph Theory

Mentorship

The program provided students with experienced mentors to guide them through the research process. The mentors for the session included:

• Christian Ennis
• Jiten Ahuja
• Dr. Isaac Michael
• Samuel Weiner

Program Details

The program was designed for motivated high-school students who are interested in pursuing mathematical research. The program provided students with the opportunity to work on authentic, publishable mathematics and to gain hands-on experience with the research process.