Program Overview

Virtual Math Research Circle 2021 Summer Research Projects

The Virtual Math Research Circle is a program that brings motivated high-school students together with university mentors to pursue authentic, publishable mathematics. The program is designed to provide students with hands-on experience in mathematical research, under the guidance of experienced mentors.

Overview of the Program

The program consists of several research projects, each with its own unique topic and mentor. The projects are designed to be challenging and engaging, and to provide students with the opportunity to develop their mathematical skills and knowledge.

Research Projects

The following research projects are available:

• Dictionary Probabilities
  • Mentor: Christian Ennis Louisiana State University
  • Project Title: Dictionary Probabilities
  • Topic Area: Probability Theory (Calculus not required)
  • Abstract: This project involves choosing a random three-letter word from a dictionary and calculating the probability that the word is a palindrome, begins with the letter A, and has other characteristics.
• Flint Hills Series
  • Mentor: Jiten Ahuja Louisiana State University
  • Project Title: Flint Hills Series
  • Topic Area: Integrals and Infinite Series (Calculus required)
  • Abstract: This project involves investigating the convergence of the Flint Hill series, which is given by n=11n2sin(n)2.
• Probabilities on the Integers
  • Mentor: Christian Ennis Louisiana State University
  • Project Title: Probabilities on the Integers
  • Topic Area: Probability Theory (Calculus not required)
  • Abstract: This project involves examining the probabilities of getting integers from different number sets when choosing an integer randomly from the entire integers.
• Probability and Geometric Series
  • Mentor: Dr. Isaac Michael Louisiana State University
  • Project Title: Probability and Geometric Series
  • Topic Area: Probability Theory and Geometric Series (some Calculus required)
  • Abstract: This project involves 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
  • Mentor: Jiten Ahuja Louisiana State University
  • Project Title: Squaring the Square
  • Topic Area: Number Theory (Calculus not required)
  • Abstract: This project involves filling an n莋 square with multiple non-overlapping squares, all with integer side lengths, and finding the fewest number of squares needed to fill the big square.
• Stacks and Queues for Graphs
  • Mentor: Samuel Weiner Louisiana State University
  • Project Title: Stacks and Queues for Graphs
  • Topic Area: Combinatorics (Calculus not required)
  • Abstract: This project involves exploring the question of whether the stack number of a graph is bounded by the queue number, and introducing students to graph theory and proof-based mathematics.

Session Details

The session for these research projects will take place from June 28, 2021, to July 16, 2021.