Virtual Math Circle — Paid Mentorships

Virtual Math Circle — Paid Mentorships

Lead a focused research cohort of motivated high-school students (grades 9–12). Design an original project, mentor a team of 3–6 students, and help them produce scholarly results and a colloquium-style talk.

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Overview

Virtual Math Circle (VMC) engages graduate students, postdocs, and faculty in mathematics and related fields as mentors for small, research-first teams. Mentors guide students through reading, conjecture, proof writing (LaTeX), and—where appropriate—computational experiments, culminating in public presentations and archived materials.

Compensation at a Glance

  • $2,500 base stipend per mentored project for the initial session (≈60 hours total).
  • +$1,500 extension stipend for approved projects continuing through the VMC Research Extension, culminating with a presentation at LSU Discover Day (~30 hours, typically October–April).
  • Per-project compensation. Default is one project per session. In rare, program-approved cases (e.g., split cohorts), a mentor may lead two distinct projects in the same session; each funded project is compensated individually.

Session Formats

  • Summer: compact 3-week intensive; groups typically meet most weekdays (about 2–3 hours/day), with a program-wide research colloquium.
  • Fall / Spring: distributed, semester-length cadence (e.g., 1–2 meetings per week) with interim milestones; students who continue often prepare for LSU Discover Day in April.

Offerings are scheduled term-by-term as mentor availability permits. Specific dates and deadlines appear on the current call.

Mentor Responsibilities

  • Design a high-school–accessible research project with a clearly scoped primary phase and one or more possible extensions for students who continue.
  • Lead a team of 3–6 students through literature, conjecture, proof writing (LaTeX), and—where appropriate—computational experiments.
  • Provide regular virtual supervision and feedback; uphold substantial criteria for peer review in research conduct and reporting.
  • Guide students to produce a final report and a 30–45-minute colloquium-style talk; materials are archived publicly.
  • Time commitment: ~60 hours for the initial session.

Research Extension (optional)

  • With approval and student interest, continue advising toward a presentation for LSU Discover Day.
  • Maintain at least weekly touchpoints and participate in a monthly research meeting.
  • Support writing, poster preparation, and the final presentation; attend VMC presentations at Discover Day.
  • Time commitment: ~30 hours total, typically October–April. Extension stipend: $1,500 (upon successful completion).

Mentor Qualifications and Eligibility

  • (a) Hold a PhD in a math-related field, or (b) be a current PhD graduate student in good standing in a math-related field.
  • International postdocs/PhDs must be eligible for employment in the U.S.
  • International graduate students must be enrolled at a U.S. university and provide institutional employment authorization (e.g., CPT, as applicable).

How to Apply

To apply, prepare the materials below. You may submit proposals for multiple sessions in a single application. When you’re ready, use the button to open the VMC Mentorship Application.

Apply

What you’ll need to complete the application:

  • CV
  • College transcript(s)
  • Research project proposal(s) (PDF and source file: LaTeX preferred, Word accepted)

Selection Process

Proposals approved by VMC organizers are posted for student registration. If at least three students enroll in a project, the project is funded and the mentor is hired for that session. The $2,500 base stipend is paid at completion of the session; the $1,500 extension stipend is paid upon successful completion of the VMC Research Extension and presentation at LSU Discover Day.

How to Prepare Your Research Proposal

Using LaTeX when possible (otherwise Word), submit a clear proposal on a topic appropriate for high-school students. Include:

  • the session(s) you are available to lead;
  • your name, position, and institutional affiliation;
  • project title and mathematical subject area (e.g., graph theory, probability, combinatorics, topology);
  • prerequisites (e.g., whether calculus is required or taught as needed) and all assumed background;
  • a concise abstract (≤250 words, minimal jargon);
  • a statement of availability for the VMC Research Extension and brief description of potential extensions;
  • a project outline/timeline (1–2 pages) with week-by-week goals appropriate to the session format;
  • references/citations to be used during the project.

For topic ideas, see the archive of past projects.

Sample Research Proposal

Virtual Math Circle Research Proposal

Example structure and formatting for mentor submissions
Session
Session 2: Jul 18, 2021 – Aug 6, 2021
Mentor
Isaac B. Michael
Postdoctoral Researcher
Department of Mathematics
Louisiana State University

Project title
Probability and Geometric Series
Topic area
Probability Theory

Background
This research project requires little background knowledge other than basic algebra and arithmetic. All required skills needed to approach the problem will be taught by the instructor. This project serves as an excellent introduction to probability theory, counting methods, sequences, series, and mathematical proofs. During the experimental stage, we will implement computational tools such as Excel, Python, and/or R Studio. During the development of the final presentation, we will use tools such as PowerPoint, Beamer, ShareLaTeX, and/or TeXShop.

Abstract
A fair coin has equal probability of obtaining heads or tails. Say you want to make an equal-probability decision between two outcomes, such as which team in a sports game gets to go first. You can accomplish this using the fair coin by assigning heads to one outcome and tails to the other. But what if you have to make an equal-probability decision between three outcomes? Is it possible to use a fair coin in some way to accomplish this?

We will develop an algorithm to use a fair coin to select from three mutually disjoint events with equal probability. We then hope to extend this result to the case of $n$ pairwise disjoint events, developing an algorithm so that, using a (two-sided) fair coin, each event has probability $1/n$.

If this can be achieved, we seek to generalize further by considering the case where the coin is no longer fair; that is, for some $0<p<1$, we have

$P(H)=p, \quad P(T)=1-p$

Under this modification, is it still possible to choose from among $n$ pairwise disjoint events so that each would occur with equal probability?

Possible extension
Once the iteration algorithm is established, let $N$ denote the random variable associated to the number of iterations needed to produce the desired outcome of equal probabilities. Can the expected value $E(N)$, variance $V(N)$, and standard deviation $STD(N)$ of $N$ be computed?

Outline/Timeline
This is a general (tentative) outline of how the research project will progress. We will adjust the schedule as needed throughout the 3-week period.

  • Week 1 (Background & Examples). The first week will be more instruction-based. We will begin with a brief overview of probability theory using references [1, 2]. The students will be introduced to basic notions such as probability functions, sampling with/without replacement, mutual independence, conditional probability, and Bayes’ Rule.

    We will introduce the basic notions of a rigorous mathematical proof, including proof by exhaustion, proof by induction, and proof by contradiction. The students will be given several examples and assignments to help strengthen their skills in proof writing.

  • Week 2 (Experimentation & Main Problem). The second week will be based heavily on experimentation. The goal during this stage is to determine an algorithm (‘game’) between three people, which, using a coin, yields a 1/3 probability of winning. All experiments will be implemented via Excel, Python, and/or R Studio.

    Once a method has been found with strong empirical evidence of success, the next stage is to prove the assertion rigorously. We will first attempt to prove the base case $n=3$ and then generalize to the case $n\ge 3$. We will then extend, if possible, to the case where the coin is no longer ‘fair’ (i.e., $P(H)=p$ and $P(T)=1-p$ for some $0<p<1$).

  • Week 3 (Finalizing Results & Presentation). The first half of week three will be spent finalizing the empirical results of the experiments and the mathematical proofs.

    The second half of the final week will be spent creating the final presentation. We will decide whether to use PowerPoint or the more sophisticated Beamer presentation using LaTeX. This will depend on the comfort levels of the students with LaTeX typesetting.

References
  1. G. Casella, R. Berger, Statistical Inference, 2nd ed., Duxbury Advanced Series, 2001.
  2. J. Rice, Mathematical Statistics and Data Analysis, 3rd ed., Duxbury Advanced Series, 2006.
  3. J. Stewart, Calculus: Early Transcendentals, 8th ed., Cengage Learning, 2016.

Questions

See our FAQ and Contact page for answers about scheduling, tuition, topics, and more.