William L
- Research Program Mentor

PhD candidate at University of Utah

Expertise

Pure Mathematics: Algebraic Geometry, Abstract Algebra, or Real Analysis

Bio

Hi! My name's Will – I'm a first year PhD student in mathematics, and I'm excited to supervise research projects in almost any related discipline. I'm especially interested in algebraic geometry, the study of shapes and polynomials, but I'm also especially experienced in both linear and abstract algebra – fields both focusing on the relationship between abstract algebraic structures (like sets of matrices, or even infinite dimensional space) and the concrete symmetries in which they arise. Outside of math, I'm super into running! I also grew up right by the ocean, so surfing is also a really big pastime for me. I can talk about sushi (or chili peppers) for hours on end.

Project ideas

Project ideas are meant to help inspire student thinking about their own project. Students are in the driver seat of their research and are free to use any or none of the ideas shared by their mentors.

Eigenvalues and the Fibonacci Sequence

The Fibonacci sequence is an ordered collection of numbers, where each number is the sum of the two preceding Fibonacci numbers. Computing the 10th, or even the 67th number in the sequence is an arduous task, requiring one to sum up a multitude of values. However, what if there was a better way to arrive at these numbers? Using linear algebra, particularly the concept of eigenvalues and eigenvectors, we can find a "closed form solution" to our problem. This means that we'll arrive at a function where, upon plugging in some number X, we'll get out the Xth Fibonacci number. This project is appropriate for any student who has taken a precalculus class.

Coding skills

LaTeX

Teaching experience

Throughout my college career, I have participated in my university's Learning Assistant Program. I would join twice weekly discussion sections in assigned math courses, and help students to solidify their understanding of the course material. This would be supplemented by weekly meetings and seminars to build pedagogical techniques. In my last quarter, I served as a head assistant for UCLA's upper-division linear algebra course. This required leading content meetings, conducting observations and providing feedback, and creating solution guides to the student worksheets.

Credentials

Work experience

Learning Assistant Program (2021 - 2020)

(Head) Learning Assistant

Education

University of California Los Angeles (UCLA)

BS Bachelor of Science

Mathematics

University of Utah

PhD Doctor of Philosophy candidate

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William L - Research Program Mentor