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portfolio
Portfolio item number 2
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publications
Paper Title Number 1
Published in Journal 1, 2009
This paper is about the number 1. The number 2 is left for future work.
Recommended citation: Your Name, You. (2009). "Paper Title Number 1." Journal 1. 1(1).
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Paper Title Number 2
Published in Journal 1, 2010
This paper is about the number 2. The number 3 is left for future work.
Recommended citation: Your Name, You. (2010). "Paper Title Number 2." Journal 1. 1(2).
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Paper Title Number 3
Published in Journal 1, 2015
This paper is about the number 3. The number 4 is left for future work.
Recommended citation: Your Name, You. (2015). "Paper Title Number 3." Journal 1. 1(3).
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Paper Title Number 4
Published in GitHub Journal of Bugs, 2024
This paper is about fixing template issue #693.
Recommended citation: Your Name, You. (2024). "Paper Title Number 3." GitHub Journal of Bugs. 1(3).
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talks
An Introduction to the Classification of Finite Simple Groups
Published:
Abstract: With a proof spanning thousands of pages across hundreds of articles, the classification of finite simple groups is a monumental achievement of 20th century mathematics. We will explore how finite simple groups act as the building blocks for all finite groups, and discuss the general strategy of the classification of such simple groups. We will introduce Feit and Thompson’s odd order solvability theorem and show how this theorem along with the Brauer-Fowler theorem provides a possible strategy of attack on the classification theorem. Recording
Similarity of Integer Matrices
Published:
Abstract: Integer matrices \(A\) and \(B\) are said to be \(\mathbb{Z}\)-similar if there exists \(C \in \text{GL}_n(\mathbb{Z})\) such that \(CAC^{-1} = B\). While the canonical forms of linear algebra provide a complete description of matrix similarity over a field, much is still unknown about \(\mathbb{Z}\)-similarity. We will briefly review finite-dimensional linear algebra and see how this theory breaks down when we try to apply it to \(\mathbb{Z}\)-similarity. We will then introduce a modern form of the Latimer-MacDuffee theorem to convert the \(\mathbb{Z}\)-similarity problem to computing isomorphism classes of certain modules. We will explain how the simplest case of this isomorphism problem reduces to the number-theoretic problem of computing ideal class groups. We will conclude by characterizing the integer matrices whose \(\mathbb{Q}\)-similarity class splits into finitely many \(\mathbb{Z}\)-similarity classes.
teaching
Real Analysis
AS.110.405, JHU, 2023
Course assistant and grader for small upper-level real analysis course taught by Richard Brown. We covered sequences, limits of functions, differentiation on the real line, integration (Darboux integral), and sequences of series of functions using Jiri Libl’s “Basic Analysis: An Introduction to Real Analysis” as our text.
Calculus I for Biological and Social Sciences
AS.110.106, JHU, 2024
Teaching assistant for large introductory calculus course taught by Fei Lu. We covered the basic theory of differentation and integral calculus up through the fundamental theorem of calculus.
Linear Algebra
AS.110.201, JHU, 2024
Teaching assistant for large introductory linear algebra course taught by Emily Riehl. We covered topics such as reduced row echelon form, linear systems of equations, abstract vector spaces and linear maps (basics, no canonical forms), determinants, eigenvalues, and inner product spaces. Otto Bretscher’s “Linear Algebra with Applications” was the course text.
- Recitation section notes (reverse chronological order)
Introduction to Abstract Algebra
AS.110.411, JHU, 2025
Teaching assistant for nine student upper-level group theory course taught by Yueqiao Wu. We covered elementary group theory up to the Sylow theorems and the fundamental theorem of finitely generated abelian groups using M. A. Armstrong’s “Groups and Symmetry” as a guide.
Multivariate Calculus
MA 261, Purdue University, 2025
Teaching assistant for introductory multivariate calculus class following “Calculus, Early Transcendentals” by Briggs, Cochran, Gillett, and Schulz.