Teaching Information

Math 701 Algebra I

Graduate Course, University of South Carolina, Department of Mathematics, 2024

Course Description: Algebra is a key discipline within mathematics and is likely to be integral to any research field you choose during your graduate studies. The Math 701/702 sequence aims to give you a comprehensive introduction to algebra and equip you with a robust foundation for exploring more complex topics in the future. Through numerous examples, problem-solving exercises, and proofs, you will hone your algebraic intuition. Another key objective of this course is to prepare you for the Algebra Qualifying Exam. In Math 701, we will start by revisiting group theory before progressing to more advanced subjects. Later in the course, we will shift our focus to ring theory. We plan to explore Chapters 1-9 of Dummit and Foote, though not every section will be covered

Math 141 Sessions 13-16 Calculus I

Undergraduate Course, University of South Carolina, Department of Mathematics, 2024

Course Description: This course is designed to introduce students to the study of (single-variable) calculus. Topics include Functions, Limits, Derivatives, Introduction to Integrals, the Fundamental Theorem of Calculus, Applications of Derivatives and Integrals. Four classroom hours and one laboratory hour per week.

Math 784 Algebraic Number Theory

Graduate Course, University of South Carolina, Department of Mathematics, 2024

Course Description: This course aims to provide an introductory exploration into algebraic numbers and algebraic integers. Algebraic number theory extends its focus beyond integers, particularly emphasizing number fields as finite algebraic extensions of Q. The following topics will be covered in the course as time permits: Algebraic Numbers/Integers, Number Fields, Quadratic Fields, Cyclotomic Fields, Dedekind Domains, Orders, Factorization of Ideals, Minkowski’s Theorem, Geometry of Numbers, Ideal Classes, Dirichlet’s Unit Theorem, Splitting of Prime Ideals, Artin Reciprocity, L-functions, Class Number Formulas, and Class Field Theory.

Math 141 Sessions 29-32 Calculus I

Undergraduate Course, University of South Carolina, Department of Mathematics, 2023

Course Description: This course is designed to introduce students to the study of (single-variable) calculus. Topics include Functions, Limits, Derivatives, Introduction to Integrals, the Fundamental Theorem of Calculus, Applications of Derivatives and Integrals. Four classroom hours and one laboratory hour per week.

Math 141 Sessions 13-16 Calculus I

Undergraduate Course, University of South Carolina, Department of Mathematics, 2023

Course Description: This course is designed to introduce students to the study of (single-variable) calculus. Topics include Functions, Limits, Derivatives, Introduction to Integrals, the Fundamental Theorem of Calculus, Applications of Derivatives and Integrals. Four classroom hours and one laboratory hour per week.

2023 Summer REU

Undergraduate Research, University of Virginia, Department of Mathematics, 2023

Mentored undergraduate students in the Number Theory Research Group.

Math 2310 Calculus III

Undergraduate Course, University of Virginia, Department of Mathematics, 2023

Course Description: A continuation of Calc I and II, this course is about functions of several variables. Topics include finding maxima and minima of functions of several variables/surfaces and curves in three-dimensional space/integration over these surfaces and curves. Additional topics: conservative vector fields/Stokes’ and the divergence theorems/how these concepts relate to real-world applications. Prerequisite: MATH 1320 or the equivalent.

Math 3354 Survey of Algebra

Undergraduate Course, University of Virginia, Department of Mathematics, 2023

Course Description: In this course, students will learn about Groups, Subgroups, Groups of Permutations, Cyclic Groups, Quotient Groups, the Isomorphism Theorems, Rings, Ideals, Quotient Rings, Integral Domains, Rings of Polynomials, Factoring Polynomials, Extensions of Fields, Galois Theory, and Solving Equations by Radicals.

Math 2310 Calculus III

Undergraduate Course, University of Virginia, Department of Mathematics, 2022

Course Description: A continuation of Calc I and II, this course is about functions of several variables. Topics include finding maxima and minima of functions of several variables/surfaces and curves in three-dimensional space/integration over these surfaces and curves. Additional topics: conservative vector fields/Stokes’ and the divergence theorems/how these concepts relate to real-world applications. Prerequisite: MATH 1320 or the equivalent.

Math 1220 A Survey of Calculus II

Undergraduate Course, University of Virginia, Department of Mathematics, 2022

Course Description: Math 1220 is a second calculus course intended for students interested primarily in business, biology, and the social sciences. Because this is the second course in calculus, you already know that calculus provides two fundamental tools for analyzing functions: the derivative and the definite integral. In this course, we will be using calculus to analyze trigonometric functions, probability density functions, functions depending on two variables, and functions defined by power series. You will also be introduced to mathematical modeling with differential equations, and learn techniques for finding exact and approximate solutions to such equations.

2022 Summer REU

Undergraduate Research, University of Virginia, Department of Mathematics, 2022

Mentored undergraduate students in the Number Theory Research Group.

Math 8600 Commutative Algebra

Graduate Course, University of Virginia, Department of Mathematics, 2022

Course Description: In this course, students will learn about Rings and Ideals, Modules, Rings and Modules of Fractions, Hilbert Basis Theorem, Cayley-Hamilton Theorem, Noether Normalization, the Nullstellensatz, Localization, Local and Global Fields, Local Zeta Functions, Primary Decomposition, Integral Dependence and Valuations, Chain Conditions, Noetherian Rings, Artin Rings, Discrete Valuation Rings and Dedekind Domains, Filtrations, Completions, Hilbert Polynomials, and Dimension Theory.

Math 2310 Sec. 300 Calculus III

Undergraduate Course, University of Virginia, Department of Mathematics, 2021

Course Description: A continuation of Calc I and II, this course is about functions of several variables. Topics include finding maxima and minima of functions of several variables/surfaces and curves in three-dimensional space/integration over these surfaces and curves. Additional topics: conservative vector fields/Stokes’ and the divergence theorems/how these concepts relate to real-world applications. Prerequisite: MATH 1320 or the equivalent.

Math 2310 Sec. 200 Calculus III

Undergraduate Course, University of Virginia, Department of Mathematics, 2021

Course Description: A continuation of Calc I and II, this course is about functions of several variables. Topics include finding maxima and minima of functions of several variables/surfaces and curves in three-dimensional space/integration over these surfaces and curves. Additional topics: conservative vector fields/Stokes’ and the divergence theorems/how these concepts relate to real-world applications. Prerequisite: MATH 1320 or the equivalent.

2021 Summer REU

Undergraduate Research, University of Virginia, Department of Mathematics, 2021

Mentored undergraduate students in the Number Theory Research Group.

Math 3354 Survey of Algebra

Undergraduate Course, University of Virginia, Department of Mathematics, 2021

Course Description: In this course, students will learn about Groups, Subgroups, Groups of Permutations, Cyclic Groups, Quotient Groups, the Isomorphism Theorems, Rings, Ideals, Quotient Rings, Integral Domains, Rings of Polynomials, Factoring Polynomials, Extensions of Fields, Galois Theory, and Solving Equations by Radicals.

Math 3310 Basic Real Analysis (Recitation Instructor)

Undergraduate Course, University of Virginia, Department of Mathematics, 2021

Course Description: A rigorous development of the properties of the real numbers and the ideas of calculus including theorems on limits, continuity, differentiability, convergence of infinite series, and the construction of the Riemann integral. Students without prior experience constructing rigorous proofs are encouraged to take Math 3000 before or concurrently with Math 3310. Prerequisite: MATH 1320.

Math 2310 Calculus III

Undergraduate Course, University of Virginia, Department of Mathematics, 2020

Course Description: A continuation of Calc I and II, this course is about functions of several variables. Topics include finding maxima and minima of functions of several variables/surfaces and curves in three-dimensional space/integration over these surfaces and curves. Additional topics: conservative vector fields/Stokes’ and the divergence theorems/how these concepts relate to real-world applications. Prerequisite: MATH 1320 or the equivalent.

2020 Summer REU

Undergraduate Research, University of Virginia, Department of Mathematics, 2020

Mentored undergraduate students in the Number Theory Research Group.

2019 Summer REU

Undergraduate Research, Texas A&M University, Department of Mathematics, 2019

Mentored undergraduate students in the Number Theory Research Group.

2019 Spring DRP

Undergraduate Research, Texas A&M University, Department of Mathematics, 2019

The Directed Reading Program (DRP) gives undergraduates the opportunity to:

1. work one-on-one with a graduate mentor for the semester,
   
2. learn an area of mathematics not covered in any course, and
   
3. gain valuable presentation skills.
   

Math 131 Mathematical Concepts-Calculus

Undergraduate Course, Texas A&M University, Department of Mathematics, 2018

Course Description: This course is designed to introduce students to the study of (single-variable) calculus. Topics include Limits and continuity; rates of change, slope; differentiation: the derivative, maxima and minima; integration: the definite and indefinite integral techniques; curve fitting. Prerequisite: High school algebra I and II and geometry.

2018 Fall DRP

Undergraduate Research, Texas A&M University, Department of Mathematics, 2018

The Directed Reading Program (DRP) gives undergraduates the opportunity to:

1. work one-on-one with a graduate mentor for the semester,
   
2. learn an area of mathematics not covered in any course, and
   
3. gain valuable presentation skills.
   

2018 Summer REU

Undergraduate Research, Texas A&M University, Department of Mathematics, 2018

Mentored undergraduate students in the Number Theory Research Group.

Math 663 Qualifier Exam Preparation Course-Complex Analysis

Graduate Course, Texas A&M University, Department of Mathematics, 2018

Course Description: This course, for graduate students in mathematics, addresses the theory of functions of one complex variable with a focus on the qualifying examination in complex analysis. The course covers the representation of holomorphic functions by power series and by integrals; complex line integrals, Cauchy’s integral formula, and some applications; singularities of holomorphic functions, Laurent series, and computation of definite integrals by residues; the maximum principle and Schwarz’s lemma, and conformal mapping, infinite products, the Weierstrass factorization theorem, Mittag-Leffler’s theorem, normal families, proof of the Riemann mapping theorem, analytic continuation, Runge’s approximation theorem, harmonic functions, and Picard’s theorems.

2017 Summer REU

Undergraduate Research, Texas A&M University, Department of Mathematics, 2017

Mentored undergraduate students in the Number Theory Research Group.