Coursework

Coursework

In addition to standard coursework in analysis and algebra, I have taken courses in the areas of numerical analysis, number theory, partial differential equations, statistics, and operations research.

• Numerical Analysis

  • Numerical Analysis, Numerical Linear Algebra, Numerical Solutions to Ordinary Differential Equations, Numerical Solutions to Partial Differential Equations

• Number Theory

  • Elementary Number Theory, Algebraic Number Theory I, Algebraic Number Theory II, Analytic Number Theory I

• Partial Differential Equations

  • Introduction to Partial Differential Equations, Partial Differential Equations I, Partial Differential Equations II

• Statistics

  • Probability and Random Variables, Mathematical Statistics, Regression Analysis, Elements of Statistical Learning

• Operations Research

  • Advanced Linear Programming, Convex Optimization

Reports and Projects

I have produced reports and projects on the following topics.

• Diophantine Equations (report + presentation)

• Diophantine Analysis + p-Adic Analysis (presentation)

• Euler Characteristic, Genus, and Orientability (report)

• Examination of Student Data in Math and Portuguese (report + presentation)

  • This report uses multiple linear regression models to examine the relationship between students' experiences and academic performance. I use AIC and BIC criteria to select models, and I consider diagnostics and remedial measures. My analyses are conducted in the R programming language.

• Gaussian Quadrature Formulas and Legendre Polynomials for Numerical Integration (presentation)

  • In this presentation, we examine Gaussian and Gauss-Legendre quadrature. We present approximation theorems.

• Hilbert Symbol (presentation)

• Microwave Imaging for Brain Stroke Detection (report + presentation)

  • In this report, we investigate the use of microwave imaging to detect brain strokes. We use MRI data to simulate propagation and scattering of microwaves on a brain with and without strokes. Our analyses are conducted in the MATLAB programming language. 

• Prediction of Chocolate Bar Ratings (report)

  • This report applies machine learning techniques to predict chocolate bar ratings. We use regression and ensemble techniques, and our analyses are conducted in the R programming language.

• p-adic Analysis—Numbers and Norms (report)

  • I investigate p-adic analysis from the lens of metric spaces. I compare analysis on the p-adic field with analysis on the field of real numbers.

• Projects in Quantitative Finance (report + presentation)