math work

MATH 221 Fall 2022, Several Variable Calculus

Explored vector algebra, solid analytic geometry, and calculus of functions of several variables. Covered Lagrange multipliers, multiple integration theory and applications, line and surface integrals, and Green's and Stokes' theorems.

MATH 409 Spring 2024, Honors Advanced Calculus/Analysis on the Real Line

Studied cardinality, properties of real numbers, and the completeness axiom. Covered sequences and series, continuity (including uniform continuity), differentiation, and the Riemann integral.

STAT 211 & 212 Spring/Fall 2023

Covered probability theory, probability distributions, sampling methods, and descriptive statistics. Focused on inference, hypothesis testing, regression analysis, and analysis of variance.

projects:

• plotted residuals vs. fitted values using R

• produced normal probability and cook’s distance plots from given data

• computed confidence intervals using R given data values

languages:

• R

MATH 323 Fall 2023

Evaluated linear equations and matrices, real vector spaces, and linear transformations. Covered change of bases, determinants, eigenvalues and eigenvectors, diagonalization, and inner products.

MATH 417 Fall 2024

Explored numerical methods for various applications, covering convergence and stability properties, and their computer implementation. Topics included interpolation, quadrature, initial and boundary value problems, matrix decompositions, solving linear and nonlinear systems, and least squares approximation.

projects:

• programmed various methods and algorithms in MATLAB

  • Newton’s method to approximate roots of an equation

  • computed and plotted Lagrange interpolating polynomials

  • implemented Euler’s method to solve ordinary differential equations

  • designed function to perform Gaussian elimination on square matrices

languages:

• MATLAB

MATH 325 Fall 2024

Explored the mathematical concepts behind interest, annuities, sinking funds, amortization, and coupon bonds. Covered valuation of noncallable bonds, yield to maturity, yield curves, spot and forward rates, internal rate of return, duration, convexity, and portfolio immunization.

skills:

• course designed to prep for Society of Actuaries Financial Mathematics (FM) Exam

MATH 419 Spring 2025

Applied mathematical and statistical methods to assess risk in the insurance and finance sectors. Focused on probability, statistics, finance, and economics, with an emphasis on using probabilistic models to estimate insurance premiums.

skills:

• course designed to prep for Society of Actuaries Probability (P) Exam