Recent Coursework

Featured Coursework

STA4322 Intro to Statistical Theory

This is the second class in a sequence of mathematical statistics classes offered to undergraduate statistics students. Topics in this course include random samples, distribution families, estimators and estimands, bias, mean-squared error, the method of moments, maximum likelihood estimators, convergence in probability/distribution, pivots, the (weak) law of large numbers, Slutsky's Theorems, the delta method, central limit theorem, confidence intervals, hypothesis testing, MLE asymptotic behavior, score functions, Fisher information, linear regression analysis, and generalized linear models. Building off of topics in analysis, probability, and intro statistics, this class combines strong mathematical concepts with previous statistical intuitions to form a complete picture of traditional statistical methods. It also serves as a gateway into future mathematical statistics with its emphasis on conceptual understanding and rigor.

MAA4211 & MAA4202 Real Analysis and Advanced Calc. I and II

The advanced calculus sequence covers important undergraduate analysis concepts, such as set supremums and infimums, epsilon convergence, sequences and their limits, function limits, continuity, series convergence and tests, differentiability, riemann integration and integrability, the fundamental theorem of calculus, function spaces, pointwise and uniform convergence, uniform continuity, metric spaces, normed vector spaces, topological spaces, characterizations of compactness, norm operators, calculus on functions $f: \mathbb{R}^n \to \mathbb{R}^m$, and inverse/implicit function theorems. This sequence serves as the foundations for higher level mathematical classes and also as a strong introduction to measure theory and sigma-algebra foundations in probability theory. These classes are meant to push undergraduates towards graduate-level work and understandings in mathematics and give strong foundations for further topics in analysis and topology.

MAS4115 Linear Algebra for Data Science

This broad course covers a wide variety of applied techniques in data science backed by a strong foundation in theoretical linear algebra, including topics in high dimensional data representation, usage of numpy, sklearn, keras, and other python tools, t-distributed stochastic neighborhood embedding, k-means, k-nearest-neighbors, kd-trees, support vector machines, singular value decomposition, dimension reduction, the Johnson-Lindenstrauss lemma, the Moore-Penrose pseudoinverse, supervised and unsupervised learning, and advanced deep learning methods. As a foundational data science course, this class touches on tons of interesting, useful, and recent developments in the field of data science while also discussing important mathematical assumptions and guarantees. This course also involved several coding labs and exploratory projects using a variety of datasets, varying both in content, size, and quality.

STA4321 Intro to Probability

Often considered the first real statistics class in an undergraduate's journey, this class explores the foundations of axiomatic probability. Throughout the semester, the course covers probability axioms, counting and combinatorics, basic set theory, probability density and cumulative density functions, various distributions and their properties, the first, second, and higher moments, moment-generating functions, and convergence in probability/distribution.

MAS4105 Linear Algebra

This class serves as the undergraduate introductory theory course for linear algebra. Starting with abstract vector spaces and their axioms, the course explores the theory behind linear (in)dependence, bases, linear transformations, matrices and dual spaces, matrix computations and operations, and (as my professor Dr. David Groisser likes to say) "eigenstuff". This course is fundamental for mathematics students and is entirely proof-based, focusing not on the vast and also important computational applications of linear algebra, but rather the (sometimes) intuitive axiomatic approach.