# Courses

## Required Core Courses (M.S. and Ph.D.)

#### MATH 201: Teaching and Learning in the Sciences

Students will be introduced to ‘scientific teaching’ - an approach to teaching science that uses many of the same skills applied in research. Topics will include how people learn, active learning, designing, organizing and facilitating teachable units, classroom management, diversity in the classroom and assessment design.

#### MATH 221: Advanced Ordinary Differential Equations

Introduces advanced topics in the theory of ordinary differential equations (ODEs). This course emphasizes conceptual understanding and critical thinking. It will include simplified problems from physics and other disciplines to motivate certain topics.

#### MATH 231: Numerical Solution of Differential Equations I

Focuses on construction and analysis of numerical methods that solve common problems in science and engineering.

#### Math 246: Numerical Linear Algebra

Introduction to rigorous numerical analysis via topics in Linear Algebra, including: Iterative solution of linear equations, Foundations of approximation theory, Solution of systems of nonlinear equations, Matrix Factorizations, Convex programming, and Conjugate gradient.

#### Math 280: Mathematical and Statistical Foundations of Data Science

Introduction to graduate Data Science, including: Foundations of probability and statistics, Classification and Regression, Dimensionality reduction, Parameter Estimation and Inference, and Model Analysis and Selection.

#### MATH 291: Applied Mathematics Seminar (to be taken at least twice)

Seminar series covering various topics in applied mathematics presented by faculty, graduate students, and visiting speakers.

## Additional Required Course (M.S. only)

#### MATH 222: Partial Differential Equations

Elements of the theory of PDEs. Topics include determining the existence, uniqueness, and well-posedness of solution of PDEs, solving first and second order linear PDEs analytically (method of characteristics, separation of variables, Fourier Series) and numerically (finite-differences, finite elements, time integrators).

Prerequisite: MATH 221

### OR

#### Math 282: Statistical and Machine Learning

Concepts in advanced statistics and machine learning including: Data processing, Decision trees and random forests, Support vector machines, Neural Networks, Assessment of ML/SL algorithms.

## Additional Required Courses (Ph.D. only)

#### MATH 222: Partial Differential Equations

Elements of the theory of PDEs. Topics include determining the existence, uniqueness, and well-posedness of solution of PDEs, solving first and second order linear PDEs analytically (method of characteristics, separation of variables, Fourier Series) and numerically (finite-differences, finite elements, time integrators).

Prerequisite: MATH 221

#### MATH 224: Advanced Methods of Applied Mathematics

Basic real analysis (metric spaces, continuity, contraction mapping theorem), Banach spaces, Hilbert spaces, linear operators, bounded operators, compact operators, spectral theory, distributions, Fourier transforms, a priori estimates, energy estimates, existence/uniqueness theory, variational calculus, and applications of the above material to concrete problems in applied mathematics.

Prerequisite: MATH 221 and MATH 222

#### MATH 233: Scientific Computing

Theoretical and practical introduction to parallel scientific computing. Survey of hardware and software environments, and selected algorithms and applications. Topics will include linear systems, N-body problems, FFTs, and methods for solving PDEs. Practical implementation and performance analysis are emphasized in the context of demonstrative applications in science and engineering.

#### Math 282: Statistical and Machine Learning

Concepts in advanced statistics and machine learning including: Data processing, Decision trees and random forests, Support vector machines, Neural Networks, Assessment of ML/SL algorithms.

## Other Courses (Ph.D. students must take at least one elective)

#### MATH 292: Special Topics in Applied Mathematics

Treatment of a special topic or theme in applied mathematics at the graduate level. May be repeated for credit in a different subject area.

Supervised research.

#### MATH 298: Directed Group Study

Group project under faculty supervision.

#### MATH 243: Interdisciplinary Computational Graduate Education

Focuses on teaching first-year graduate students from a variety of graduate programs skills in computational methods, programming languages, team science, project development, problem solving, social networking, and career preparation.