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Master of Science in Applied Mathematics

The Master of Science in Applied Mathematics degree prepares students for careers in science, engineering, and business, where advanced methods in differential equations, nonlinear optimization, statistics, and computational mathematics play a significant role in technology development and innovation. It accommodates individuals with varying academic backgrounds and career objectives, including students interested in pursuing a Ph.D. in the mathematical sciences. 

Upon completion of the program, students should have acquired significant knowledge and fundamental understanding across a broad range of subjects including: 

  • Analysis

  • Differential equations

  • Probability

  • Nonlinear optimization

  • Statistics

  • Numerical methods

Concentrations

To better prepare themselves for careers at the interface between mathematics and applications in science, engineering and business, our students are strongly encouraged to pursue deeper understanding in one of the three areas (program concentrations): 

  • Differential Equations

  • Optimization of Stochastic Systems

  • Data Science

Program Objectives

The program prepares students to:

  • have broad knowledge and fundamental understanding of real analysis, differential equations, probability, nonlinear optimization, statistics, and numerical methods.

  • gain expertise in at least one of the following areas, where they will be familiarized with most recent mathematical approaches and will study in-depth the most recent results: continuous and discrete dynamical systems; partial differential equations and integro-differential equations; inverse methods in differential equations and optimization; probability and statistics, stochastic processes, statistical estimation techniques, the theory and numerical methods of optimization; control of dynamical systems; optimization under uncertainty and risk.

  • develop awareness of the interplay between these mathematical disciplines and their relevance to science, engineering, and business.

Program Outcomes

Program Educational Outcomes common to all concentrations:

  • Develop

    • models from the governing laws and theories in physics, chemistry, biology,

    • stochastic models using experimental/observed data,

    • mathematical models of optimal decision, optimal design, and optimal control situations.

  • Identify proper methodology to analyze these models.

  • Identify and/or develop a proper numerical method and use or develop software to solve the formulated mathematical problem.

  • Analyze the obtained solution and infer consequences for the practical situation.

  • Validate and fine-tune the mathematical model and the solution method.

  • Effectively communicate their mathematical expertise. 

Program outcomes specific to the concentration in Differential Equations:

  • Acquire deeper theoretical knowledge in at least one of the following areas: continuous and discrete dynamical systems; partial differential equations and integro-differential equations; and inverse methods in differential equations and optimization.

  • Gain hands-on experience in developing mathematical models with differential equations in various applications and in implementing those models in software packages such as Matlab, Mathematica and COMSOL Multiphysics.

  •  Broaden knowledge of applications of differential equations and gain intimate knowledge of some of those applications.

Program outcomes specific to the concentration in Optimization of Stochastic Systems

  • Acquire deeper theoretical knowledge in at least one of the following areas: stochastic processes, statistical estimation techniques, the theory and numerical methods of optimization; control of dynamical systems; optimization under uncertainty and risk.

  • Gain hands-on experience in formulating optimization problems in various applications dealing with uncertainty and risk and in solving those problems with modern optimization software.

  •  Broaden the knowledge of applications areas where the need for stochastic systems models and their analysis is crucial and provide opportunity to gain intimate knowledge of some of those areas.

Program outcomes specific to the concentration in Data Science

  • Acquire deeper theoretical knowledge in at least one of the following areas: statistical models used for independent and non-independent data (e.g. time series, Markov processes, spatio-temporal data); fundamental principles underlying statistical estimation and inference; general stochastic processes and their properties pertaining to modeling; optimization and computational methods related to parameter estimation and prediction.

  • Gain hands-on experience in developing mathematical and statistical models with software packages such as R, MATLAB toolboxes, and dedicated libraries in Python and C++.

  • Broaden knowledge of applications of stochastic and statistical models tailored to various real world data applications in ecology, epidemiology, and actuarial science, among others.


Degree Requirements

The program is a 30-credit degree program. Students are required to complete:

  • 3 core courses (9 credits)

  • 7 elective courses (21 credits).


Students may choose MA 900 - Thesis in Mathematics for 6 credits as one of their electives to work on a specific project with an advisor. Enrolling in MA 900 is subject to approval by the program coordinator.

Common Core Courses

MA 547Advanced Calculus I

3
Or
MA 635Functional Analysis I

3

MA 540Introduction to Probability Theory

3
Or
MA 611Probability

3

MA 615Numerical Analysis I

3

Concentration in Differential Equations Elective Courses

Choose at least 3 courses from the following list for the concentration in Differential Equations:

MA 649Intermediate Differential Equations

3
MA 650Intermediate Partial Differential Equations

3
MA 653Numerical Solutions of Partial Differential Equations

3
MA 681Complex Analysis with Applications

3

Concentration in Optimization of Stochastic Systems Elective Courses

Choose at least 3 courses from the following list for the concentration in Optimization of Stochastic Systems:

MA 541Statistical Methods

3
Or
MA 612Mathematical Statistics

3

MA 623Stochastic Processes

3
MA 629Nonlinear Optimization

3
MA 662Stochastic Programming

3

Concentration in Data Science Elective Courses

Choose at least 3 courses from the following list for the concentration in Data Science:

MA 544Numerical Linear Algebra for Big Data

3

MA 541Statistical Methods

3
Or
MA 612Mathematical Statistics

3

MA 641Time Series Analysis I

3
MA 661Dynamic Programming and Reinforcement Learning

3

Electives

MA 544Numerical Linear Algebra for Big Data

3
MA 541Statistical Methods

3
MA 612Mathematical Statistics

3
MA 613Spatial and Spatio-Temporal Statistical Modeling

3
MA 617Tensor Methods for Data Analysis

3
MA 620Intro Network & Graph Theory

3
MA 623Stochastic Processes

3
MA 627Combinatorial Analysis

3
MA 629Nonlinear Optimization

3
MA 630Advanced Optimization Methods

3
MA 631Calculus of Variations

3
MA 632Theory of Games

3
MA 641Time Series Analysis I

3
MA 649Intermediate Differential Equations

3
MA 650Intermediate Partial Differential Equations

3
MA 651Topology I

3
MA 653Numerical Solutions of Partial Differential Equations

3
MA 655Optimal Control Theory

3
MA 661Dynamic Programming and Reinforcement Learning

3
MA 662Stochastic Programming

3
MA 681Complex Analysis with Applications

3
MA 711Inverse Problems in Science and Engineering

3
MA 712Mathematical Models of Risk

3
MA 720Advanced Statistics

3
MA 800Special Problems in Mathematics (MS)

1 - 6
MA 810Special Topics in Mathematics

1 - 3
MA 900Thesis in Mathematics

1 - 10

Students may choose MA 900 - Thesis in Mathematics for six credits as one of their electives to work on a specific project with an advisor. Enrolling in MA 900 is subject to approval by the program coordinator.