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):
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 indepth the most recent results: continuous and discrete dynamical systems; partial differential equations and integrodifferential 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 finetune 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 integrodifferential equations; and inverse methods in differential equations and optimization.

Gain handson 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 handson 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 nonindependent data (e.g. time series, Markov processes, spatiotemporal 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 handson 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 30credit degree program. Students are required to complete:
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 547  Advanced Calculus I  3 
 Or  
MA 635  Functional Analysis I  3 
  
MA 540  Introduction to Probability Theory  3 
 Or  
MA 611  Probability  3 
  
MA 615  Numerical 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 649  Intermediate Differential Equations  3 
MA 650  Intermediate Partial Differential Equations  3 
MA 653  Numerical Solutions of Partial Differential Equations  3 
MA 681  Complex Analysis with Applications  0 
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:
Concentration in Data Science Elective Courses
Choose at least 3 courses from the following list for the concentration in Data Science:
MA 544  Numerical Linear Algebra for Big Data  3 
  
MA 541  Statistical Methods  3 
 Or  
MA 612  Mathematical Statistics  3 
  
MA 641  Time Series Analysis I  3 
MA 661  Dynamic Programming and Reinforcement Learning  3 
Electives
MA 544  Numerical Linear Algebra for Big Data  3 
MA 541  Statistical Methods  3 
MA 612  Mathematical Statistics  3 
MA 613  Spatial and SpatioTemporal Statistical Modeling  3 
MA 617  Tensor Methods for Data Analysis  3 
MA 620  Intro Network & Graph Theory  3 
MA 623  Stochastic Processes  3 
MA 627  Combinatorial Analysis  3 
MA 629  Nonlinear Optimization  3 
MA 630  Advanced Optimization Methods  3 
MA 631  Calculus of Variations  3 
MA 632  Theory of Games  3 
MA 641  Time Series Analysis I  3 
MA 649  Intermediate Differential Equations  3 
MA 650  Intermediate Partial Differential Equations  3 
MA 651  Topology I  3 
MA 653  Numerical Solutions of Partial Differential Equations  3 
MA 655  Optimal Control Theory  3 
MA 661  Dynamic Programming and Reinforcement Learning  3 
MA 662  Stochastic Programming  3 
MA 681  Complex Analysis with Applications  0 
MA 711  Inverse Problems in Science and Engineering  3 
MA 712  Mathematical Models of Risk  3 
MA 720  Advanced Statistics  3 
MA 800  Special Problems in Mathematics (MS)  16 
MA 810  Special Topics in Mathematics  110 
MA 900  Thesis in Mathematics  160 
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.