# Master of Science in Applied Mathematics

The program 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, and numerical methods. 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, or Data Science.

**Program Educational Objectives:**

- 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 Educational Outcomes common to all ****concentrations****:**

Upon the completion of the program students should be able to:

- 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.
- Communicate effectively 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.

**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.

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## Applied Mathematics Requirements

### 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 | 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 541 | Statistical Methods | 3 |

Or | ||

MA 612 | Mathematical Statistics | 3 |

MA 623 | Stochastic Processes | 3 |

MA 629 | Nonlinear Optimization | 3 |

MA 662 | Stochastic Programming | 3 |

### 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 Spatio-Temporal Statistical Modeling | 3 |

MA 617 | Tensor Methods for Data Analysis | 3 |

MA 620 | Introduction to Network and 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 | 3 |

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) | 1-6 |

MA 810 | Special Topics in Mathematics | 1-3 |

MA 900 | Thesis in Mathematics | 1-10 |