Applied mathematics

Applied mathematics involves applications of mathematical methods and techniques to explore, and describe behavior of scientific, industrial, and engineering phenomena. The applied mathematics program is interdisciplinary in spirit. It is based on principles of mathematical continuous modeling, computer simulation, linear programming, optimization, operations research, bioinformatics, numerical methods, etc. The applied mathematics program appeals to individuals who are interested in applying their mathematical interests and skills to real-world problems.

Applicants should have an undergraduate degree in Mathematics or its equivalent. Candidates are expected to have approved undergraduate courses in Multivariable calculus, Linear Algebra, Ordinary Differential Equations, Numerical Analysis and Advanced Calculus. It is also recommended to have some programming experience using a high level language such as C\C++, and/or a mathematical package such as Matlab and Mathematica.

In addition to the requirements of the Office of Graduate Studies, the Master of Science degree in Applied Mathematics with Thesis, Option I, requires

1. 9 credits in core courses

  • MATE 6261, Real Analysis ·
  • MATE 6672, Numerical Mathematical Analysis
  • MATE 6677, Partial Differential Equations
2. 9 credits from the following (area of specialization)
  • MATE 5016, Game Theory
  • MATE 5047, Intermediate Differential Equations ·
  • MATE 5049, Calculus of Variations
  • MATE 5055, Vector Analysis
  • MATE 5056, Tensor Analysis
  • MATE 5150, Linear Algebra
  • MATE 6025, Numerical Linear Algebra
  • MATE 6026, Numerical Optimization
  • MATE 6035, Topics in Operation Research I
  • MATE 6036, Topics in Operations Research II
  • MATE 6045, Optimization Theory
  • MATE 6262, Real Variable II
  • MATE 6301, Complex Variable
  • MATE 6530, Differential Geometry
  • MATE 6622, Topics in Complex Variable
  • MATE 6627, Topics in Analysis I
  • MATE 6628, Topics in Analysis II
  • MATE 6674, Numerical Methods for Partial Differential Equations
  • MATE 6675, Mathematics in Modern Science I
  • MATE 6676, Mathematics in Modern Science II
  • MATE 6678, Topics in Partial Differential Equations


3. 6 credits outside the area of specialization or major. The requirement of a minimum of two out-of-discipline courses is to ensure cross-disciplinary breadth. The courses must be related to mathematics and should be chosen in a coherent way. These should be of level 5000 or higher. It is recommended that student chooses these courses with the help of their advisor

  • 6000 or 5000 level courses not listed in the area of specialization
  • 6000 or 5000 level courses outside the Mathematics department
4. 2 credits in Seminar
  • MATE 6991, Seminar (1 credit )
  • MATE 6992, Seminar (1 credit )

5. 6 credits in Thesis

  • MATE 6999, ( 6 credits )

In addition, the candidate must pass one qualifying exam from

Option II: project option: the course and examination requirements are similar to Option I, however the 6 Thesis credits must be replaced by 6 Project credits. An oral examination on the project is also required.

Option III, no project, no thesis: the student should approve a minimum of 36 course credits:

  • A minimum of 27 credits at graduate level
  • A minimum of 21 credits in the area of specialization
  • A minimum of 6 credits in courses related to, but outside the area of specialization.

In addition the student must pass two (2) exams from the above list.

List of faculty associated with this track and their research interests

 

Robert Acar, (Numerical Analysis, Partial Differential Equations, Inverse problems)

Omar Colón, (Non-Linear Dynamics of Discrete Dynamical Systems. Math Olympiads)

Arturo Portnoy, (Inverse Problems, Optimization, Regularization, Math Education, Technology in Math Education)

Karen Ríos, (Mathematical epidemiology and ecology, population and social dynamics)

Roberto Rivera (Data Science, Machine Learning, Statistics, Time Series) Juan Romero, (Harmonic Analysis and wavelet theory, biomedical imaging)

Lev Steinberg, (Mathematical Modeling, Nonlinear Mechanics)

Alexander Urintsev, (Fluid Dynamics, Stability, Symbolic Computation)

Pedro Vásquez, (Applied Mathematics, Optimization, Scheduling)

Alejandro Vélez-Santiago (Analysis, PDEs, Potential Theory, Fractal Geometry)


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