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Department of Mathematical Sciences

Pure and Applied Analysis

The study of analysis provides a basic understanding of qualitative and quantitative problem-solving techniques, the ability to analyze new areas of interest, and the ability to interact with colleagues from other disciplines in a problem-solving situation. Modern applications of analysis include biomedical modeling, image analysis, robotic control, ecology, environmental modeling, and financial engineering.

Faculty

  • J. Brannan : Mathematical modeling, stochastic analysis, financial mathematics
  • T. Khan : Inverse problems, parameter estimation, optical tomography, biomedical imaging, control problems
  • S. Liu : Inverse problems, boundary control theory, partial differential equations
  • M. Mitkovski : Complex analysis, harmonic analysis, operator theory
  • J. Peterson : West nile virus and tularaemia infection models, soft computing and cognitive modeling
  • M. Schmoll : (geometric) control theory, differential topology, symplectic geometry, differential geometry, dynamical systems, in particular, polygonal billiards
  • J. R. Yoon : Medical imaging, inverse problems, elasticity theory, seismic inversion

Curriculum

A plan of study for students concentrating in analysis will include courses in theoretical analysis, applied analysis, numerical analysis, and physical system modeling.

Courses ( Course Descriptions)

  • Linear Analysis (821)
  • Measure and Integration (822)
  • Complex Analysis (823)
  • Dynamical Systems (825)
  • Partial Differential Equations (826)
  • Neural Networks (827)
  • Fourier Series (831)
  • Optimal Control (837)
  • Applied Mathematics (841)
  • Numerical Analysis (861)
  • Functional Analysis (927)
  • Investment Science (974)
  • Stochastic Calculus for Finance (982)
  • Computational Finance (982)

Course Substitution Policy

Sample Curricula

  • Sample Program for M.S. Concentration in Analysis
    • Fall:  810, 853, 825/826
    • Spring:  805, 821, 860
    • Summer:  803
    • Fall:  841, 861, 825/826
    • Spring:  809, 811, 831, 892
  • Sample Program for M.S. Concentration in Financial Mathematics
    • Fall:  805, 810, 853
    • Spring:  821, 860, 974
    • Summer:  803
    • Fall:  804, 982, MBA 846
    • Spring:  809/811, ECON 855, 982, 892

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