Department of Mathematics
Math 01.520 Topics in Applied Mathematics
Topics in Applied Mathematics ……………………………………………………………3
This course provides an overview of the mathematical modeling process
and includes applications to optimization, dynamical systems, and Stochastic
process. Models of specific real world systems will be developed and studied
using an analytical and numerical methods.
(Prerequisite: 1701.231, 1701.502)
This course is intended to provide a sufficient background in linear
algebra and matrix theory for students in the program of M.A. in mathematics
and those in the program of M.A. in Subject Matter Teaching Mathematics.
After completing this course a student will be able to
1. construct mathematical models of real world systems
2. to describe the recursive process for the construction of mathematical
3. to use methods of linear algebra and differential equations toward
solving mathematical models.
4. to describe at least three different types of mathematical models.
5. to use statistical techniques to estimate model parameters and fit
a particular model to available data
6. to evaluate the validity and robustness of a mathematical model
1. Mathematical Models and Mathematical Modeling
• The Modeling Process, Dimensional Analysis, and Curve Fitting
2. The Mathematics of Optimization
• One-Variable and Multivariable Optimization, Sensitivity Analysis,
Robustness, and Computational Methods (could include applications to transportation,
economics, production control, and harvesting)
3. Dynamical Systems
• Steady State Analysis, Discrete and Continuous Time Dynamical
Systems, Eigenvalue Methods, Phase Portraits, and Numerical Methods (could
include applications to epidemiology, planetary motion, ecology, and traffic
4. Stochastic Processes
• Discrete and Continuous Probability Models, Markov Processes,
and Monte Carlo Simulation (could include applications to inventory control,
operations research, and epidemiology.)
Evaluations of Students: Students will be evaluated based on exams, and
individual and/or team projects
Course Evaluation: The course will be evaluated through student surveys
and faculty focus groups within the graduate mathematics program.
Rev.: 10/04 DM