MA410 MATHEMATICAL MODELING (3 Cr.)

COURSE DESCRIPTION

Prerequisite: MA 312, MA361, MA371, MA380

Course Description

The focus of this course is the application of a wide variety of mathematical tools and techniques to construct and analyze several substantial classes of discrete, continuous, deterministic, and stochastic models arising in many areas of science, engineering, operations research, and other disciplines outside of mathematics.  The nature of the complex linkages between formulation and solution of real-world problems as well as the major issues pertaining to the implementation phase of the modeling process will be discussed.

Course Outline

1. Introduction to Mathematical Modeling
   1. Models and Reality
   2. Properties of Models
   3. Types of Models
   4. Examples of Mathematical Models
2. The Mathematical Modeling Process
   1. The Cyclical Nature of Mathematical Modeling
   2. Steps in the Mathematical Modeling Cycle
   3. Model Construction
3. Mathematical Programming Models
   1. Linear Programming Models
   2. Integer Programming Models
   3. Network Flow Models
   4. Nonlinear Programming Models
   5. Dynamic Programming Models
4. Discrete and Continuous Models for Growth and Decay Processes
5. Discrete and Continuous Models for Epidemic, Rumors, and Queues
6. Markov Chain Models
7. Models Involving Chance, Choice, and Competition
   1. Two-Person Zero-Sum Games
   2. Two-Person Nonzero-Sum Games
   3. General Games and Applications of Game Theory

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