Typically offered during the spring semester.

Catalog description:

Use of deterministic models and computers to study and optimize systems. Includes an introduction to modeling, calculus-based models, financial models, spreadsheet models, and linear programming models.

 
Prerequisite: MTH 251

Miami Plan:

MPT - First course in thematic sequence, CSA 3 - Mathematical & Computer Modeling .

 
Course Objectives:

• Explain the role of mathematical models in problem solving and contrast with other problem solving methods.
• Formulate word problems as mathematical models.
• Use electronic spreadsheet software as a modeling tool.
• Understand the role of data in modeling and be able to perform simple data analysis tasks.
• Explain the difference between deterministic and stochastic models, linear and nonlinear models, and continuous and integer models.
• Solve simple non linear optimization models with calculus and search.
• Formulate and solve linear optimization models.
• Understand and execute the simplex method.
• Represent a linear programming problem and its solution in matrix notation.
• Perform sensitivity analysis to interpret the impact of changes in the objective coefficients, the constraint coefficients, and the constraint limits.

Required topics (approximate weeks allocated):

• Introduction to models and how models are used (1.5)
  • introduction to mathematical models, advantages, disadvantages
  • classification of mathematical models
  • mathematical model terminology
  • examples of mathematical needs
  • model formulation
• Model examples (3)
  • calculus based optimization models
  • financial models
  • spreadsheet models
  • non linear models
  • solving simple unconstrained problems by search
• Introduction to linear programming, problem formulation (2)
• Systems of equations and matrix algebra (.5)
• Simplex algorithm (2)
• Sensitivity analysis and duality (2)
• Heuristic search methods (1)
• Optional optimization applications (2)
  • Transportation problem
  • Assignment problem
  • Network models
  • Data envelopment analysis
  • Other applications
• Exams/Review (1)