(April 2003)

Rutgers Business School Newark/New Brunswick
 Dept of Management Science & Information Systems
Prof. Papayanopoulos

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3 credit course: 26:711:561:01
Introduction to Mathematical Economics (IME)
 


Sessions/Course Outline
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Course description: Exploration of the quantitative tools and principles used to model operational procedures in economic and business systems -- types of variables, mathematical sets, and functional forms in constrained and unconstrained optimization. Other topics include tractability, duality, Kuhn-Tucker theory, algorithms and computation. Prerequisite: admission to the doctoral program or special permission.

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Text:
Ronald L. Rardin Optimization in Operations Research
Prentice Hall, 1998 ISBN # 0-02-398415-5)

Course Outline: (Subject to minor modification. Additional homework and handouts will be given in class)

 

Session/Topic

Chap./sections/notes
  Introduction: sets; discrete, continuous, homogeneous, functions; convexity  
  Properties of matrices; differential & integral calculus

Notes
  Partial derivatives; matrix notation for derivatives; classical (unconstrained) optimization; supporting hyperplanes

13 & notes
  Deterministic/stochastic modeling; motivation & economic interpretation of optimization; decisions, constraints & objectives; feasible, optimal, exact, & heuristic solutions; tractability, validity, & sensitivity; linear & nonlinear programs; graphing linear models (feasibility, optimality)

1 & 2
  Searches: local-global optima; feasible & improving directions; Problem session

3
  Midterm (1 hour); computer methods & software; (rest of 3-hr makeup class)

Notes
  Fixed point theorems, envelope theorem  
  Linear programming I -- fundamentals, formulation

4
  Linear programming II -- Basic & special algorithms

5 & 6
  Constrained optimization (Kuhn-Tucker); duality

7 & 14
  Omega distributions in optimization; discrete/integer models

2.5, part of 11, notes
  Difference and differential equations

Notes
  Review; discussion of extensions & special problems  
  Final Exam  

 

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