Anne Arundel Community College

MAT 133: Finite Mathematics



CATALOG DESCRIPTION:

An introduction to finite mathematics. Topics include systems of linear equations, matrices, the Gauss-Jordan method, inequalities and linear programming, sets and counting techniques, probability, difference equations, Markov processes and game theory. Applications to economics, business and social science are discussed.

Prerequisite: Achieving an appropriate score on the mathematics part of the ACT or SAT, or completion of MAT 012 with a grade of at least C or scoring at an appropriate level on the Mathematics Placement Test.

LEARNING OBJECTIVES:

Upon completion of this course, the student will be able to:
  1. Solve applications involving matrices by using the Gauss-Jordan method, inverse matrices and matrix operations.
  2. Solve linear programming problems using the graphical approach.
  3. Use set theory, the principles of counting and probability concepts to calculate probabilities.
  4. Apply Markov processes to the solution of probability problems.
  5. Use difference equations to model interest and finance applications.
  6. Apply elementary game theory to produce optimal strategies in games.

COURSE OUTLINE:

Matrices:
  • Solving Systems of Linear Equations
  • Arithmetic Operations on Matrices
  • The Inverse of a Matrix
  • Gauss-Jordan Method for Calculating Inverses
  • Input-Output Analysis

Linear Programming:
  • Graphing Inequalities
  • Linear Programming Theorem
  • Applications of Linear Programming

Sets and Counting:
  • Sets
  • Venn Diagrams and Counting
  • A Fundamental Principle of Counting
  • The Multiplication Principle
  • Permutations and Combinations
  • The Binomial Theorem

Probability:
  • Introduction to Probability
  • Sample Spaces, Exponents, Outcomes and Events
  • Assignment of Probabilities
  • Calculating Probabilities of Events
  • Conditional Probability and Independence
  • Tree Diagrams
  • Simulation

Markov Processes:
  • The Transition Matrix
  • Regular Stochastic Matrices

Difference Equations:
  • Introduction to Difference Equations
  • Graphing Difference Equations
  • Mathematics of Personal Finance
  • Modeling with Difference Equations

Game Theory:
  • Games and Strategies
  • Mixed Strategies
  • Determining Optimal Mixed Strategies

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