# Course Syllabus for Finite Mathematics

Prerequisites

Satisfactory placement test score or "C" or better in MATH
131 or

equivalent.

Catalog Description

A course designed especially for students in areas such as business, economics,
social science, and

nonphysical sciences. It emphasizes the concepts and applications of mathematics
rather than

mathematical structures. Topics include: matrix algebra, applications of
matrices (including solution of

systems of linear equations), linear programming and the simplex method, set
theory, logic, Boolean

Algebra, counting and probability, stochastic processes, game theory, Markov
Chains, mathematical

modeling, and the mathematics of finance.

Course Objectives: See attached.

**Topical Outline**

Approximate Week | Topic or Class Activity |

1 | Linear Functions and Equations |

2 | Matrices and Systems of Linear Equations |

1 | Linear Programming – Graphically |

1 | Linear Programming – Simplex Method |

1 1/2 | Finance |

2 | Logic |

1 1/2 | Sets |

1 | Counting Techniques |

1 1/2 | Probability |

1 1/2 | Markov Chains |

15 – 16 weeks |

**OBJECTIVES
**

Upon completion of this course, the student will be able to complete the following objectives.

Linear Functions and Equations

• Find the slope and equation of a given line.

• Find equations of parallel and perpendicular lines.

• Graph linear functions and their applications.

• Construct linear models such as supply and demand functions.

• Find a Least Squares Line.

Matrices and Systems of Linear Equations

• Solve a system of m linear equations in n variables by getting reduced row echelon form of the

corresponding matrix (by hand and on the graphing calculator).

• Solve a system of linear equations using the Gauss-Jordan Method.

• Add, subtract, and multiply matrices.

• Find the inverse (if it exists) of a given matrix (by hand and on the graphing calculator).

• Determine whether two given matrices are inverses of each other.

• Solve systems of linear equations using the Matrix Inverse Method.

• Use the Leontief model to solve problems involving an economy.

Linear Programming

• Graph linear inequalities.

• Set up a model for a linear programming problem.

• Solve linear programming problems, including applications, in two variables graphically.

• Solve linear programming problems, including applications, using the Simplex method (by hand

and on the graphing calculator).

• Solve linear programming problems in minimization using duality (by hand and on the graphing

calculator).

• (Optional) Solve linear programming problems with mixed constraints.

Finance

• Review geometric sequence and the sum of a geometric sequence.

• Solve problems involving simple interest.

• Solve problems involving compound interest.

• Compute effective rate of interest.

• Solve problems involving the future value of an ordinary annuity and sinking funds.

• Solve problems involving the present value of an ordinary annuity.

• Create an amortization schedule.

Logic

• Define the compound statements “conjunction,” “disjunction,” and “negation” and recognize the

symbols used for the compound statements.

• Construct truth tables for compound statements.

• Determine whether statements are equivalent using truth tables.

• Know the laws of logic in symbolic form including DeMorgan’s Laws. Prove them using a truth

table.

• Define a conditional statement and give the truth table.

• Define the converse, contrapositive, and inverse of a conditional statement and give the truth

tables.

• Determine whether a compound proposition is a tautology.

• Determine whether arguments are valid using a truth table.

• Give common valid argument and invalid argument forms. Prove them using a truth table.

• (Optional) Analyze arguments with quantifiers.