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.
