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# Course Outline for Finite Mathematics

Catalog description: An overview of topics in finite mathematics with applications. Topics
include systems of equations, matrices, linear programming, probability and statistics
.

(This course is intended primarily for students in non-scientific / non-technical majors. Rutgers
accepts this course as equivalent to their course for liberal arts majors.)

Prerequisite: MAT135 or MAT141 or appropriate College Level Math placement test score.

Corequisite: None

Required texts/other materials:
1. Tan, S.T., Finite Mathematics for the Managerial, Life, and Social Sciences, 8th ed., Pacific
Grove, CA: Brooks/Cole, 2006.
2. Scientific calculator

Last revised: N/A

Course coordinator: Prof. Paul Toppo

The general course outline consists of five units:

Unit I:

(12 hours) System of Equations and Matrices (2.1-2.7)
A. Solving Systems of Linear Equations
B. Underdetermined and overdetermined systems
C. Solving Systems of Linear Equations using technology
D. Arithmetic of matrices
E. Determinants
F. Inverse matrices
G. Row and column vectors
F. The Leontief Input-Output Model

The student will be able to:

1. Solve systems of linear equations using algebraic techniques.
2. Learn and apply the arithmetic of matrices.
3. Use matrix mechanics to solve systems.
4. Predict the nature, and analyze and interpret the solutions of systems of linear
equations.
5. Decide whether a system is overdetermined or underdetermined.
6. Apply systems of equations to “real-world” problems.
7. Use determinants to find inverses of matrices.
8. Apply the Leontief method of inputs and outputs to solve problems in economic.

Exercises from the text selected to reinforce and apply the above concepts to real-world
situations should be completed. Applications include, but are not limited to, topics in the
natural and social sciences.

A project exploring the Leontief economic model of inputs and outputs is provided in the day to day
syllabus.

Specific applications which facilitate student goals include:
▪ revenue from gasoline sales
▪ mixtures
▪ investments
▪ diet planning
▪ Inputs and outputs (Leontief Model)

Unit II:

(10 hours) Linear Programming (3.1-3.3 and 4.1-4.2)
A. Graphing Systems of Linear Inequalities in Two Variables
B. The feasible region
C. Linear Programming Problems
D. The Simplex Method

The student will be able to:

1. Define and determine corner points and feasible regions.
2. Graph feasible regions.
3. Optimize functions over feasible regions.
4. Define and determine the simplex tableau.
5. Use the simplex method to maximize functions.
6. Use the simplex method to minimize functions.
7. Solve “real-world applications.

Exercises from the text selected to reinforce and apply the above concepts to real-world
situations should be completed. Applications include, but are not limited to, finance,
agriculture, mining and advertising.

Specific applications which facilitate student goals include:

▪ shipping schedules and costs
▪ crop planning
▪ allocation of funds
▪ mining production

Unit III:

(11 hours) Counting Techniques (Chapter 6)
A. Basic Set theory
B. Set operations
C. Venn Diagrams
D. Fundamental theorem of counting
E. Permutations
F. Combinations
G. Applications

The student will be able to:

1. Define sets, set operations, and the cardinality of a set.
2. Use set theory to solve mathematical and real-world problems.
3. Define and apply counting arguments.
4. Define and apply the multiplication principle.
5. Define permutation.
6. Define combination and distinguish it from a permutation.
7. Apply permutations and combinations to solve counting problems.

Exercises from the text selected to reinforce and apply the above concepts to real-world
situations should be completed. Applications include, but are not limited to topics such as
games of chance, management, voting and sports.

Specific applications which facilitate student goals include:

▪ surveys
▪ combination locks
▪ investment options
▪ committee selection
▪ blood typing
▪ quality control

Unit IV:

(12 hours) Probability and Statistics (Chapters 7 and 8)
A. Basic concepts
C. Multiplication rule
D. Independent events
E. Conditional probability
F. Bayes’ theorem
G. Binomial probability
H. Applications
I. Samples and populations
J. Organizing data
K. Measures of central tendency
L. Measures of dispersion
M. Continuous random variables and the Normal Distribution
N. The Normal approximation to the Binomial Distribution

The student will be able to:

1. Define and analyze sample spaces and events in the context of set theory.
2. Define probability and enunciate the rules of probability.
3. Use counting techniques to solve problems in probability.
4. Define conditional probabilities.
5. Define independence of events.
6. Interpret conditional probabilities using probability trees.
7. Apply the ideas of events, independence and conditional probabilities to solve
mathematical problems.
8. Learn and use Bayes’ Theorem.
9. Apply probabilistic techniques to “real-world” situations.
10. Define and interpret distributions and random variables.
11. Interpret data geometrically using a histogram.
12. Determine and interpret the significance of the expected value of a random variable.
13. Define and interpret expected value.
14. Discuss in more detail the significance of distributions.
15. Define, interpret and analyze the binomial and normal distributions.
16. Apply statistical methods to “real-world” situations.

Exercises from the text selected to reinforce and apply the above concepts to real-world
situations should be completed. Applications include, but are not limited to topics in the
natural and social sciences.
A project on the “birthday problem” is included in the day to day syllabus.

Specific applications which facilitate student goals include:

▪ investment analysis
▪ odds in games of chance
▪ sales, premiums and profits
▪ wage, age, grade and weight distributions

Evaluation Of Student Progress:
The following suggested grading scheme may be modified, at the discretion of the instructor.

Tests:

 Unit I 10% Units II and III 10% Unit IV 10% Collected Projects (3) 25% In-class Quizzes, group work, etc. 15% Final Exam 30%