# FINITE MATHEMATICS FOR BUSINESS AND MANAGEMENT

**COURSE DESCRIPTION:**

While this course may be used to fulfill part of the six-hour general education

mathematics requirement for the A.S. degree at John A. Logan College , it is
designed

primarily for economics majors, business administration, and accounting majors.
Those

students will be required to take a calculus course to complete their
mathematics

sequences. This course will fulfill the mathematics requirement for the A.A.
degree.

Topics covered include functions and lines, linear systems , linear programming ,
the

Simplex Method, mathematics of finance, set theory, and probability. This course
is not

de signed for mathematics or science majors. The Texas Instruments TI-83 graphing

calculator or a graphing calculator approved by the instructor is required for
this course.

**PREREQUISITES:**

MAT 108 with a grade of “C” or higher or assessment

**COURSE OBJECTIVES:**

1. Construct cost, revenue, and profit functions and perform break-even
analysis.

2. Solve straight -line depreciation problems utilizing linear functions.

3. Calculate future value and present value for simple interest accounts,
compound

interest accounts, and annuities.

4. Calculate effective rate of interest for a compound interest account.

5. Calculate the point of equilibrium in supply and demand analysis.

6. Write the parametric form of an infinite solution to a system of linear
equations.

7. Solve a system of linear equations using matrices and elementary row

operations.

8. Apply matrix ope rations in performing tests for equality, addition,
subtraction,

scalar multiplication, and matrix multiplication.

9. Calculate the inverse of a square matrix.

10. Utilize inverse matrices to aid in solving for the sector production levels
that will

meet internal and external demands of a Leontief Input-Output model.

11. Calculate the feasible region and its corner points relating to a system of
linear

inequalities involving two variables .

12. Use the feasible region and its corner points to solve a two- variable linear

programming problem.

13. Apply the Simplex Method to solve a linear programming problem involving

standard and mixed constraints.

14. Utilize the Dual to solve a linear programming problem.

15. Apply set operations and use Venn diagrams to aid in performing tests for

equality, unions, intersections, complements, and subset analysis.

16. Count the number of elements in a set using Venn diagrams, the
inclusionexclusion

principle, the addition rule, the multiplication rule, tree diagrams,

permutations, and combinations.

17. Calculate regular and conditional probabilities using set counting
procedures,

mutual exclusion, independence, the complement rule, the union rule, the

multiplication rule, and Bayes’ rule.

**COURSE OUTLINE:**

Topics to be covered in this course include:

I. FUNCTIONS AND LINES

A. Functions

B. Graphs and Lines

C. Mathematical Models and Applications of Linear Functions

II. MATHEMATICS OF FINANCE

A. Simple Interest

B. Compound Interest

C. Annuities and Sinking Funds

D. Present Value of an Annuity and Amortization

III. LINEAR SYSTEMS

A. Systems of Two Equations

B. Systems with Three Variables: An Introduction to a Matrix Representation of

a Linear System of Equations

C. Gauss-Jordan Method for General Systems of Equations

D. Matrix Operations

E. Multiplication of Matrices

F. The Inverse of a Matrix

G. Leontief Input-Output Model in Economics

IV. LINEAR PROGRAMMING

A. Linear Inequalities in Two Variables

B. Solutions of Systems of Inequalities: A Geometric Picture

C. Linear Programming: A Geometric Approach

D. Applications

V. LINEAR PROGRAMMING: THE SIMPLEX METHOD

A. Setting Up the Simplex Method

B. The Simplex Method

C. The Standard Minimum Problem: Duality

D. Mixed Constraints

E. Multiple Solutions, Unbounded Solutions, and No Solutions

VI. SETS AND COUNTING

A. Sets

B. Counting Elements in a Subset Using a Venn Diagram

C. Basic Counting Principles

D. Permutations

E. Combinations

F. A Mixture of Counting Problems

VII. PROBABILITY

A. Introduction to Probability

B. Equally Likely Events

C. Compound Events: Union, Intersection, and Complement

D. Conditional Probability

E. Independent Events

F. Bayes’ Rule

**COURSE REQUIREMENTS:**

Homework. Homework will be assigned at every class session. The student should

realize that, as a general rule of thumb , a minimum of two hours of study
outside of

class is required for every one hour of class time. This course will require a
minimum of

twelve to twenty-two hours per week of outside class work.

Attendance. Attendance to this class is both expected and required. John A.
Logan

College’s attendance policy will be enforced:

A. Students are expected to attend all scheduled class periods for the courses
in

which they are enrolled unless they are participating in a scheduled, supervised

college trip or function. There are no excused absences or minimum number of

class “cuts.” All absences must be made up in a manner acceptable to the

instructor.

B. A student who is absent from class for three consecutive meetings or who is

excessively absent as defined by the instructor (more than 5 absences), without

prior approval, may be required by the instructor to meet with the appropriate

administrator before being readmitted to the class. Students who claim illness
as

a cause for excessive absences may be required to present a physician’s

statement before being readmitted to the class.

Required Materials. The textbook, along with the usual notebook, paper, pencils,
etc.

represent the required materials for the class. The utilization of the Texas
Instruments

TI-83 Graphing Calculator will be emphasized in classroom presentations as well
as on

homework assignments and tests. Hence, the student is required to use the TI-83
on

appropriate assignments and should be knowledgeable of its workings. The
functions

provided by** the Texas Instruments TI-83 Graphing Calculator** will be
utilized

throughout the course and **will be required for successful completion of
certain**

**homework assignments and tests.**

Student Success Center. Tutors may be obtained through the Student Success
Center.

Contact the staff in C219 if this service is desired. John A. Logan College will
make

reasonable accommodations for students with documented disabilities under
Section

504 of the Rehabilitation Act of 1973, and the Americans with Disabilities Act
of 1990.

Any student with a disability that may have some impact on work in this class,
who feels

she/he needs an accommodation, should make an appointment with the Coordinator
of

Services for Students with Disabilities on campus, Christy McBride, Room C219B,
Ext.

8516. Before services can be provided, this advisor must de termine eligibility
and

arrange appropriate academic adjustments. **It is the student’s responsibility
to
register in advance of a school term with this office and to turn in a schedule
each term to ensure that there is every opportunity for success in this class.**

English Writing Center/Tutoring: For assistance with writing assignments in any college

courses, students are encouraged to visit “The Write Place” in E109. English instructors

are available for one-on-one tutoring each semester during hours posted at the center.

Financial Aid. Students who receive financial assistance and completely with draw from

classes prior to 60% of the semester being completed (approximately 2-3 weeks after

midterm) could be responsible to return a portion of their Federal Pell Grant award.

Prior to withdrawing from courses, students should contact the Financial Aid Office.

**METHOD OF EVALUATION:**

Evaluation will be made on the basis of:

1. A maximum of five 100-point exams that will be administered periodically over

the course of the semester.

2. A 200-point comprehensive final exam.

The combined average of the tests and the final exam will determine the
student’s

overall course percentage grade.

No make-ups will be given on the tests. Students attending a required
school-sponsored

activity must make arrangements with the instructor to complete the exam

before attending the obligatory event. Any answers, which have been copied from

someone else, will result in a zero for all parties involved.

Grades are assigned according to the following scale:

**METHOD OF PRESENTATION:**

Most instruction will be of the lecture-discussion type. Homework will be
assigned

which, together with announced exams serve to amplify and clarify the classroom

discussions. Occasionally, topics will be assigned to be performed through
independent

study. Ample opportunity will be provided for the student to meet with the
instructor on

a one-to-one basis during office hours to clear up any difficulties that may
arise.

**TEXT:**

Finite Mathematics, Fifth Edition: by Rolf; Harcourt, Inc.; 2002.

**INSTRUCTOR: **

Scott Elliott

Office: E209G

Ext.: 8394

**DATE: **Summer, 2005

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