# Finite Mathematics

## Course Description

**MATH 160 - Finite Mathematics**

Hours: 4 lecture - 0 lab - 4 credit

Mathematics 160, Finite Mathematics, is an introductory level course covering
mathematical ideas

needed by students of business management, social science, or biology. The
topics include sets and

counting, functions, introduction to probability and statistics, interest and
annuities, matrix theory, linear

systems, and linear programming.

Applicable toward graduation where program structure permits:

• Certificate or Degree - All Certificates, A.A.S.,
A.L.S., A.A., A.S.

• Group Requirement - Mathematics

• Area of Concentration - Mathematics

## Illinois Articulation Initiative (IAI)

The mathematics component of general education focuses on
quantitative reasoning to provide a base

for developing a quantitatively literate college graduate. Every college
graduate should be able to apply

simple mathematical methods to the solution of real-world problems. A
quantitatively literate college

graduate should be able to:

• interpret mathematical models such as formulas,
graphs, tables, and schematics, and draw inferences from them;

• represent mathematical information symbolically, visually, numerically,
and verbally;

• use arithmetic, algebraic, geometric, and statistical methods to solve
problems;

• estimate and check answers to mathematical problems in order to
determine reasonableness, identify alternatives, and select optimal results; and

• recognize the limitations of mathematical and statistical models.

Courses accepted in fulfilling the general education
mathematics requirement emphasize the

development of the student's capability to do mathematical reasoning and problem
solving in settings the

college graduate may encounter in the future. General education mathematics
courses should not lead

simply to an appreciation of the place of mathematics in society, nor should
they be merely mechanical

or computational in character.

To accomplish this purpose, students should have at least
one course at the lower-division level that

emphasizes the foundations of quantitative literacy and, preferably, a second
course that solidifies and

deepens this foundation to enable the student to internalize these habits of
thought.

Math 160, Finite Mathematics, satisfies the Illinois
Articulation Initiative Definition of a

General Education Mathematics Course. It corresponds to M1 906, Finite
Mathematics.

## General Course Objectives

While learning Finite Mathematics is certainly one of the
goals of this course, it is not the only

objective. Upon completion of this course, the student should be able to ...

• demonstrate comprehension and understanding in the
topics of the course through symbolic, numeric, and graphic methods

• demonstrate the use of proper mathematical notation

• use technology when appropriate and know the limitations of technology

• work with others towards the completion of a common goal

• use deductive reasoning and critical thinking to solve problems

## Specific Course Objectives

Upon completion of this course, the student should be able to ...

• solve finance problems involving compound
interest, future value annuities, and present value annuities

• apply ordinary annuities to plan retirement of purchase a house

• solve a system of linear equations having an unique solution, no
solution, and many solutions

• transform between a system of linear equations and an augmented matrix

• read the solution to a system of linear equations from an augmented
matrix

• use matrices to solve applied problems such as network flow, incidence
matrices, and the Leontief input-output model

• graph a system of linear inequalities in two variables

• solve a linear programming problem with two decision variables
graphically

• solve a linear programming problem using a table

• explain the simplex method

• apply the simplex method to solve a standard maximization problem

• apply the dual method to solve a standard minimization problem

• solve non-standard minimization and maximization problems

• understand basic logic

• find the union, intersection, complement of sets

• apply basic counting principles to determine the number of ways an event
can occur

• use permutations and combinations

• find probabilities of simple and compound events

• find conditional probabilities including Bayesian probabilities

• find the expected value of a probability distribution

• apply the Bayesian (expected value), maximax, maximin, and minimax
criteria to decision making

• solve regular Markov chain problems to find the long term probabilities
of being in any state

• solve absorbing Markov chain problems to find the expected number of
states encountered before exiting the system and find the long term
probabilities of ending in any absorbing state

• solve strictly determined two player, zero sum games

• solve 2×2 non-strictly determined games

• apply the simplex procedure to solve larger games

A detailed topical outline of the content covered in this course is at the end of this syllabus.

## Type of Instruction

Lecture, discussion, problem solving, and group work will
be used. Students should come to class with

a prepared list of questions.

## Method of Evaluation

Could include any of the following: problem solving exams,
objective exams, essays, written papers,

oral presentations, group and individual projects, quizzes, and homework.

## Grading Policy

Letter grades will be assigned to final adjusted scores as follows:

• A: 90 - 100%

• B: 80 - 89%

• C: 70 - 79%

• D: 60 - 69%

• F: below 60%

Consideration may be given to such qualities as
attendance, class participation, attentiveness, attitude in

class, and cooperation to produce the maximum learning situation for everyone.

The instructor will give you a grade sheet so that you can
record your scores and keep track of your

progress in the course. There is also a web page that you can use to check your
grades throughout the

semester. If you are concerned about your grades, see the instructor.

Assignments are due at the beginning of the class period
on the date they are due. The instructor may be

gracious and allow you to turn them in later that day without counting them
late, but do not count on his

graciousness. Late assignments lose 20% of their value per class period. The
instructor reserves the

right to apply this rule to missed exams as well as regular assignments.

## Attendance Policy

Regular attendance is essential for satisfactory
completion of this course. Mathematics is a cumulative

subject and each day builds on the previous day's material. If you have
excessive absences, you cannot

develop to your fullest potential in the course.

Students who, because of excessive absences, cannot
complete the course successfully, are required to

be administratively dropped from the class at midterm. If a student stops
attending after midterm, it is

the student's responsibility to withdraw to avoid an "F". Do not stop attending
and assume that you will

be withdrawn from the class by the instructor.

Although dropping students for non-attendance at midterm
is required, students whose attendance is

occasional or sporadic may be dropped from the class at any point during the
semester at the instructor's

discretion. The safest way to make sure you're not dropped for non-attendance is
to continue to attend

classes.

The student is responsible for all assignments, changes in
assignments, or other verbal information given

in the class, whether in attendance or not.

If a student must miss class, a call to the instructor (RCC's
phone system has an answering system)

should be made or an email message sent. When a test is going to be missed, the
student should contact

the instructor ahead of time if at all possible. Under certain circumstances,
arrangements can be made to

take the test before the scheduled time. If circumstances arise where
arrangements cannot be made

ahead of time, the instructor should be notified and a brief explanation of why
given by either voice or

email. This notification must occur before the next class period begins. At the
instructor's discretion,

the score on the final exam may be substituted for the missed exam.

## Calculators

The TI-82 or TI-83 graphing calculator will be
incorporated into the course heavily. Use of this

calculator will allow the student to concentrate on the concepts being taught
instead of the mechanical

steps to solving the problems. It will allow the student to solve more problems
in less time, and more

difficult problems which would be too time consuming by hand. Calculators may be
used to do

homework. Calculators may be used on exams and/or quizzes in class unless
otherwise announced.

The instructor has written several programs for the TI-82
or TI-83 that will be used in this course.

These programs are also available for the TI-84, TI-85, and TI-86 calculators.
However, the programs

are not available for other Texas Instrument calculators or for any other brand
of graphing calculator. It

is expected that you will have a suitable calculator and bring it every day to
class.

## Additional Supplies

The student should have a red pen, ruler, graph paper,
stapler, and paper punch. The student is expected

to bring calculators and supplies as needed to class. The calculator should be
brought daily. There will

be a paper punch and stapler in the classroom.

## Additional Help

The student is encouraged to seek additional help when the
material is not comprehended. Mathematics

is a cumulative subject; therefore, getting behind is a very difficult situation
for the student. There are

several places where you can seek additional help in your classes.

### Instructor

I try to make myself as available to the students as I
can. My office hours are listed at the beginning of

this syllabus, but those are just the times I'm scheduled to be in my office.
Grab me and ask me

questions if you see me in the hallway. Ask questions before or after class. If
I'm in my office and it's

not my scheduled office hours, go ahead and stop in.

The instructor should be considered the authoritative
source for material related to this class. If a tutor or

other student says something that disagrees with the instructor, believe the
instructor.

### Study Groups

Probably the best thing you can do for outside help is to
form a study group with other students in your

class. Work with those students and hold them accountable. You will understand
things much better if

you explain it to someone else and study groups will also keep you focused,
involved, and current in the

course.

### Student Learning Center

The Student Learning Center is located in rooms S116,
S117, and S118. There is mathematics tutoring

available in room S116. The Student Learning Center and the tutoring is a
service that Richland

Community College offers you free of charge.

### Learning Accommodation Services

There are accommodations available for students who need
extended time on tests, note takers, readers,

adaptive computer equipment, braille, enlarged print, accessible seating, sign
language interpreters,

books on tape, taped classroom lectures, writers, or tutoring. If you need one
of these services, then you

should see Learning Accommodation Services in room C136. If you request an
accommodation, you

will be required to provide documentation that you need that accommodation.

Some of you will need additional time on tests. There is
no need to go to learning accommodation

services to request that. If you need additional time, just let me know and in
most cases, I'll allow you to

continue working past the allotted time. You may need to move to another room as
there may be

another class coming into your room. If you're unable to finish the test by
staying late, it may be

possible to start the test earlier to gain additional time. There may be
circumstances where extra time is

not allowed.

## Homework

Homework is crucial to your success in this course. There
is a correlation between doing your

homework and success in the course. Not only does the homework count towards
your grade, but it also

prepares you for the tests. Studies show that the average student will need to
spend two hours outside of

class for each hour in class. Do not expect to master the subject without doing
homework

## Academic Dishonesty

Each student is expected to be honest in his/her class
work or in the submission of information to the

College. Richland regards dishonesty in classroom and laboratories, on
assignments and examinations,

and the submission of false and misleading information to the College as a
serious offense.

A student who cheats, plagiarizes, or furnishes false,
misleading information to the College is subject to

disciplinary action up to and including failure of a class or
suspension/expulsion from the College.

## Non-Discrimination Policy

Richland Community College policy prohibits discrimination
on the basis of race, color, religion, sex,

marital or parental status, national origin or ancestry, age, mental or physical
disability (except where it

is a bonafide occupational qualification), sexual orientation, military status,
status as a disabled or

Vietnam-era veteran.

## Electronic Communication Devices

The Mathematics and Sciences Division prohibits the use of
cell phones, pagers, and other non-learning

electronic communication equipment within the classroom. All equipment must be
turned off to avoid

disturbances to the learning environment. If a student uses these devices during
an examination, quiz, or

any graded activity, the instructor reserves the right to issue no credit for
these assignments. The

instructor needs to approve any exceptions to this policy.

## Topical Outline:

Hours |
Topic |

7 | Finance• Simple interest • Compound interest • Future value annuities • Present value annuities |

9 | Systems of Linear Equations and Matrices• Review of solving systems of linear equations • Augmented matrices • Gauss-Jordan elimination • Equality, addition, subtraction, and multiplication of matrices • Inverses of matrices • Matrix equations and systems of equations • Leontief Input-Output analysis |

18 | Linear Programming• Systems of linear inequalities • Geometric approach to linear programming • Geometric approach to the Simplex method • Standard maximization problems using Simplex • Standard minimization problems using the Dual problem • Non-standard maximization and minimization problems |

6 | Logic, Sets, and Counting• Logic, • Sets • Basic counting principles • Permutations, combinations, and distinguishable permutations |

8 | Probability• Sample spaces, events, and probability • Joint frequency tables, Venn diagrams • Unions, intersections, complements, odds, mutually exclusive events • Conditional probability, intersections, independence • Bayesian type problems • Random variables, probability distributions, expected values • Decision theory: expected value, maximax, maximin, minimax criteria |

6 | Markov Chains• Properties of Markov chains • Regular Markov chains • Absorbing Markov chains |

8 | Two-player, Zero-sum Games• Strictly determined games • Mixed strategy games • Geometric approach to 2×2 games using linear programming • Simplex approach to 2×2 games using linear programming • Extension of simplex method to m×n games |