# MATH 110 Finite Mathematics

## I. MTH 110 Finite Mathematics - 3 Semester Hours

Core Area III, Code A

## II. Course Description

This course is intended to give an overview of topics in finite mathematics
together with

their applications, and is taken primarily by students who are not majoring in
science,

engineering, commerce, or mathematics (i.e. students who are not required to
take

Calculus). This course will draw on and significantly enhance the student’ s
arithmetic

and algebraic skills. The course includes sets, counting, permutations,
combinations,

basic probability (including Baye’s Theorem) and introduction to statistics
(including

work with Binomial Distributions and Normal Distributions), matrices and their

applications to Markov chains and decision theory. Additional topics may include

symbolic logic , linear models , linear programming, the simplex method and
applications.

## III. Prerequisite

All core mathematics courses in Alabama must have as a minimum prerequisite
high

school Algebra I, Geometry, and Algebra II with an appropriate mathematics
placement

score. An alternative to this is that the student should successfully pass with
a C or

higher in Intermediate College Algebra.

## IV. Textbook

Finite Mathematics, For the Managerial, Life, and Social Sciences, Tan 8^{th} Ed.
Thomson

Brooks/Cole, 2006.

## V. Course Objectives

The objective of this course is to provide the
non-calculus mathematics needed for

students in many disciplines. This course shows through applications the
relevance of

mathematics to both real life and future courses in many disciplines. It also
provides a

general mathematics background for students who need a terminal core mathematics

course. The student will develop an understanding of the concepts, develop
competent

skills, and demonstrate applications in the following areas.

1. Analytic interpretation of linear systems, matrix algebra, and set theory.

2. Analytic interpretation of measurements of central tendency, probability, and

statistics.

## VI. Course Outline of Topics

A. This course shall include the following topics as a
minimum.

1. Applications of linear functions

2. Equations of straight lines

3. Two lines: relating the geometry to the equations

4. Systems of linear equations

5. Linear systems having one or no solutions

6. Linear systems having many solutions

7. Matrix algebra

8. Matrix multiplication and applications

9. The inverse of a matrix

10. Counting techniques

11. Sets

12. Application of Venn diagrams

13. The multiplication principle

14. Permutations

15. Combinations

16. Basic concepts of probability

17. Outcomes with unequal probability; odds

18. Discrete random variables and expected value

19. Additional topics in probability

20. Conditional probability

21. Multiplication rules for probability ; independent events

22. Bayes’ Theorem

23. Statistics

24. Measures of central tendency

25. Measuring the dispersion of data

26. Continuous random variables and the normal distribution

27. The normal approximation to the binomial distribution

28. Markov chains

29. Regular Markov chains

30. Absorbing Markov chains

B. Optimal topics may include the following.

1. Linear modeling

2. Regression and correlation

3. Linear programming

4. Linear inequalities in two variables

5. Solving linear programming problems graphically

6. Slack variables and pivoting

7. The simplex algorithm

## VII. Evaluation and Assessment

Evaluation and assessment techniques may include any or
all of the following.

Exams

Projects

Homework

Computer assignments

Participation

Grades will be given based upon A = 90 – 100%, B = 80 – 89%, C = 70 – 79%, D =
60 –

69%, and F = below 60%.

## VIII. Class Activities

A. Lecture

B. Recitation

C. Discussion

D. Individual instruction

E. Testing

## IX. GENERAL COURSE COMPETENCIES

A. The student will acquire knowledge of mathematical
terminology.

B. The student will be able to apply knowledge of algebra.

C. The student will acquire knowledge of sets and counting.

D. The student will acquire knowledge of probability and statistics.

## X. COURSE OBJECTIVES STATED IN PERFORMANCE TERMS

A. The student will demonstrate knowledge of mathematical
terminology as

measured by his/her ability to

1. recall the meaning of the concepts of and concepts related to the following

in order to work problems requiring a knowledge of these terms:

a. Bayes' Theorem | h. probability |

b. Cartesian coordinate system | i. statistics |

c. linear function | j. binomial distribution |

d. matrices and matrix operations | k. normal distribution |

e. sets and set operations | l. measures of dispersion |

f. permutation | m. measures of central tendency |

g. combination |

2. state whether a line has a positive , negative, zero, or nonexistent slope.

B. The student will demonstrate knowledge of algebra by
his/her ability to

1. calculate:

a. the distance between two given points, stating and using the

appropriate formula

b. the slope of the line passing through two given points, stating and

using the appropriate formula.

2. express a linear equation in slope-intercept form.

3. graph linear functions.

4. perform matrix addition, subtraction , and multiplication.

5. determine the scalar product and the transpose of a matrix.

6. determine the inverse of a given matrix, if it exists.

7. use matrices to solve systems of linear equations.

8. use Markov chains for problem solving.

C. The student will demonstrate knowledge of sets and
counting by his/her ability to:

1. perform the union and intersection of given sets.

2. draw a tree diagram displaying possible outcomes of an event.

3. use the generalized multiplication principle.

4. classify a given problem as a permutation or a combination.

5. determine the number of permutations of an event.

6. determine the number of combinations of an event .

D. The student will demonstrate knowledge of probability
and statistics by

his/her ability to

1. determine the sample space for a given experiment.

2. find the probability distribution associated with a given set of data.

3. use the laws of probability to find the probability of a given event in an

experiment.

4. find the expected value of a random variable X from a given probability
distribution.

5. calculate the following measures of central tendency from a given set of
data:

a. mean

b. median

c. mode

6. calculate the following measures of dispersion of data from a given
probability distribution:

a. variance

b. standard deviation

7. use normal distributions to solve applied problems.

8. use binomial distributions to solve applied problems.

## XI. Attendance

Students are expected to attend all classes for which they
are registered. Students who are

unable to attend class regularly, regardless of the reason or circumstance,
should

withdraw from that class before poor attendance interferes with the student’s
ability to

achieve the objectives required in the course. Withdrawal from class can affect
eligibility

for federal financial aid.

## XII. Statement on Discrimination/Harassment

The College and the Alabama State Board of Education are
committed to providing both

employment and educational environments free of harassment or discrimination
related to

an individual’s race, color, gender, religion, national origin, age, or
disability. Such

harassment is a violation of State Board of Education policy. Any practice or
behavior

that constitutes harassment or discrimination will not be tolerated.

## XIII. Americans with Disabilities

The Rehabilitation Act of 1973 (Section 504) and the
Americans with Disabilities Act of

1990 state that qualified students with disabilities who meet the essential
functions and

academic requirements are entitled to reasonable accommodations. It is the
student’s

responsibility to provide appropriate disability documentation to the College.
The ADA

Accommodations office is located in FSC 300 (205-856-7731).

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