NORTHWEST-SHOALS COMMUNITY COLLEGE

GENERAL COURSE SYLLABUS

 

 

TITLE OF COURSE:  Finite Mathematics (MTH 110)

 

DIVISION:  Mathematics, Science, and Technology

 

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 skill. The course includes sets, counting, permutations, combinations, basic probability (including Bayes’ 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.

 

HOURS:                     Credit:  3                                  Contact:  3

                        Lecture:  3                                Clinical:  0

                        Lab:  0     

 

PREREQUISITE(S):  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 (S if taken as pass/fail) Intermediate College Algebra.

 

COREQUISITE(S): None

 

REQUIRED TEXTBOOK(S):  Finite Mathematics, 9th edition, Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey, Addison-Wesley Educational Publishers Inc., 2008. 

 

SUPPLIES:   A graphing calculator is highly recommended.

 

GENERAL EDUCATION OBJECTIVE:   All associate degree graduates should be able to use the mathematical concepts, notations, and manipulations needed in their field of study or occupation. (3)

 

COURSE OBJECTIVE(S):  Upon successfully completing Finite Mathematics, the student should be able to:

 

1.         Find the slope of a line, write the equation of a line in slope-intercept form, and construct and solve linear mathematical models for real life situations.

 

2.         Perform arithmetic operations on matrices, find the inverse of a matrix, and solve systems of equations using matrices.

 

3.         Define concept of sets and draw Venn diagrams to illustrate the union, intersection, and complement of sets.

 

4.         Use permutations and combinations to solve problems.

 

5.         Find basic probability and the odds in favor of or the odds against an event and solve statistical problems using probability formulas, including Bayes’ Theorem.

 

6.         Calculate binomial probability and find the expected value of a probability distribution.

 

7.         Calculate statistical measures such as mean, standard deviation, and variance.

 

8.         Calculate the area under a normal curve, use the concept of area under the curve to solve problems that are normally distributed, and use the normal curve to approximate binomial probability.

 

9.         Identify regular and absorbing Markov chains and use them, along with transition matrices, to make long range predictions about probability.

 

10.      Understand strategies involved with decision (game) theory.

 

METHODS OF EVALUATION: 

 

  1. Course Grade Evaluation: (Minimum of 4 measurements)

A comprehensive final exam will be given and counted toward the student’s final average.  Make-up examinations, as such, will not generally be given. 

                        

  1. Evaluation of General Educational Objectives:  Student success on the General Educational Objective (3) is measured by student performance on each of the course objectives, which require use of mathematical concepts, notations, and manipulations.  Performance on each course objective will be evaluated using appropriate problems from the final exam.  Results will be tallied for each course objective.

 

  1. Use of Findings: Instructors will analyze data gathered from the assessment(s) for each course objective and changes will be made based on identified weaknesses.  The math department will meet once every two years to discuss findings and implement strategies to improve department and student performance.
     

   

OUTLINE OF COURSE TOPICS:

 

I.           Linear Functions

A.    Slope and Equations of a line

B.     Linear Functions and Applications.

C.     Linear Mathematical Models

II.                 Systems of Linear Equations and Matrices

A.       Solution of Linear Systems by the Echelon Method

B.        Solution of Linear Systems by the Gauss-Jordon Method

C.        Matrices

1.         Addition and Subtraction

2.         Multiplication

3.         Inverses

4.         Input-Output models  (optional)

 III.       Linear Programming:  The Graphical Method   (optional)

A.       Graphing Linear Inequalities

B.        Solving Linear Programming Problems Graphically 

C.        Applications of Linear Programming

IV.     Linear Programming: The Simplex Method   (optional)

A.       Slack Variables and the Pivot

B.        Maximization Problems

C.        Minimization Problems; Duality

D.       Nonstandard Problems

V.       Logic  (optional)

A.        Statements and quantifiers

B.        Truth Tables and Equivalent Statements

C.        The Conditional and Circuits

D.     Analyzing Arguments with Euler Diagrams and Truth Tables

VI.      Sets and Probability

A.       Sets 

B.        Applications of Venn Diagrams

C.        Introduction to Probability

D.       Basic Concepts of Probability

E.        Conditional Probability and Independent Events

F.         Bayes’ Theorem

VII.      Counting Principles; Further Probability Topic

A.       Multiplication Principle; Permutations

B.        Combinations

C.        Probability Applications of Counting Principles

D.       Binomial Probability

E.        Probability Distribution; Expected Value

VIII.        Statistics

A.       Frequency Distribution; Measures of Central Tendency

B.        Measures of Variation

C.        Normal Distribution

D.       Normal Approximation to the Binomial Distribution.

IX.        Markov Chains

A.       Basic Properties of Markov Chains

B.        Regular Markov Chains

C.        Absorbing Markov Chains

X.      Game Theory 

A.    Strictly Determined Games

B.    Mixed Strategies

             C.    Game Theory and Linear Programming (optional)

 

 

AMERICANS WITH DISABILITIES ACT POLICY: It is the policy of Northwest-Shoals Community College to comply with the Americans with Disabilities (ADA) Act. Any student covered under this act needing and desiring reasonable accommodations for this class should notify Linda Waide at 331-5321. See NWSCC catalog for additional details.

 

ATTENDANCE POLICY: Because class attendance is considered to be essential to the accomplishment of course objectives, excessive absences are discouraged. At no time should a student miss more than 20% of the class meetings for a course. These absences also include any absences accrued during late registration. Failure to adhere to the 20% policy may result in a failing grade based on academic performance. Students should discuss with the instructor what is considered “excessive” for a particular course. Any variation of this policy must be approved through the Chief Instructional Officer. A student who is absent due to required participation in a school activity must be allowed to make up work, according to guidelines issued by individual instructors.

 

WITHDRAWAL POLICY:  A student who is unable to complete a course is expected to withdraw from that course by the end of 60% of class meetings.  A student who withdraws by the date published in the schedule will receive a grade of “W” for the course.  This withdrawal is done only by student request.  The grade of “W” is allowed regardless of the student’s grades to the point of withdrawal. 

 

After the designated date of class withdrawal, the approval of the Chief Instructional Officer is required prior to allowing a student to withdraw. The determination of “WP” (withdrawal passing) or “WF” (withdrawal failing) will be made by the instructor for the course and is based on the student’s grades to the point of withdrawal.