THE COLLEGE OF THE BAHAMAS
Course Outline
Title: Finite Mathematics
Abbreviation and Number: MATH163
AB Paper No.: 15-75
School: Mathematics, Physics & Technology
Department: Mathematics
Credits: 3
Course Sequence: ( ) Fall
( ) Spring
( x ) Fall and Spring
( 3 ) Lecture
( ) Seminar
( ) Laboratory
( ) Studio
(
Hours Per Week:
( ) Other (Specify)
Pre-requisite(s): MATH140 or BGCSE Mathematics grade “A” or “B” or permission of Chair/Instructor
Co-requisite(s): None
) Kitchen
COURSE DESCRIPTION
Designed for non-science majors, this course is a survey of mathematical techniques used to analyse data and solve
problems. With the aid of technology, students explore linear functions and models, systems of equations and
inequalities, matrices, linear programming (LP), sets, Venn diagrams and counting, basic probability and statistics.
SPECIFIC OBJECTIVES
Upon successful completion of this course, students will be able to
1) evaluate functions defined numerically, algebraically, and graphically;
2) apply linear models;
3) determine ‘best-fit’ models;
4) solve systems of linear equations graphically, algebraically, and by using matrices;
5) perform matrix operations to solve problems;
6) solve linear programming problems graphically;
7) use sets and Venn diagrams to solve survey problems;
8) apply counting principles and formulas to determining the number of ways the elements of a set can be
arranged or selected;
9) apply basic probability theory to obtain event probabilities;
10) apply statistical methods to determine measures of central tendency and measures of dispersion; and
11) use a graphing calculator to explore and evaluate functions, solve equations and systems of equations,
determine regression lines, operate on matrices, compute counting formulae, probabilities, and sample
statistics.
COURSE CONTENT
I.
Functions and Linear Models
A. Functions
i. Terminology and notation, independent and dependent variables, domain and range
ii. Numerically specified
iii. Algebraically defined
iv. Graphically specified
v. Piecewise-defined
B. Linear functions
i. Algebraically, numerically and graphically defined
ii. Slopes of lines
iii. Slope and y-intercept from a table of values, a linear graph and equation
iv. Slope-intercept equation of a line
v. Graphing lines
The College of The Bahamas
AB Paper No.: 15-75
Course Outline
Title: Finite Mathematics
Abbreviation and Number: MATH163
C. Linear models
i. Cost, revenue, and profit functions; break-even point
ii. Demand and supply functions; equilibrium point
iii. Change-over-time functions
D. Linear regression
i. Sum-of-squares error (SSE) to compare linear models
ii. Scatter plot and regression line
II.
Systems of Linear Equations and Matrices
A. Graphical solution
B. Algebraic solution methods
i. Elimination
ii. Substitution
C. Augmented matrix solution
Elementary row operations and row reduction, reduced row echelon form
D. Matrix operations and applications
i. Terminology, notation, types of matrices
ii. Addition, subtraction, transposition, scalar multiplication
iii. Matrix multiplication
iv. Matrix inversion
v. Solution of a system of linear equations using the inverse of the coefficient matrix
III.
Linear Programming
A. Graphical solution of systems of linear inequalities in two variables
B. The Fundamental Theorem
C. Construction of LP problems
i. Objective function
ii. Linear constraints
D. Graphical solutions of LP problems
IV.
Sets and Counting
A. Sets and operations
i. Set notation and types of sets
ii. Union, intersection, complement, Cartesian product
iii. Venn diagrams to represent set relations and operations
iv. Survey problems
B. Cardinality
i. Cardinal number of a set
ii. Union, intersection, complement, Cartesian product
C. Basic Counting Principles
i. Addition
ii. Multiplication
D. Permutations and combinations
i. n items arranged r at a time
ii. n items selected r at a time
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The College of The Bahamas
AB Paper No.: 15-75
Course Outline
Title: Finite Mathematics
Abbreviation and Number: MATH163
V.
Probability
A. Basic concepts
i. Experiments, outcomes, sample spaces, events
ii. Complement, union, intersection of events and mutually exclusive events
B. Empirical and Theoretical Probability
i. Experimental
a. Relative frequency or estimated probability
b. Properties
ii. Theoretical
a. Equally likely outcomes
b. Properties
C. Compound Events
i. Union, intersection, complement of events and mutually exclusive events
ii. Conditional probability
iii. Independent events
iv. Tree diagrams
a. Multiplication rule
b. Addition rule
VI.
Statistics
A. Frequency distributions
B. Measures of central tendency
i. Mean
ii. Median
iii. Mode
iv. Range
v. Percentile
vi. Quartiles and interquartile range
C. Measures of dispersion
i. Variance
ii. Standard deviation
ASSESSMENT
Assignments……………………………………… 15%
Quizzes…………………………………………… 15%
In-class Tests…………………………………….. 30%
Final Examination……………………………….. 40%
Total……………………….………………………100%
REQUIRED RESOURCE
Each student will need a scientific graphing, calculator for use in class and in examinations.
Lectures will be geared towards the use of the TI-83/84 calculator.
REQUIRED TEXT
Waner, S., & Costenoble, S. (2011). Finite mathematics and applied calculus (6th ed.). Pacific Grove, CA:
Brooks/Cole Publishers.
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The College of The Bahamas
AB Paper No.: 15-75
Course Outline
Title: Finite Mathematics
Abbreviation and Number: MATH163
SUPPLEMENTARY READINGS/MATERIALS
Lial, M., Greenwell, R., & Ritchey, N. (2012). Finite mathematics and calculus with applications (10th ed.). Upper
Saddle River, NJ. Pearson Inc.
Sullivan, M. (2011). Finite mathematics – An applied approach (11th ed.). Hoboken, NJ, John Wiley & Sons, Inc.
JOURNALS
International Journal of Mathematical Education in Science & Technology
Mathematical Spectrum
Mathematics Teacher
Teaching Mathematics & Its Applications.
WEBSITES
www.coolmath.com (Coolmath)
www.purplemath.com (Purplemath)
www.zweigmedia.com/RealWorld/index.html (Text resource website)
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