Download Major Topics

PROPOSAL - NEW COURSE
Name of course being
changed:
MATH-121 Finite Mathematics
New Course is MATH-141 College Algebra
SUBMISSION
COURSE
What change is being
proposed?
Please select your choice(s)
[by typing an X in the
box (es)].
X
x
x
x
x
x
Delete the course MATH-121
Change the course name to College Algebra
Change the course number to MATH-141
Change the course description
Change the pre-requisites or co-requisites
Change the course content substantially
Other: New course will be 3 credits and 4 contact hours
Explanation of proposed
change
Why is this change
needed?
Changing the sequence of math courses. Some of this material will
be blended with content from the old MATH-131
Content contains a blend of content from previous college algebra
and finite mathematics to focus on applied topics making the new
course a closer match to other colleges’ descriptions of college
algebra. Since more of the topics relate to the old college algebra
course we are maintaining that title.
What effect will this None
change have on other
courses, transfer patterns,
and/or programs?
Date of this proposal:
9/24/2009
Submitted by:
Guy Bunyard
Division(s):
Mathematics
APPROVAL
Electronic signature from
the division chair (s):
Comments from division
chair(s):
After reviewing the course outlines from many other Maryland
colleges, we found that a number of them have an applied college
algebra focus. Using a function approach allows us to increase the
use of technology in problem-solving and to add topics involving
matrices and linear programming that were previously taught in
Finite Mathematics. This revised version will better serve the needs
of students taking college algebra as a terminal course and for
business majors going on to Business Calculus.
When saving this file, please use the following naming format: Change in Course ENGL-999
Attach the original course outline and the revised course outline to this form. Include the words
“revised” and “old” on the appropriate outlines and highlight the changes made on the revised course
outline.
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OLD
COURSE OUTLINE
MATH-121
Finite Mathematics
3 Semester Hours
HOWARD COMMUNITY COLLEGE
Description
In this course students will learn the language of sets and be introduced to counting
theory, tree diagrams, probability, the binomial theorem, independence, Bayes’ theorem,
probability distributions, and random variables. Other topics include approximating data
by linear models, graphing and analysis of systems of inequalities, matrix algebra and
linear programming, and the mathematics of finance. Prerequisite: MATH 070 or
appropriate math placement score. (3 hours weekly)
Statement on General Education and Liberal Learning
A liberal education prepares students to lead ethical, productive, and creative lives and to understand how the
pursuit of lifelong learning and critical thinking fosters good citizenship. General education courses form the
core of a liberal education within the higher education curriculum and provide a coherent intellectual experience
for all students by introducing the fundamental concepts and methods of inquiry in the areas of mathematics, the
physical and natural sciences, the social sciences, the arts and the humanities, and composition. This course is
part of the general education core experience at Howard Community College.
Overall Course Objectives
Upon completion of this course, the student will have demonstrated the ability to:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
Find linear best-fit models.
Solve a linear system of equations.
Perform matrix operations and solve applications using matrices.
Solve linear programming problems.
Use the Simplex method to optimize linear functions in two or more variables
subject to linear constraints in two or more variables.
Calculate present value and future values for compound interest.
Calculate present and future values of an annuity.
Calculate amortizations.
Use set theory, the principles of counting and probability concepts to calculate
probabilities.
Use the binomial probability theorem.
Calculate and interpret expected values.
Major Topics
I. Linear functions
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A. Graphs
B. Applications
C. Linear regression
II. Systems on linear equations and matrices
A. Solutions of linear systems
B. Addition and subtraction of matrices
C. Multiplication of matrices
D. Matrix inverses
III. Linear programming
A. Graphing systems of linear inequalities
B. Linear programming
C. Graphical solution of linear programming problems
D. The Simplex method
IV. Mathematics of finance
A. Compound interest
B. Annuities
C. Amortization
V. Sets and counting
A. Sets and set operations
B. Multiplication principle
C. Permutations and Combinations
VI. Probability and statistics
A. Rules of Probability
B. Counting techniques
C. Conditional probability and independence
D. Bayes’ theorem
E. Probability Distributions
F. Measures of central tendency and variation.
Course Requirements
Grading procedures will be determined by the individual faculty member but will
include the following:
There will be several unit exams, a final exam and written assignments.
A graphing calculator such as the TI83+ is required.
Other Course Information
This course may be used as a mathematics core course or as a mathematics
elective. Check your transfer institution to guarantee transferability.
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OLD
COURSE OUTLINE
MATH-131
College Algebra
3 Semester Hours
HOWARD COMMUNITY COLLEGE
Description
In this course, students will further develop their algebraic skills. The concept of a function as a tool to model
the real world will play a central role. Polynomial, rational, exponential and logarithmic functions will be
studied, along with techniques for solving equations and inequalities, complex numbers, operations on functions
and inverse functions. A graphical approach will be utilized throughout, with an emphasis on solving
application problems. The use of a graphing calculator is required. ( TI – 83 or TI – 84 required)
Prerequisite: MATH 070 or appropriate score on math placement test.
Statement on General Education and Liberal Learning
A liberal education prepares students to lead ethical, productive, and creative lives and to understand how the
pursuit of lifelong learning and critical thinking fosters good citizenship. General education courses form the
core of a liberal education within the higher education curriculum and provide a coherent intellectual experience
for all students by introducing the fundamental concepts and methods of inquiry in the areas of mathematics, the
physical and natural sciences, the social sciences, the arts and the humanities, and composition. This course is
part of the general education core experience at Howard Community College.
Overall Course Objectives
Upon completion of this course, the student will be able to:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Use the basic properties and rules of the real number system to solve problems involving radical and
absolute value expressions.
Evaluate and graph functions, some of which are altered by shifts, reflections, and/or transformations.
Perform the basic operations or find the composite of two or more functions.
Find and graph the inverse of a function.
Solve absolute value and non-linear inequalities.
Apply classic theorems to find the zeros of polynomial equations and graph its corresponding function.
Operate with complex numbers in standard (rectangular) form.
Graph rational functions.
Use exponents and logarithms to solve equations and application problems.
Solve application problems.
Use a scientific programmable graphing calculator in solving problems.
Find models that best fit a set of data.
Major Topics
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I.
Graphs, Functions, and Models
A.
Functions, and Graphs
B.
Slope (Rate of Change)
C.
Curve Fitting, and Linear Regression
D.
Analysis of Functions
E.
Symmetry and Transformations
II.
Functions and Equations: Zeros and Solutions
A.
Complex Numbers
B.
Quadratic Like Functions
C.
Analyzing Graphs of Quadratic Functions
D.
Quadratic Regression
E.
Radical and Absolute Value Equations
F.
Solving Inequalities
Polynomial and Rational Functions
A.
Polynomial Functions and Modeling
B.
Polynomial Division; The Remainder and Factor Theorems
C.
Theorems about Zeros of Polynomial Functions
D.
Rational Functions
E.
Polynomial and Rational Inequalities
F.
Modeling with Polynomial Functions
III.
IV.
Exponential and Logarithmic Functions
A.
Composite and Inverse Functions
B.
Exponential Functions and Graphs
C.
Logarithmic Functions and Graphs
D.
Properties of Logarithmic Functions
E.
Solving Exponential and Logarithmic Equations
F.
Applications and Models: Growth and Decay
G.
Modeling with Exponential, Logarithmic and Logistic Functions.
Course Requirements
Grading procedures will be determined by the individual faculty member but will include several unit exams, a
comprehensive final exam and written assignments.
Required Text :
A Graphical Approach to Precalculus with Limits, a Unit Circle Approach.
4th ed. By Hornsby, Lial & Rockswold
Required Calculator : Programmable Graphing Calculator (TI-83 or TI-84 )
Other Course Information
This course may be used as a mathematics core course or as a mathematics elective. Check your transfer
institution to guarantee transferability.
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NEW
COURSE OUTLINE
MATH-141
College Algebra
3 Semester Hours
HOWARD COMMUNITY COLLEGE
Description
In this course students will learn the language of functions and be introduced to families of functions
and their applications. Topics include linear, quadratic, exponential, and logarithmic functions. Other
topics include solving systems of linear equations using matrices, matrix algebra and linear
programming. Emphasis will be placed on solving problems algebraically and with the technological
tools used in business and the social sciences. Prerequisite: MATH 070 or appropriate math
placement score. (4 hours weekly)
Statement on General Education and Liberal Learning
A liberal education prepares students to lead ethical, productive, and creative lives and to understand
how the pursuit of lifelong learning and critical thinking fosters good citizenship. General education
courses form the core of a liberal education within the higher education curriculum and provide a
coherent intellectual experience for all students by introducing the fundamental concepts and
methods of inquiry in the areas of mathematics, the physical and natural sciences, the social
sciences, the arts and the humanities, and composition. This course is part of the general education
core experience at Howard Community College.
Overall Course Objectives
Upon completion of this course, the student will have demonstrated the ability to:
1.
Identify the basic properties of a function.
2.
Perform basic operations and determine the composition of two or more functions.
3.
Determine and graph the inverse of a function.
4.
Model applications using the families of functions.
5.
Solve equations algebraically and graphically.
6.
Solve a linear system of equations using matrices.
7.
Perform matrix operations and solve applications using matrices.
8.
Solve linear programming problems using the graphing and/or simplex method.
9.
Solve applications related to real world issues including global awareness, sustainability
and financial literacy.
10.
Use appropriate software to solve and explain problem solutions clearly using correct
mathematical notation.
Major Topics
I.
Basic Function Theory
A.
Function Notation
B.
Domain and Range
C.
Operations on Functions
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II.
III.
IV.
D.
Composition/Decomposition of Functions
E.
Inverse Functions
Families of Functions
A.
Linear Functions
B.
Power/Rational Functions
C.
Polynomial Functions
D.
Exponential Functions
E.
Logarithmic Functions
F.
Modeling Real-World Applications
Systems on Linear Equations and Matrices
A.
Solving Linear Systems using the Echelon and Gauss-Jordan Methods
B.
Addition and Subtraction of Matrices
C.
Multiplication of Matrices
D.
Matrix Inverses
E.
Solving Linear Systems Using the Inverse Method
Linear programming
A.
Graphing Systems of Linear Inequalities
B.
Graphical Method of Solving Linear Programming Problems
C.
The Simplex Method
Course Requirements
Grading/Exams: Grading procedures will be determined by the individual faculty member within the
guidelines of the Mathematics Division and will include several unit exams, projects and a
comprehensive departmental final exam.
Technology requirements: Graphing calculator (TI-84 recommended) and required course software.
Other Course Information
This course may be used as a Mathematics core course or as an Arts and Science elective. Check with your
transfer institution concerning transferability for your program.
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