Course Description
This course is a comprehensive study of
algebraic concepts. The course will emphasize linear,
quadratic, polynomial,
rational, exponential and logarithmic equations . In particular we will
look at
these functions from a graphical, analytical, and modeling approach. We will
also have
an introduction to summation notation, sequences, and series.
Prerequisites
Grade C or better in MATH 106, or a score of 21 or above on the
math portion of the ACT (or if
the ACT was taken before September 1989, a score
of 20 on the "old form"), or a passing grade
on the Columbia College math
placement exam.
I. Course Overview
Week 1: Rational exponents, Equations, Inequalities, Mathematical Models
Week 2:
Linear, Quadratic and other equations, Inequalities, Lines & Slope
Week 3:
Linear, rational, and quadratic inequalities/Functions
Week 4: Polynomial and
Rational Functions
Week 5: Zeros of polynomial functions, The Fundamental
Theorem of Algebra
Week 6: Exponential and Logarithmic Functions
Week 7: Systems
of Equations, Summation Notation
Week 8: Final Exam
II. Course Objectives
• To
communicate mathematically in both written and verbal forms
• To reason with
symbolic and graphical representations
• To use mathematics to solve real-world
problems
• To use appropriate technology, such as graphing calculators and
computers, to enhance
their mathematical understanding
• To understand intuitively
and formally the mathematical idea of a function and its real
world applications
Measurable Learning Outcomes
• Simplify exponential and
radical expressions and solve equations containing such
expressions
• Solve
linear, quadratic and polynomial equations and inequalities in both real number
and
complex number domains
• Add , subtract, multiply, and divide complex numbers
• Find and graph equations of lines in both point- slope and slope -intercept form
• Find equations for circles and graph circles in the Cartesian plane
• Determine if
a relation is a function
• Identify the domain and range of polynomial, radical,
rational, exponential, logarithmic,
and piecewise-defined functions, and
evaluate their values
• Graph polynomial, radical, rational, exponential,
logarithmic, and piecewise-defined functions
• Use the graph of a function to
identify characteristics of the function such as specific
values and symmetry
• Recognize graphs of common functions and graph transformations of these common
functions
• Combine functions arithmetically and through composition and identify
the domain of
the resulting functions
• Demonstrate an understanding of the
fundamental concepts associated with inverse
functions including the definition
of one-to-one functions and the graphical interpretation
of inverses
• Identify
characteristics of the graphs of polynomial functions including end behavior and
degree
• Apply the Fundamental Theorem of Algebra and related results to obtain a
complete
factorization of a polynomial function
• Identify vertical, horizontal,
and slant asymptotes of rational functions
• Simplify exponential and logarithmic
expressions and solve exponential and logarithmic
equations
• Solve systems of
linear equations in two and three variables and nonlinear systems in two
variables
• Find terms of sequences and identify arithmetic and geometric
sequences
• Use summation notation and compute the sum of sequences including
arithmetic and
geometric sequences
• Solve real-world problems using a variety of
linear, polynomial, rational, exponential,
and logarithmic models
Topical Outline
• Radicals, integer and rational exponents (Review)
• Linear and
Quadratic equations and inequalities
• The Cartesian Plane and Graphs Functions
and their
• Graphs Polynomial and rational functions and graphs
• Exponential and
Logarithmic functions and graphs
• Systems of equations
• Sequences and series
III. Course Policies
There will be no discrimination on the basis of sex, race, color, national
origin, sexual
orientation, religion, ideology, political affiliation, veteran
status, age, physical handicap, or
marital status. Students with documented
disabilities who may need academic services for this
course are required to
register with the Coordinator for Disability Services. Until the student
has
been cleared through the disability services office, accommodations do not have
to be
granted. It is vital if you are a student who has a documented disability
to read the entire
syllabus before signing up for the course. The structure or
the content of the course can make an
accommodation not feasible. The policies
and related syllabus matters remain subject to change
in the event of
extenuating circumstances.
Student Conduct
The instructor reserves the right to
manage a positive learning environment and thus will not
tolerate inappropriate
conduct in the course. All Columbia College students, whether enrolled in
a
land-based or online course, are responsible for behaving in a manner consistent
with
Columbia College's Code of Student Conduct and Ethics Code for Computer
Users. Students
violating these codes will be referred to the Campus Life Office
for possible disciplinary action.
The Code for Student Conduct and the Ethics
Code for Computer Users can be found in the
Columbia College Student Handbook, a
copy of which can be obtained by calling the Campus
Life office at (573)
875-7425.
Online Participation
Participation online is expected to be continuous
throughout the course. Failure to complete
assignments by the date due, or
timely participation in online discussions may result in the
student failing the
course. Emergencies should be communicated and documented to the
instructor as
soon as possible. Students are expected to read the assigned texts each week,
login
to the course discussion area at least 4 times per week, and post messages
as required in the
Course Schedule section of this syllabus. Active
participation in the course will guide students
in preparing assignments and
exams. The instructor will facilitate online discussion in the
Discussion room
by responding to posted messages.
Class Week and Due Dates
A class week is
defined as the period of time between Sunday and Saturday. The exception is
the
first week which begins on the first day of the session (Monday) and ends at
midnight the
fol lowing Saturday . Homework, quizzes, and discussion assignments
should be submitted by the
weekly due dates stated on the grading schedule. Late
assignments will not be accepted.
Ground Rules for Online Participation
• Students
should use email for private messages to the instructor and other students. The
Class Discussion is for public messages so we can see what each other have to
say about
any given topic and respond to if desired.
•
Students are expected to participate in online discussions as well as with other
appropriate online activities including sending/receiving email and completing
homework
assignments.
• All students will observe Conventions of "online
etiquette" when communicating online,
which includes courtesy to all users.
• Homework will be submitted via MyMathLab/Course Compass. Quizzes will be
submitted in D2L.
VI. Course Schedule
Week 1: Rational exponents, Equations, Inequalities, Mathematical Models
• Reading: Read sections p.3, 1.1, 1.2, 1.3, 1.4
• Video: Watch the video lectures
for these sections
• Homework: Complete the 5 homework assignments on these
sections. This is
due by midnight on Saturday.
• Discussion: Post your
introduction by Thursday at midnight
• Quiz 1: The quiz questions are located in MML under the weekly assignments
and also in D2L under Content. You will enter
your answers in a shell in D2L.
This is due by midnight on Saturday
Week 2: Linear, Quadratic and other equations, Inequalities, Lines & Slope
• Reading: Read sections 1.5, 1.6, 1.7, 2.1, 2.2
• Video: Watch the video lectures
for these sections
• Homework: Complete the 5 homework assignments on these
sections. This is
due by midnight on Saturday.
• Discussion: One post is due by
midnight on Thursday. The choice for questions
is located on the Assignment Page
• Quiz 2: The quiz questions are located in MML under the weekly assignments
and
also in D2L under Content. You will enter your answers in a shell in D2L.
This
is due by midnight on Saturday
Week 3: Linear, rational, and quadratic inequalities/Functions
• Readings: Read
sections 2.3, 2.4, 2.5, 2.6, 2.7, 2.8
• Video: Watch the video lectures for these
sections
• Homework: Complete the 6 homework assignments on these sections. This
is
due by midnight on Saturday.
• Discussion: One post is due by midnight on
Thursday.
• Quiz 3: The quiz questions are located in MML under the weekly
assignments
and also in D2L under Content. You will enter your answers in a
shell in D2L.
This is due by midnight on Saturday
Week 4: Polynomial and Rational Functions
• Readings: Read sections 3.1, 3.2
• Video: Watch the video lectures for these sections
• Homework: Complete the 2
homework assignments on these sections. This is
due by midnight on Saturday.
• Discussion: One post is due by midnight on Thursday.
• Quiz 4: The quiz questions
are located in MML under the weekly assignments
and also in D2L under Content.
You will enter your answers in a shell in D2L.
This is due by midnight on
Saturday. This quiz is optional and will replace your
lowest quiz score.
• Midterm: Due by Saturday at midnight. The Midterm is over
the material
covered in weeks 1 ¨C 3.
Week 5: Zeros of polynomial functions, The Fundamental Theorem of Algebra
• Readings: Read sections 3.3, 3.4, 3.5, 3.6, 3.7
• Video: Watch the video lectures
for these sections
• Homework: Complete the 5 homework assignments on these
sections. This is
due by midnight on Saturday.
• Discussion: One post is due by
midnight on Thursday.
• Quiz 5: The quiz questions are located in MML under the
weekly assignments
and also in D2L under Content. You will enter your answers in
a shell in D2L.
This is due by midnight on Saturday
Week 6: Exponential and Logarithmic Functions
• Readings: Read sections 4.1, 4.2,
4.3, 4.4, 4.5
• Video: Watch the video lectures for these sections
• Homework:
Complete the 5 homework assignments on these sections. This is due
by midnight
on Saturday.
• Discussion: One post is due by midnight on Thursday.
• Quiz 6: The
quiz questions are located in MML under the weekly assignments
and also in D2L
under Content. You will enter your answers in a shell in D2L.
This is due by
midnight on Saturday
Week 7: Systems of Equations, Summation Notation
• Readings: Read sections 5.1,
5.2, 5.4, and the document on Summation Notation
• Video: Watch the video lectures
for these sections
• Homework: Complete the 3 homework assignments on these
sections. Work the
problems on the handout. This is due by midnight on Saturday.
• Discussion: One post is due by midnight on Thursday.
• Quiz 7: The quiz questions
are located in MML under the weekly assignments
and also in D2L under Content.
You will enter your answers in a shell in D2L.
This is due by midnight on
Saturday
Week 8: Final Exam
• Homework: Complete the final review. All homework is due by
midnight Thursday night.
• Discussion: One post is due by midnight on Thursday.
• Quiz 8: This is located on Week 8 Assignment page and also in D2L under
Content.
It is due by midnight on Saturday. This quiz is optional and will replace
a
lower quiz score. The quiz will be open on Monday this week.
• Final Exam is due
by midnight on Saturday.
