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Contemporary College Algebra:
Data, Functions, Modeling
A reformed college algebra course focused on meeting the quantitative needs of students for academic, workplace and society.
The text which follows is the Preface to Contemporary College Algebra: Data, Functions, Modeling, By Don Small, The United States Military Academy, West Point, New York, published by McGrawHill Primis Custom Publishing, © 2002 by The McGrawHill Companies. Editorial Board members are listed in the left hand sidebar.
Textbook and a companion Interactive CD Rom are available from McGrawHill or, for assistance, contact Don Small directly.
"The mind is not a vessel to be filled, but a flame to be kindled." — Plutarch
Primary Goal
Our philosophy is to educate students for the future rather than train
them for the past. We therefore have made a conscious effort to incorporate
into our goals the common qualifications for entering the work force as
enunciated by social, business, and industrial leaders.
The primary goal of this text is to empower students to become
exploratory learners, not to master a list of algebraic rules. Each
section contains Queries that engage students in questioning and
exploring the material being presented. Exercises that explicitly ask students
to explore, ask whatif type questions, make up examples, further investigate
worked examples, iterate for the purpose of recognizing a pattern and
developing a sense for the behavior of a solution, and graphically fit a curve
to a data set are some of the means that are used to establish an exploratory
environment for the students.
Other Goals of this Text
 Improve communication skills  reading, writing,
presenting, listening.
The large majority of the exercises are presented in the story problem format
in order to address the reading aspect of this goal. The story problem format
also addresses the applicability aspect of college algebra as reallife
situations are usually described verbally or in written form rather than in
terms of equations.
 Small group work  inclass group activities and
outofclass group projects. Inclass activities culminate in student
presentations to the class and outofclass projects culminate in both a
written report and a student presentation.
 Use of technology  every student is expected to have daily
access to a graphing calculator and/or computer. The ability to use technology
for plotting and computation is a very important skill.
 Modeling  to empower students to use mathematics to
quantify reallife situations.
 Confidence  develop personal confidence as a problem
solver. Develop confidence in the iterative process: ``try something, note the
errors, modify previous attempt to lessen the errors, and try again'' until a
satisfactory approximation has been obtained. The initial attempt is usually
informed by sketching a picture.
 Enjoy applying mathematics to meaningful situations.
This text is to be read, studied, and annotated. Students should
study the worked examples for the purpose of understanding the concepts and
reasoning involved. Students are expected to personalize their text by filling
in missing details, making up examples and illustrations, and raising
questions. The purpose of the exercises is to help clarify and expand the
reasoning process. As such, working exercises is secondary in importance to
studying the written material in the sections.
Realworld Contexts
Concepts and techniques are introduced and motivated by reallife situations.
Computational techniques are introduced in response to the need to solve
reallife situations. For example, the quadratic formula is introduced in
Chapter 4 in order to solve motion problems that involve quadratic
equations. The ability to understand elementary data analysis, to
extract function relations from data, and to mathematically model reallife
situations in different disciplines is fundamental to the liberal arts
education of every student.
Fun Projects
Fun Projects are small group (three to five students) outofclass projects.
The projects are designed for six to ten hours of work and culminate in a
written report. Instructors are encouraged to assign two or three projects
during the course. The purpose of the projects are to provide opportunities
 Mathematically model realworld situations.
 Research a topic (usually on the Internet)
 Provide a writing assignment
 Provide a small group experience
 Have fun exploring and creating solutions to meaningful problems
The Project Report should consist of:
Cover Page (creative design by students)
Title Page (project name, date, instructor name, students' names)
Executive Summary (one page abstract of the problem, approach used,
results obtained)
Supporting Data (computations, labeled drawings, labeled computer plots
and/or printouts)
Group Log (time, date, location, and brief description of each meeting)
Evaluation Summary of the group's learning experience in working on the project
List of references consulted
All group members should be involved in answering each of the
questions. In addition, each member of the group should be assigned a
particular responsibility in connection with the project, such as one of the following:
Leader: Responsible for developing the group. Responsible for
seeing that the project is completed in a satisfactory manner and on time.
Recorder: Arranges group meetings and records group activities.
Checker: Checks accuracy of all computations. Checks to see
that all questions are answered.
Typist: Types Executive and Evaluation Summaries.
Reader: Responsible for proofreading and final assembly of the
report.
A Few Suggestions to Students
 Be an exploratory learner: sketch pictures, question, create whatif
questions, make up examples, question the reasonableness of results, look for applications.
 Read with a pencil in hand. Make your text useful to you by using the
margins or additional paper to write explanatory notes, questions, fill in
missing computations, make up additional worked problems, and so on. When you
personalize your text by augmenting it, you transform it into an effective
learning tool for you.
 Do not get bogged down in computations. The course is about applying
mathematics to realworld situations, not about computations.
 Be patient and persevere in your studying. Focus on understanding the
reasoning in the worked examples.
 Answer the Queries.
 Make up examples and whatif exercises.
Chapter Content
The analysis of data is the starting point for most of the topics in this
text. The analysis of data motivates the concept of function for the purpose
of drawing predictions from data. Just as data is displayed differently for
varied purposes, functions are represented differently (graphically,
symbolically, numerically, and verbally) to address varied concerns. The
ability to graphically approximate a data set is a key skill in applying
mathematics. A strong foundation in elementary data analysis and the function
concept prepares the student to model reallife situations.
Chapter 1  Overview
Chapter 2  Data and Variables:
We study how to read and display data:
table, pie chart, scatter and line plots, and bar charts. We learn the
meanings, use, and methods to compute the three principle summary measures of
a set: average (mean), median, and mode. Our understanding that data is
information about a variable, introduces us to an understanding of the meaning
of variable and its use as a mathematical pronoun. The exploration of
relations between variables leads to the study of straight lines, a
fundamental concept in the application of mathematics to reallife situations.
Applications of linear equations lead naturally to systems of linear
equations, linear inequalities, and their applications in linear programming.
Chapter 3  Functions: The concept of a function is one of the most
important concepts in mathematics. The concept is developed informally through
discussion of academic grades, modeling water level in a well, and warming a
can of soda. Definitions of a function and related terms are clearly presented
and illustrated. Graphically extracting functional relations from data
introduces the shapes of the basic functions: power, radical, exponential,
logarithmic, and periodic (sine, cosine). The skill to graphically fit a curve
to a data plot is enhanced by studying the basic graph transformations of
shifting and scaling. The algebra of functions (addition, multiplication,
composition, and inverses) is developed graphically, symbolically, and
numerically. The ability to display data and to graphically approximate
numerical solutions of equations and zeros of functions is an important thread
throughout the text. The development of symbolic approximation of data (that
is, regression analysis) completes the chapter.
Chapter 4  Modeling: College algebra is a college or university
program in the sense that it or an equivalent course is required by all
disciplines. Therefore an appropriate goal of \textit{Contemporary College
Algebra} is to prepare students to mathematically model reallife situations
arising in different disciplines. To illustrate the breadth of the
applicability of college algebra, the focus of Chapter 4 is on modeling
problems in business, physical and life Sciences, and the arts. The primary
modeling techniques are graphical approximations and recursive sequences. The
recursive sequence model developed on the reasoning
{(New Situation) = (Old Situation) + (Change)
is applicable across the disciplines. In particular, the recursive
sequence model of the accumulation of money in a savings account serves as
paradigm for most of the discrete models developed in Contemporary
College Algebra.
Exercises
There is a rich assortment of exercises at the end of each section to augment
the Queries and worked examples in the section. The purpose of the
exercises is to support and expand the conceptual understanding of the
material. As such, several of the exercises refer to worked examples in the
section. Many of the exercises are suitable for small group inclass
activities or small group outofclass projects.
Labels
Queries are numbered consecutively within sections. Examples, figures, and
tables have 3place labels, the first location denotes the chapter, the second
location denotes the section, and the third location denotes the example,
figure, or table within the section. For example, Figure 3.4.6 is the sixth
figure in section 4 of chapter 3 and Table 3.FunProject2.4 denotes the fourth
table in Fun Project number 2 in chapter 3.
Computational Skill
Development of computational skill aided by the calculator and/or computer is
an expected outcome of studying this text. Computational skill, including
approximation of answers and checking the reasonableness of answers, will
develop by working on reallife problems. Each section's exercise set begins
with three Computational Skill exercises, the third of which is to make up
three additional exercises similar to the first two. The purpose is to
highlight the important computational techniques used in the section and to
encourage students to ask whatif type questions. Appendix A on Computational
Skills and Basic Functions is included for reference. Time should not be spent
on drilling to master hand computation skills, such as factoring. In educating
students to become contributing and productive members of society, we need to
engage them in the use of the computational tools used in society  graphing
calculators and computers.
The following table indicates where important algebraic or arithmetic
techniques are introduced in the text.
Percentage  Section 2.1 
Factoring  Section 3.6 
Fractions  Section 2.2 
Iteration  Section 4.1 
Radian & Degree Measure  Section 2.4 
Geometric Series  Section 4.1 
Inequalities, Absolute Value  Section 2.7 
Exponential & Logarithmic Functions  Section 4.2 
Evaluation of Functions  Section 3.1 
Quadratic Formula  Section 4.3 
Basic Functions  Section 3.3 
Parametric Functions  Section 4.3 
Graph Transformation  Section 3.4 
Trigonometric Functions  Section 4.3 
Algebraic Operations  Section 3.5 
Logistic Function  Section 4.6 
Let us begin an exciting journey through Contemporary
College Algebra. Fasten your seat belts, you are driving!
Don Small
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Contemporary College Algebra, 7th Edition (ISBN13: 9780073394879) (ISBN10:0073394874) can be obtained directly from McGrawHill.
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