Mathematical modeling is the process of looking at a situation, formulating a problem, finding a
mathematical core, working within that core, and coming back to see what mathematics tells us about the
original problem. We do not know in advance what mathematics to apply. The mathematics we settle on
may be a mix of geometry, algebra, trigonometry, data analysis, and probability. We may need to use
computers or graphing calculators, spreadsheets, or other utilities.
At heart, we want to demonstrate to students that mathematics is the most useful subject they will learn.
More importantly, we hope to demonstrate that using mathematics to solve interesting problems about
how our world works can be a truly enjoyable and rewarding experience. Ultimately, learning to model is
learning to learn.
For those of you who have taught the earlier courses in this series, you will note one major difference. In Mathematics: Modeling Our World Courses 1, 2, and 3 all of the chapters were organized around a major
context. We did this to emphasize further the broad applicability of the subject. In this text we have used
mathematical concepts as chapter titles. We have done this to emphasize that mathematics as a discipline
has a structure of its own, and that as students go on into the study of mathematics they will learn more
and more of that structure and the power it provides to solve an amazingly wide array of problems.
This course is the gateway to collegiate mathematics. As such, students will see a number of essential new
concepts and be asked to learn a number of important new skills.
While we have subtitled the course, precalculus, we believe that the material in this text can provide
students with a firm background for any entrylevel undergraduate mathematics course—continuous or
discrete. For example, we have provided substantial material on matrices and vectors as well as a full
chapter on discrete dynamical systems. We believe that the treatment of these topics will prepare students
for a deeper understanding of the concepts underlying the calculus as well as those underlying discrete
mathematical structures.
What you will find here is a challenging precalculus course for serious students. And, in the COMAP
tradition, you will find exciting, contemporary, applications and models presented in novel ways to help
teach and motivate the further study of our discipline.
Click here to download a Scope and Sequence Chart for
Mathematics: Modeling Our World (MMOW) Course 4.
Click Here To Download A Detailed Overview of Course 4.
Chapter 1
Functions in Modeling 

LESSON 1.1
A TheoryDriven Model
LESSON 1.2
Building a Tool Kit
of Functions
LESSON 1.3
Expanding the
Tool Kit of Functions
LESSON 1.4
Transformations
of Functions
LESSON 1.5
Operations
on Functions
Chapter 1 Review 


Chapter 2
The Exponential and Logarithmic Functions 

LESSON 2.1
Exponential Functions
LESSON 2.2
Logarithmic Scale
LESSON 2.3
Changing Bases
LESSON 2.4
Logarithmic Functions
LESSON 2.5
Modeling with Exponential
and Logarithm Functions
LESSON 2.6
Composition and
Inverses of Functions
Chapter 2 Review 


Chapter 3
Polynomial Models 

LESSON 3.1
Modeling Falling Objects
LESSON 3.2
The Merits of
Polynomial Models
LESSON 3.3
The Power
of Polynomials
LESSON 3.4
Zeroing in
on Polynomials
LESSON 3.5
Polynomial Divisions
LESSON 3.6
Polynomial Approximations
Chapter 3 Review 


Chapter 4
Coordinate Systems and Vectors 

LESSON 4.1
Polar Coordinates
LESSON 4.2
Polar Form of
Complex Numbers
LESSON 4.3
The Geometry of Vectors
LESSON 4.4
The Algebra of Vectors
LESSON 4.5
Vector Equations
in Two Dimensions
LESSON 4.6
Vector Equations
in Three Dimensions
Chapter 4 Review 


Chapter 5
Matrices 

LESSON 5.1
Matrix Basics
LESSON 5.2
The Multiplicative Inverse
LESSON 5.3
Systems of Equations
in Three Variables
Chapter 5 Review 


Chapter 6
Analytic Geometry 

LESSON 6.1
Analytic Geometry and Loci
LESSON 6.2
Modeling with Circles
LESSON 6.3
Modeling with Parabolas
LESSON 6.4
Modeling with Ellipses
LESSON 6.5
Modeling with Hyperbolas
Chapter 6 Review 


Chapter 7
Counting and the Binomial Theorem 

LESSON 7.1
Counting Basics
LESSON 7.2
Compound Events
LESSON 7.3
The Binomial Theorem
Chapter 7 Review 


Chapter 8
Modeling Change with Discrete Dynamical Systems 

LESSON 8.1
Modeling Change with
Difference Equations
LESSON 8.2
Approximating Change
with Difference Equations
LESSON 8.3
Numerical Solutions
LESSON 8.4
Systems of
Difference Equations
Chapter 8 Review 


Course 4 of the Mathematics: Modeling Our World (MMOW) curriculum offers additional resources to supplement the text:
Teacher's Edition
CDROM
Calculator and computer software
Calculator and computer software written specifically for Mathematics: Modeling Our World (MMOW). With software programs for each unit allows students to explore realworld themes with the same tools used by scientists, technicians, and business people. The software includes graphing calculator programs, specialty computers, spreadsheet template, data sets, and geometric drawing utility sketches.
Teacher Development
Teacher training and support available through COMAP staff trainers, through a tollfree support line (18007726627), and via our Teacher Support Website.
Ordering Information
To download a Mathematics: Modeling Our World (MMOW) Courses 4 price list click here.
