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Mathematics: Modeling Our World (MMOW)
Course 4

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, pre-calculus, we believe that the material in this text can provide students with a firm background for any entry-level 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 pre-calculus 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 Theory-Driven 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 CD-ROM


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 real-world 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 toll-free support line (1-800-772-6627), and via our Teacher Support Website.

Ordering Information

To download a Mathematics: Modeling Our World (MMOW) Courses 4 price list click here.