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.

 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.

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