College Algebra: Concepts and Contexts

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Overview


This text bridges the gap between traditional and reform approaches to algebra encouraging students to see mathematics in context. It presents fewer topics in greater depth, prioritizing data analysis as a foundation for mathematical modeling, and emphasizing the verbal, numerical, graphical and symbolic representations of mathematical concepts as well as connecting mathematics to real life situations drawn from the students' majors.
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Editorial Reviews

From the Publisher

"I'm excited. I want to do all of the explorations now. When can I get my copy to teach with?"

"It's a college algebra text that is built on real life examples and concepts. Students learn through using real data, hands on activities, and sections that slowly guide them to extensions of the previous concept. The explorations are wonderful."

"[This book] gets the students to think beyond the manipulations and see that the mathematics they are learning really does have a purpose."

"…These are exactly the type of examples that I look for when I review college algebra books for adoption! The applications included are also similar to problems discussed in prominent research articles in mathematics education…"

"Very promising. I like how the exercises are categorized (Fundamentals, Think About It, Skills, Contexts). I also like how material is not used and then forgotten but is used in upcoming sections…"

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Product Details

  • ISBN-13: 9780495387893
  • Publisher: Cengage Learning
  • Publication date: 1/5/2010
  • Series: College Algebra Series
  • Edition description: New Edition
  • Pages: 816
  • Sales rank: 641,666
  • Product dimensions: 8.20 (w) x 10.00 (h) x 1.20 (d)

Meet the Author


James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He did research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Stewart is currently Professor of Mathematics at McMaster University, and his research field is harmonic analysis. Stewart is the author of a best-selling calculus textbook series published by Cengage Learning, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS, and CALCULUS: CONCEPTS AND CONTEXTS, as well as a series of precalculus texts.

Lothar Redlin grew up on Vancouver Island, received a Bachelor of Science degree from the University of Victoria, and a Ph.D. from McMaster University in 1978. He subsequently did research and taught at the University of Washington, the University of Waterloo, and California State University, Long Beach. He is currently Professor of Mathematics at The Pennsylvania State University, Abington Campus. His research field is topology.

Saleem Watson received his Bachelor of Science degree from Andrews University in Michigan. He did graduate studies at Dalhousie University and McMaster University, where he received his Ph.D. in 1978. He subsequently did research at the Mathematics Institute of the University of Warsaw in Poland. He also taught at The Pennsylvania State University. He is currently Professor of Mathematics at California State University, Long Beach. His research field is functional analysis.

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Table of Contents


1. DATA, FUNCTIONS, AND MODELS. Making Sense of Data. Visualizing Relationships in Data. Equations: Describing Relationships in Data. Functions: Describing Change. Function Notation: The Concept of Function as a Rule. Working with Functions: Graphs and Graphing Calculators. Working with Functions: Getting Information from the Graph. Working with Functions: Modeling Real-World Relationships. Making and Using Formulas. Concept Check and Review. EXPLORATION 1: Bias in Presenting Data. EXPLORATION 2: Collecting and Analyzing Data. EXPLORATION 3: Every Graph Tells a Story. 2. LINEAR FUNCTIONS AND MODELS. Working with Functions: Average Rate of Change. Linear Functions: Constant Rate of Change. Equations of Lines: Making Linear Models. Varying the Coefficients: Direct Proportionality. Linear Regression: Fitting Lines to Data. Linear Equations: Getting Information from a Model. Linear Equations: Where Lines Meet. Concept Check and Review. EXPLORATION 1: When Rates of Change. EXPLORATION 2: Linear Patterns. EXPLORATION 3: Bridge Science. EXPLORATION 4: Correlation and Causation. EXPLORATION 5: Fair Division of Assets. 3. EXPONENTIAL FUNCTIONS AND MODELS. Exponential Growth and Decay. Exponential Models: Comparing Rates. Comparing Linear and Exponential Growth. Graphs of Exponential Functions. Fitting Exponential Curves to Data. Concept Check and Review. EXPLORATION 1: Extreme Numbers: Scientific Notation. EXPLORATION 2: So You Want to be a Millionaire? EXPLORATION 3: Linear Patterns. EXPLORATION 4: Modeling Radioactivity with Coins and Dice. 4. LOGARITHMS AND EXPONENTIAL MODELS. Logarithmic Functions. Laws of Logarithms. Logarithmic Scales. The Natural Exponential and Logarithmic Functions. Exponential Equations: Getting Information from Model. Working With Functions: Composition and Inverse. Concept Check and Review. EXPLORATION 1: Super Origami. EXPLORATION 2: Orders of Magnitude. EXPLORATION 3: Semi-Log Graphs. EXPLORATION 4: The Even-Tempered Clavier. 5. QUADRATIC FUNCTIONS AND MODELS. Working with Functions: Shifting and Stretching. Quadratic Functions and their Graphs. Maxima and Minima: Getting Information from a Model. Quadratic Equations: Getting Information from a Model. Fitting Quadratic Curves to Data. Concept Check and Review. EXPLORATION 1: Transformation Stories. EXPLORATION 2: Toricelli's Law. EXPLORATION 2: Quadratic Patterns. 6. POWER, POLYNOMIAL, AND RATIONAL FUNCTIONS. Working with Functions: Algebraic Operations. Power Functions: Positive Powers. Polynomial Functions: Combining Power Functions. Fitting Power and Polynomial Curves to Data. Power Functions: Negative Powers. Rational Functions. Concept Check and Review. EXPLORATION 1: Only in the Movies? EXPLORATION 2: Proportionality: Shape and Size. EXPLORATION 3: Managing Traffic. EXPLORATION 4: Alcohol and the Surge Function. 7. SYSTEMS OF EQUATIONS AND CATEGORICAL DATA. Systems of Linear Equations in Two Variables. Systems of Linear Equations in Several Variables. Using Matrices to Solve Systems of Linear Equations. Matrices and Categorical Data. Matrix Operations: Getting Information from Data. Matrix Equations: Solving a Linear System. Concept Check and Review. EXPLORATION 1: Collecting Categorical Data. EXPLORATION 2: Will the Species Survive? ALGEBRA TOOLKIT A: WORKING WITH NUMBERS. Numbers and Their Properties. The Number Line and Intervals. Integer Exponents. Radicals and Rational Exponents. ALGEBRA TOOLKIT B: WORKING WITH EXPRESSIONS. Combining Algebraic Expressions. Factoring Algebraic Expressions. Rational Expressions. ALGEBRA TOOLKIT C: WORKING WITH EQUATIONS. Solving Basic Equations. Solving Quadratic Equations. Solving Basic Inequalities. ALGEBRA TOOLKIT D: WORKING WITH GRAPHS. The Coordinate Plane. Graphs of Two-Variable Equations. Using a Graphing Calculator. Solving Equations and Inequalities Graphically.
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