Mathematical Ideas & Awl Tutor Center Pkg / Edition 10

Mathematical Ideas & Awl Tutor Center Pkg / Edition 10

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Mathematical Ideas & Awl Tutor Center Pkg / Edition 10

One of the biggest issues college math instructors face is capturing and keeping student interest. Over the years, John Hornsby has refined a creative solution--bringing the best of Hollywood into his mathematics classroom. Mathematical Ideas applies this same strategy of engaging students through video clips from popular cinema and television to the textbook. Alongside fresh data and tools, this Eleventh Edition uses up-to-the-minute images as well as old favorites of math being done in Hollywood. In addition, examples are clarified with additional annotations, chapter summaries are made more intuitive to aid review, and chapter tests now include specific section references, making it easier for students to refer back to topics that need more attention. With great care and effort, the authors have crafted this new edition to serve the needs of today's students and instructors.

Product Details

ISBN-13: 9780321203687
Publisher: Addison-Wesley
Publication date: 06/28/2003
Edition description: Older Edition
Product dimensions: 6.50(w) x 1.50(h) x 9.50(d)

About the Author

Vern Heeren received his bachelor's degree from Occidental College and his master's degree from the University of California, Davis, both in mathematics. He is a retired professor of mathematics from American River College where he was active in all aspects of mathematics education and curriculum development for thirty-eight years. Teaming with Charles D. Miller in 1969 to write Mathematical Ideas, the pair later collaborated on Mathematics: An Everyday Experience; John Hornsby joined as co-author of Mathematical Ideas on the later six editions. Vern enjoys the support of his wife, three sons, three daughters in-law, and eight grandchildren.

John Hornsby When a young John Hornsby enrolled in Lousiana State University, he was uncertain whether he wanted to study mathematics education or journalism. Ultimately, he decided to become a teacher. After twenty five years in high school and university classrooms, each of his goals has been realized. His passion for teaching and mathematics manifests itself in his dedicated work with students and teachers, while his penchant for writing has, for twenty five years, been exercised in the writing of mathematics textbooks. Devotion to his family (wife Gwen and sons Chris, Jack, and Josh), numismatics (the study of coins) and record collecting keep him busy when he is not involved in teaching or writing. He is also an avid fan of baseball and music of the 1960's. Instructors, students, and the 'general public' are raving about his recent Math Goes to Hollywood presentations across the country.

Table of Contents

1. The Art of Problem Solving.
Solving Problems by Inductive Reasoning.
An Application of Inductive Reasoning: Number Patterns.
Strategies for Problem Solving.
Calculating, Estimating, and Reading Graphs.
Extension: Writing to Learn about Mathematics.
Collaborative Investigation: Discovering Mathematics in Pascal's Triangle.

2. The Basic Concepts of Set Theory.
Symbols and Terminology.
Venn Diagrams and Subsets.
Set Operations and Cartesian Products.
Cardinal Numbers and Surveys.
Infinite Sets and Their Cardinalities.
Collaborative Investigation: A Survey of Your Class.

3. Introduction to Logic.
Statements and Quantifiers.
Truth Tables and Equivalent Statements.
The Conditional and Circuits.
More on the Conditional.
Analyzing Arguments with Euler Diagrams.
Extension: Logic Puzzles.
Analyzing Arguments with Truth Tables.
Collaborative Investigation: Logic Puzzles Revisited.

4. Numeration and Mathematical Systems.
Historical Numeration Systems.
Arithmetic in the Hindu-Arabic System.
Converting Between Number Bases.
Other Finite Mathematical Systems.
Collaborative Investigation: A Perpetual Calendar Algorithm.

5. Number Theory.
Prime and Composite Numbers.
Selected Topics from Number Theory.
Greatest Common Factor and Least Common Multiple.
The Fibonacci Sequence and the Golden Ratio.
Extension: Magic Squares.
Collaborative Investigation: Investigating an Interesting Property of Number Squares.

6. The Real Number System.
Real Numbers, Order, and Absolute Value.
Operations, Properties, and Applications of Real Numbers.
Rational Numbers and Decimal Representation.
Irrational Numbers and Decimal Representation.
Applications of Decimals and Percents.
Extension: Complex Numbers.
Collaborative Investigation: Budgeting to Buy a Car.

7. The Basic Concepts of Algebra.
Linear Equations.
Applications of Linear Equations.
Ratio, Proportion, and Variation.
Linear Inequalities.
Properties of Exponents and Scientific Notation.
Polynomials and Factoring.
Quadratic Equations and Applications.
Collaborative Investigation: Calculating the Magic Number in Sports.

8. Graphs, Functions, and Systems of Equations and Inequalities.
The Rectangular Coordinate System and Circles.
Lines and Their Slopes.
Equations of Lines.
An Introduction to Functions: Linear Functions and Applications.
Quadratic Functions and Their Tables.
Exponential and Logarithmic Functions and Applications.
Systems of Equations and Applications.
Extension: Using Matrix Row Operations to Solve Systems.
Linear Inequalities and Systems of Inequalities.
Collaborative Investigation: Olympic Track and Field Results.

9. Geometry.
Points, Lines, Planes, and Angles.
Curves, Polygons, and Circles.
Perimeter, Area, and Circumference.
The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem.
Extension: Right Angle Trigonometry.
Space Figures, Volume, and Surface Area.
Non-Euclidean Geometry, Topology, and Networks.
Chaos and Fractal Geometry.
Collaborative Investigation: Generalizing the Angle Sum Concept.

10. Counting Methods.
Counting by Systematic Listing.
Using the Fundamental Counting Principle.
Using Permutations and Combinations.
Using Pascal's Triangle and the Binomial Theorem.
Counting Problems Involving "Not" and "Or".
Collaborative Investigation: Approximating Factorials Using Stirling's Formula.

11. Probability.
Basic Concepts.
Events Involving "Not" and "Or".
Events Involving "And".
Binomial Probability.
Expected Value.
Estimating Probabilities by Simulation.
Collaborative Investigation: Finding Empirical Values of pi.

12. Statistics.
Frequency Distributions and Graphs.
Measures of Central Tendency.
Measures of Dispersion.
Measures of Position.
The Normal Distribution.
Extension: How to Lie with Statistics.
Regression and Correlation.
Collaborative Investigation: Combining Sets of Data.

13. Consumer Mathematics.
Interest and Inflation.
Extension: Annuities.
Consumer Credit.
Truth in Lending.
Buying a Home.
Investing in the Stock Market.
Collaborative Investigation: To Buy or to Rent?

14. Graph Theory.
Basic Concepts.
Euler Circuits.
Hamilton Circuits.
Minimum Spanning Trees.
Collaborative Investigation: The Number of Edges in a Complege Graph and a Special Sum Formula.

15. Voting and Apportionment.
The Possibilities of Voting.
The Impossibilities of Voting.
The Possibilities of Apportionment.
The Imposibilities of Apportionment.
Collaborative Investigation: Class Favorites, An Election Exploration.

Appendix: The Metric System.

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