Mathematical Ideas & Awl Tutor Center Pkg / Edition 10by Charles Miller, Vern Heeren, John Hornsby
Pub. Date: 06/28/2003
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/i>… See more details below
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.
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Table of Contents1. The Art of Problem Solving.
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.
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.
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.
Arithmetic in the Hindu-Arabic System.
Converting Between Number Bases.
Other Finite Mathematical Systems.
Collaborative Investigation: A Perpetual Calendar Algorithm.
5. Number Theory.
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.
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.
Applications of Linear Equations.
Ratio, Proportion, and Variation.
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.
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.
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.
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.
Events Involving "Not" and "Or".
Events Involving "And".
Estimating Probabilities by Simulation.
Collaborative Investigation: Finding Empirical Values of pi.
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.
Truth in Lending.
Buying a Home.
Investing in the Stock Market.
Collaborative Investigation: To Buy or to Rent?
14. Graph Theory.
Minimum Spanning Trees.
Collaborative Investigation: The Number of Edges in a Complege Graph and a Special Sum Formula.
15. Voting and Apportionment.
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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