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Mathematical Ideas

Mathematical Ideas - 9th edition

Mathematical Ideas - 9th edition

ISBN13: 9780321043245

ISBN10: 0321043243

Mathematical Ideas by Charles D. Miller, Vern E. Heeren and John Hornsby - ISBN 9780321043245
Edition: 9TH 01
Copyright: 2001
Publisher: Addison-Wesley Longman, Inc.
International: No
Mathematical Ideas by Charles D. Miller, Vern E. Heeren and John Hornsby - ISBN 9780321043245

ISBN13: 9780321043245

ISBN10: 0321043243

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This best-selling text is written for the non-science, non-mathematics major. The book's flexible organization and self-contained chapters enable instructors to tailor the text to their preferred syllabus. It focuses on essential concepts and skills while imparting an appreciation for the many practical and fascinating applications of mathematics to everyday life. The ninth edition continues to adhere to NCTM and AMATYC standards with an emphasis on cooperative learning through collaborative investigations, the inclusion of real data and the optional use of graphing technology.

Features :

  • NEW! Enhanced supplements package now includes InterAct Math tutorial software, MathXL, Digital Video Tutor, a Web site and an Instructor's Edition with answers to all exercises.
  • NEW! Collaborative Investigations have been expanded to increase the opportunity for group activity, motivate student involvement, and promote critical thinking.
  • NEW! Inductive Reasoning is now covered before deductive reasoning in Chapter One to help build student confidence.
  • NEW! Sections 5.1 and 5.2 were updated to reflect important developments in identifying and factoring large prime numbers, demonstrating to students the impact of computers in this area.
  • The Consumer Mathematics chapter (13) now has more coverage of mutual funds.
  • 25% new exercises.
  • Enhanced problem-solving theme woven throughout the text.
  • Problem-solving strategies relate the discussion of strategies to techniques that are covered in the text.
  • Applications using real data, graphs and charts are now more thoroughly integrated into the text, examples and exercises. An Index of Applications has been added.
  • Optional coverage of graphing calculators is included in the textual material, activities and exercises.
  • Optional Extension sections cover additional topics in greater depth.

Author Bio

Miller, Charles David : American River College

Hornsby, John : University of New Orleans

Heeren, Vern E. : American River College

Table of Contents

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.
Modular Systems.
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?

Appendix: The Metric System.