9780618347551

Topics in Contemporary Mathematics Expanded Version

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  • ISBN13:

    9780618347551

  • ISBN10:

    0618347550

  • Edition: 8th
  • Format: Hardcover
  • Copyright: 2/17/2004
  • Publisher: Cengage Learning
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Summary

Topics in Contemporary Mathematics is uniquely designed to help students see math at work in the contemporary world by presenting problem solving in purposeful and meaningful contexts. This Expanded Eighth Edition contains two additional chapters on Voting and Apportionment and Graph Theory. Strong technology focus encourages students to learn and apply their knowledge using the most up-to-date web links maintained by the author on a companion web site. Instructors may also use this site to access PowerPoint slides for convenient class presentations. In addition to these web resources, lecture and practice test videos have been developed to provide extra support and foster confidence outside of the classroom. For those students in Florida, a CLAST Test software package and video are available as well. A variety of pedagogical features reinforce ideas and motivate students to learn. Getting Started offers a motivating introduction for the techniques and ideas in each section. Through web references and Web It exercises, students utilize the Internet as an educational and creative tool to study mathematical concepts. Collaborative Learning encourages student interaction as they work together to solve problems. The Graph It feature found in the book margins provides step-by-step directions for solving specific examples using the TI-83 graphing calculator. Problem-solving approach throughout the text helps students learn techniques and methods that will benefit them throughout their lives and careers. These special examples use George Polya\'s problem-solving strategy (RSTUVRead, Select, Think of a plan, Use the techniques, Verify) and a unique two-column format for describing the general problem-solving method and demonstrating specific uses. Abundant applications and examples include more than 500 examples and 4100 carefully developed exercises that cover a wide range of topics and provide the instructor and student with flexibility in choosing computational, drill, or conceptual problems. Real-world applications motivate students and pique their interest. Other problems such as Using Your Knowledge, Discovery, Calculator Corner, and Research questions help reinforce concepts and further develop the students critical-thinking and problem-solving skills. Skill Checker helps students test their knowledge with a variety of problems to ensure they have a thorough grasp of the material before continuing on to new concepts. The Chapter Summary provides definitions and section references for key topics within a given chapter. A Practice Test after each chapter is followed by Answers to the Practice Test, with references to the appropriate section, page, and example for review, as needed.

Table of Contents

Note: Each chapter concludes with a Summary, Research Questions, a Practice Test, and Answers to Practice Test
Problem Solving
Inductive Reasoning
Estimation: A Problem-Solving Tool
Graph Interpretation: A Problem-Solving Tool
Sets
Sets: A Problem-Solving Tool
Set Operations
Venn Diagrams
The Number of Elements in a Set: A Problem-Solving Tool
Infinite Sets
Logic
Statements
Truth Tables: A Problem-Solving Tool
The Conditional and the Biconditional
Variations of the Conditional and Implications
Euler Diagrams: A Problem-Solving Tool
Truth Tables and Validity of Arguments
Switching Networks: A Problem-Solving Tool
Numeration Systems
Egyptian, Babylonian, and Roman Numeration Systems
The Hindu-Arabic (Decimal) System
Number Systems with Bases Other Than 10
Binary Arithmetic
Octal and Hexadecimal Arithmetic
Number Theory and the Real Numbers
Number Theory: Primes and Composites
Whole Numbers, Integers, and Order of Operations
The Rational Numbers
Decimals, Scientific Notation, Significant Digits
Rationals as Decimals: Percents
Real Numbers, Square Roots, and Decimal Representation
Radicals
Number Sequences
Equations, Inequalities, and Problem Solving
Solutions of First-Degree Sentences
Graphs of Algebraic Sentences
Sentences Involving Absolute Values
Quadratic Equations
Modeling and Problem Solving
Ratio, Proportion, and Variation
Functions and Graphs
Graphing Relations and Functions
Linear Functions, Relations, and Applications
Slopes and Equations of a Line
Quadratic Functions and Their Graphs
Exponential and Logarithmic Functions
Two Linear Equations in Two Variables
Linear Inequalities
Linear Programming
Geometry
Points, Lines, Planes, and Angles
Triangles and Other Polygons
Perimeter and Circumference
Area Measure and the Pythagorean Theorem
Volume and Surface Area
Networks, Non-Euclidean Geometry, and Topology
Chaos and Fractals
Mathematical Systems and Matrices
Matrix Operations
Solving Systems of Linear Equations with Matrices
Clock and Modular Arithmetic
Abstract Mathematical Systems: Groups and Fields
Game Theory
Counting Techniques
The Sequential Counting Principle (SCP): A Problem-Solving Tool
Permutations
Combinations
Miscellaneous Counting Methods
Probability
Sample Spaces and Probability
Counting Techniques and Probability
Computation of Probabilities
Conditional Probability
Independent Events
Odds and Mathematical Expectation
Statistics
Sampling and Frequency Distributions
Measures of Central Tendency: The Mean, Median, and Mode
Measures of Dispersion: The Range and Standard Deviation
The Normal Distribution: A Problem-Solving Tool
Statistical Graphs: A Problem-Solving Tool
Making Predictions: Linear Regression
Scattergrams and Correlation
Your Money and Your Math
Interest, Taxes, and Discounts
Credit Cards and Consumer Credit
Annual Percentage Rate (APR) and the Rule of 78
Buying a House
Voting and Apportionment
Voting Systems
Voting Objections
Apportionment Methods
Apportionment Objections
Graph Theory
Introduction to Graph Theory
Euler Paths and Euler Circuits
Hamilton Paths and Hamilton Circuits
Trees Appendix: The Metric System
Answers to Odd-Numbered Problems
Research Bibliography
Acknowledgments
Photo Credits
Index
Table of Contents provided by Publisher. All Rights Reserved.

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