# Mathematical Ideas

**by**Miller, Charles D.; Heeren, Vern E.; Hornsby, John

### 9780321168085

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## Summary

## Author Biography

**Vern Heeren** received his bachelor's degree from Occidental College andHis master's degree from the University of California, Davis, both inMathematics. He is Professor of Mathematics at American River College,where he has been active in all aspects of mathematics education andcurriculum development. Mr. Heeren coauthored Mathematical Ideas withCharles D. Miller in 1969, and later they coauthored Mathematics: AnEveryday Experience. The latest five editions of Mathematical IdeasHave been coauthored with E. John Hornsby of the University of New Orleans.

Mr. Heeren enjoys the support of his wife, three sons, three daughters in-law, and five grandchildren.

**John Hornsby** When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics, education, or journalism. His ultimate decision was to become a teacher, but after twenty-five years of teaching at the high school and university levels and ten years of writing mathematics textbooks, both of his goals have been realized. His love for teaching and for mathematics is evident in his passion for working with students and fellow teachers as well. His specific professional interests are recreational mathematics, mathematics history, and incorporating graphing calculators into the curriculum.

John's personal life is busy as he devotes time to his family (wife Gwen, and sons Chris, Jack, and Josh). He has been a rabid baseball fan all of his life. John's other hobbies include numismatics (the study of coins) and record collecting. He loves the music of the 1960s and has an extensive collection of the recorded works of Frankie Valli and the Four Seasons.

## Table of Contents

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: Using Writing to Learn About Mathematics | |

Collaborative Investigation: Discovering Mathematics in Pascal's Triangle | |

Chapter 1 Test | |

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 | |

Chapter 2 Test | |

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 | |

Chapter 3 Test | |

Numeration and Mathematical Systems | |

Historical Numeration Systems | |

Arithmetic in the Hindu-Arabic System | |

Conversion Between Number Bases | |

Finite Mathematical Systems | |

Groups | |

Collaborative Investigation: A Perpetual Calendar Algorithm | |

Chapter 4 Test | |

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 | |

Chapter 5 Test | |

The Real Numbers and Their Representations | |

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 | |

Table of Contents provided by Publisher. All Rights Reserved. |