# Mathematical Ideas Expanded Edition

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

### 9780321361462

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## Summary

## Author Biography

**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

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. |