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by Richard N. Aufmann and Joanne S. Lockwood

Cover type: HardbackEdition: 04

Copyright: 2004

Publisher: Houghton Mifflin Harcourt

Published: 2004

International: No

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A new text for the liberal arts math course by a seasoned author team, Mathematical Excursions, is uniquely designed to help students see math at work in the contemporary world. Using the proven Aufmann Interactive Method, students learn to master problem-solving in meaningful contexts. In addition, multi-part Excursion exercises emphasize collaborative learning. The text's extensive topical coverage offers instructors flexibility in designing a course that meets their students' needs and curriculum requirements.

- The Excursions activity and corresponding Excursion Exercises, denoted by an icon, conclude each section, providing opportunities for in-class cooperative work, hands-on learning, and development of critical-thinking skills. These activities are also ideal for projects or extra credit assignments. The Excursions are designed to reinforce the material that has just been covered in the section in a fun and engaging manner that will enhance a student's journey and discovery of mathematics.
- The proven Aufmann Interactive Method ensures that students try concepts and manipulate real-life data as they progress through the material. Every objective contains at least one set of matched-pair examples. The method begins with a worked-out example with a solution in numerical and verbal formats to address different learning styles. The matched problem, called Check Your Progress, is left for the student to try. Each problem includes a reference to a fully worked out solution in an appendix to which the student can refer for immediate feedback, concept reinforcement, identification of problem areas, and prevention of frustration.
- Each Chapter Opener begins with a short introduction to a real data application, which is then highlighted again in one Excursions activity and in the corresponding Excursion Exercises at the end of a section. This specific Excursion will be denoted by an icon. A section-by-section table of contents is accompanied by a brief summary of the topics that will be covered in the chapter.

**Aufmann, Richard N. : Palomar College**

** **Richard Aufmann is Professor of Mathematics at Palomar College in California. He is the lead author of two best-selling developmental math series, a best-selling college algebra and trigonometry series, as well as several derivative math texts. The Aufmann name is highly recognized and respected among college mathematics faculty.

Lockwood, Joanne S. : Plymouth State College

Joanne Lockwood is Assistant Professor of Mathematics at Plymouth State College in Plymouth, New Hampshire. She is co-author with Aufmann and Vernon Barker on the hardback developmental series, Business Mathematics, Algebra with Trigonometry for College Students, and numerous software ancillaries that accompany Aufmann titles. She is also co-authoring Mathematical Excursions with Aufmann.

**1. Problem Solving**

Section 1.1 Inductive and Deductive Reasoning

Excursion: The Game of Sprouts by John H. Conway

Section 1.2 Problem Solving with Patterns

Excursion: Polygonal Numbers

Section 1.3 Problem-Solving Strategies

Excursion: Routes on a Probability Demonstrator

**2. Sets**

Section 2.1 Basic Properties of Sets

Excursion: Fuzzy Sets

Section 2.2 Subsets

Excursion: Subsets and Complements of Fuzzy Sets

Section 2.3 Set Operations

Excursion: Union and Intersection of Fuzzy Sets

Section 2.4 Applications of Sets

Excursion: Voting Systems

Section 2.5 Infinite Sets

Excursion: Transfinite Arithmetic

**3. Logic**

Section 3.1 Logic Statements and Quantifiers

Excursion: Switching Networks

Section 3.2 Truth Tables and Applications

Excursion: Switching Networks--Part II

Section 3.3 The Conditional and the Biconditional

Excursion: Logic Gates

Section 3.4 The Conditional and Related Statements

Excursion: Sheffer's Stroke and the NAND Gate

Section 3.5 Arguments

Excursion: Fallacies

Section 3.6 Euler Diagrams

Excursion: Use Logic to Solve Puzzles

**4. Numeration Systems and Topics from Number Theory**

Section 4.1 Early Numeration Systems

Excursion: A Rosetta Tablet for the Traditional Chinese Numeration System

Section 4.2 Place-Value Systems

Excursion: Subtraction via the Nines Complement and the End-Around Carry

Section 4.3 Different Base Systems

Excursion: Information Retrieval via a Binary Search

Section 4.4 Arithmetic in Different Bases

Excursion: Subtraction in Base Two via the Ones Complement and the End-Around Carry

Section 4.5 Prime Numbers and Selected Topics from Number Theory

Excursion: The Distribution of the Primes

Section 4.6 Additional Topics from Number Theory

Excursion: A Sum of the Divisors Formula

**5. Applications of Equations**

Section 5.1 First-Degree Equations

Excursion: Body Mass Index

Section 5.2 Rate, Ratio, and Proportion

Excursion: Earned Run Average

Section 5.3 Percent

Excursion: Federal Income Tax

Section 5.4 Second-Degree Equations

Excursion: The Sum and Product of the Solutions of Quadratic Equations

**6. Applications of Functions**

Section 6.1 Rectangular Coordinates and Functions

Excursion: Dilations of a Geometric Figure

Section 6.2 Properties of Linear Functions

Excursion: Negative Velocity

Section 6.3 Finding Linear Models

Excursion: A Linear Business Model

Section 6.4 Quadratic Functions

Excursion: Reflective Properties of a Parabola

Section 6.5 Exponential Functions and Their Applications

Excursion: Chess and Exponential Functions

Section 6.6 Logarithmic Functions and Their Applications

Excursion: Benford's Law

**7. Mathematical Systems**

Section 7.1 Modular Arithmetic

Excursion: Computing the Day of the Week

Section 7.2 Applications of Modular Arithmetic

Excursion: Public Key Cryptography

Section 7.3 Introduction to Group Theory

Excursion: Wallpaper Groups

**8. Geometry**

Section 8.1 Basic Concepts of Euclidean Geometry

Excursion: Preparing a Circle Graph

Section 8.2 Perimeter and Area of Plane Figures

Excursion: Slicing Polygons into Triangles

Section 8.3 Similar Triangles

Excursion: Topology

Section 8.4 Volume and Surface Area

Excursion: Water Displacement

Section 8.5 Non-Euclidean Geometry

Excursion: Find Geodesics

Section 8.6 Fractals

Excursion: The Heighway Dragon Fractal

**9. The Mathematics of Graphs**

Section 9.1 Traveling Roads and Visiting Cities

Excursion: Pen-Tracing Puzzles

Section 9.2 Efficient Routes

Excursion: Extending the Greedy Algorithm

Section 9.3 Planarity and Euler's Formula

Excursion: The Five Regular Convex Polyhedra

Section 9.4 Map Coloring and Graphs

Excursion: Modeling Traffic Lights with Graphs

**10. The Mathematics of Finance**

Section 10.1 Simple Interest

Excursion: Treasury Bills

Section 10.2 Compound Interest

Excursion: Consumer Price Index

Section 10.3 Consumer Loans

Excursion: Leasing versus Buying a Car

Section 10.4 Home Ownership

Excursion: Home Ownership Issues

**11. Combinatorics and Probability**

Section 11.1 The Counting Principle

Excursion: Decision Trees

Section 11.2 Permutations and Combinations

Excursion: Choosing Numbers in Keno

Section 11.3 Probability and Odds

Excursion: The Value of Pi by Simulation

Section 11.4 Addition and Complement Rules

Excursion: Keno Revisited

Section 11.5 Conditional Probability

Excursion: Sharing Birthdays

Section 11.6 Expectation

Excursion: Chuck-a-luck

**12. Statistics**

Section 12.1 Measures of Central Tendency

Excursion: Linear Interpolation and Animation

Section 12.2 Measures of Dispersion

Excursion: A Geometric View of Variance and Standard Deviation

Section 12.3 Measures of Relative Position

Excursion: Stem-and-Leaf Diagrams

Section 12.4 Normal Distributions

Excursion: Cut-Off Scores

Section 12.5 Linear Regression and Correlation

Excursion: An Application of Linear Regression

**13. Apportionment and Voting**

Section 13.1 Introduction to Apportionment

Excursion: Apportioning the 1790 House of Representatives

Section 13.2 Introduction to Voting

Excursion: Variations of the Borda Count Method

Section 13.3 Weighted Voting Systems

Excursion: Blocking Coalitions and the Banzhaf Power Index

Summary

A new text for the liberal arts math course by a seasoned author team, Mathematical Excursions, is uniquely designed to help students see math at work in the contemporary world. Using the proven Aufmann Interactive Method, students learn to master problem-solving in meaningful contexts. In addition, multi-part Excursion exercises emphasize collaborative learning. The text's extensive topical coverage offers instructors flexibility in designing a course that meets their students' needs and curriculum requirements.

- The Excursions activity and corresponding Excursion Exercises, denoted by an icon, conclude each section, providing opportunities for in-class cooperative work, hands-on learning, and development of critical-thinking skills. These activities are also ideal for projects or extra credit assignments. The Excursions are designed to reinforce the material that has just been covered in the section in a fun and engaging manner that will enhance a student's journey and discovery of mathematics.
- The proven Aufmann Interactive Method ensures that students try concepts and manipulate real-life data as they progress through the material. Every objective contains at least one set of matched-pair examples. The method begins with a worked-out example with a solution in numerical and verbal formats to address different learning styles. The matched problem, called Check Your Progress, is left for the student to try. Each problem includes a reference to a fully worked out solution in an appendix to which the student can refer for immediate feedback, concept reinforcement, identification of problem areas, and prevention of frustration.
- Each Chapter Opener begins with a short introduction to a real data application, which is then highlighted again in one Excursions activity and in the corresponding Excursion Exercises at the end of a section. This specific Excursion will be denoted by an icon. A section-by-section table of contents is accompanied by a brief summary of the topics that will be covered in the chapter.

Author Bio

**Aufmann, Richard N. : Palomar College**

** **Richard Aufmann is Professor of Mathematics at Palomar College in California. He is the lead author of two best-selling developmental math series, a best-selling college algebra and trigonometry series, as well as several derivative math texts. The Aufmann name is highly recognized and respected among college mathematics faculty.

Lockwood, Joanne S. : Plymouth State College

Joanne Lockwood is Assistant Professor of Mathematics at Plymouth State College in Plymouth, New Hampshire. She is co-author with Aufmann and Vernon Barker on the hardback developmental series, Business Mathematics, Algebra with Trigonometry for College Students, and numerous software ancillaries that accompany Aufmann titles. She is also co-authoring Mathematical Excursions with Aufmann.

Table of Contents

**1. Problem Solving**

Section 1.1 Inductive and Deductive Reasoning

Excursion: The Game of Sprouts by John H. Conway

Section 1.2 Problem Solving with Patterns

Excursion: Polygonal Numbers

Section 1.3 Problem-Solving Strategies

Excursion: Routes on a Probability Demonstrator

**2. Sets**

Section 2.1 Basic Properties of Sets

Excursion: Fuzzy Sets

Section 2.2 Subsets

Excursion: Subsets and Complements of Fuzzy Sets

Section 2.3 Set Operations

Excursion: Union and Intersection of Fuzzy Sets

Section 2.4 Applications of Sets

Excursion: Voting Systems

Section 2.5 Infinite Sets

Excursion: Transfinite Arithmetic

**3. Logic**

Section 3.1 Logic Statements and Quantifiers

Excursion: Switching Networks

Section 3.2 Truth Tables and Applications

Excursion: Switching Networks--Part II

Section 3.3 The Conditional and the Biconditional

Excursion: Logic Gates

Section 3.4 The Conditional and Related Statements

Excursion: Sheffer's Stroke and the NAND Gate

Section 3.5 Arguments

Excursion: Fallacies

Section 3.6 Euler Diagrams

Excursion: Use Logic to Solve Puzzles

**4. Numeration Systems and Topics from Number Theory**

Section 4.1 Early Numeration Systems

Excursion: A Rosetta Tablet for the Traditional Chinese Numeration System

Section 4.2 Place-Value Systems

Excursion: Subtraction via the Nines Complement and the End-Around Carry

Section 4.3 Different Base Systems

Excursion: Information Retrieval via a Binary Search

Section 4.4 Arithmetic in Different Bases

Excursion: Subtraction in Base Two via the Ones Complement and the End-Around Carry

Section 4.5 Prime Numbers and Selected Topics from Number Theory

Excursion: The Distribution of the Primes

Section 4.6 Additional Topics from Number Theory

Excursion: A Sum of the Divisors Formula

**5. Applications of Equations**

Section 5.1 First-Degree Equations

Excursion: Body Mass Index

Section 5.2 Rate, Ratio, and Proportion

Excursion: Earned Run Average

Section 5.3 Percent

Excursion: Federal Income Tax

Section 5.4 Second-Degree Equations

Excursion: The Sum and Product of the Solutions of Quadratic Equations

**6. Applications of Functions**

Section 6.1 Rectangular Coordinates and Functions

Excursion: Dilations of a Geometric Figure

Section 6.2 Properties of Linear Functions

Excursion: Negative Velocity

Section 6.3 Finding Linear Models

Excursion: A Linear Business Model

Section 6.4 Quadratic Functions

Excursion: Reflective Properties of a Parabola

Section 6.5 Exponential Functions and Their Applications

Excursion: Chess and Exponential Functions

Section 6.6 Logarithmic Functions and Their Applications

Excursion: Benford's Law

**7. Mathematical Systems**

Section 7.1 Modular Arithmetic

Excursion: Computing the Day of the Week

Section 7.2 Applications of Modular Arithmetic

Excursion: Public Key Cryptography

Section 7.3 Introduction to Group Theory

Excursion: Wallpaper Groups

**8. Geometry**

Section 8.1 Basic Concepts of Euclidean Geometry

Excursion: Preparing a Circle Graph

Section 8.2 Perimeter and Area of Plane Figures

Excursion: Slicing Polygons into Triangles

Section 8.3 Similar Triangles

Excursion: Topology

Section 8.4 Volume and Surface Area

Excursion: Water Displacement

Section 8.5 Non-Euclidean Geometry

Excursion: Find Geodesics

Section 8.6 Fractals

Excursion: The Heighway Dragon Fractal

**9. The Mathematics of Graphs**

Section 9.1 Traveling Roads and Visiting Cities

Excursion: Pen-Tracing Puzzles

Section 9.2 Efficient Routes

Excursion: Extending the Greedy Algorithm

Section 9.3 Planarity and Euler's Formula

Excursion: The Five Regular Convex Polyhedra

Section 9.4 Map Coloring and Graphs

Excursion: Modeling Traffic Lights with Graphs

**10. The Mathematics of Finance**

Section 10.1 Simple Interest

Excursion: Treasury Bills

Section 10.2 Compound Interest

Excursion: Consumer Price Index

Section 10.3 Consumer Loans

Excursion: Leasing versus Buying a Car

Section 10.4 Home Ownership

Excursion: Home Ownership Issues

**11. Combinatorics and Probability**

Section 11.1 The Counting Principle

Excursion: Decision Trees

Section 11.2 Permutations and Combinations

Excursion: Choosing Numbers in Keno

Section 11.3 Probability and Odds

Excursion: The Value of Pi by Simulation

Section 11.4 Addition and Complement Rules

Excursion: Keno Revisited

Section 11.5 Conditional Probability

Excursion: Sharing Birthdays

Section 11.6 Expectation

Excursion: Chuck-a-luck

**12. Statistics**

Section 12.1 Measures of Central Tendency

Excursion: Linear Interpolation and Animation

Section 12.2 Measures of Dispersion

Excursion: A Geometric View of Variance and Standard Deviation

Section 12.3 Measures of Relative Position

Excursion: Stem-and-Leaf Diagrams

Section 12.4 Normal Distributions

Excursion: Cut-Off Scores

Section 12.5 Linear Regression and Correlation

Excursion: An Application of Linear Regression

**13. Apportionment and Voting**

Section 13.1 Introduction to Apportionment

Excursion: Apportioning the 1790 House of Representatives

Section 13.2 Introduction to Voting

Excursion: Variations of the Borda Count Method

Section 13.3 Weighted Voting Systems

Excursion: Blocking Coalitions and the Banzhaf Power Index

Publisher Info

Publisher: Houghton Mifflin Harcourt

Published: 2004

International: No

Published: 2004

International: No

A new text for the liberal arts math course by a seasoned author team, Mathematical Excursions, is uniquely designed to help students see math at work in the contemporary world. Using the proven Aufmann Interactive Method, students learn to master problem-solving in meaningful contexts. In addition, multi-part Excursion exercises emphasize collaborative learning. The text's extensive topical coverage offers instructors flexibility in designing a course that meets their students' needs and curriculum requirements.

- The Excursions activity and corresponding Excursion Exercises, denoted by an icon, conclude each section, providing opportunities for in-class cooperative work, hands-on learning, and development of critical-thinking skills. These activities are also ideal for projects or extra credit assignments. The Excursions are designed to reinforce the material that has just been covered in the section in a fun and engaging manner that will enhance a student's journey and discovery of mathematics.
- The proven Aufmann Interactive Method ensures that students try concepts and manipulate real-life data as they progress through the material. Every objective contains at least one set of matched-pair examples. The method begins with a worked-out example with a solution in numerical and verbal formats to address different learning styles. The matched problem, called Check Your Progress, is left for the student to try. Each problem includes a reference to a fully worked out solution in an appendix to which the student can refer for immediate feedback, concept reinforcement, identification of problem areas, and prevention of frustration.
- Each Chapter Opener begins with a short introduction to a real data application, which is then highlighted again in one Excursions activity and in the corresponding Excursion Exercises at the end of a section. This specific Excursion will be denoted by an icon. A section-by-section table of contents is accompanied by a brief summary of the topics that will be covered in the chapter.

**Aufmann, Richard N. : Palomar College**

** **Richard Aufmann is Professor of Mathematics at Palomar College in California. He is the lead author of two best-selling developmental math series, a best-selling college algebra and trigonometry series, as well as several derivative math texts. The Aufmann name is highly recognized and respected among college mathematics faculty.

Lockwood, Joanne S. : Plymouth State College

Joanne Lockwood is Assistant Professor of Mathematics at Plymouth State College in Plymouth, New Hampshire. She is co-author with Aufmann and Vernon Barker on the hardback developmental series, Business Mathematics, Algebra with Trigonometry for College Students, and numerous software ancillaries that accompany Aufmann titles. She is also co-authoring Mathematical Excursions with Aufmann.

**1. Problem Solving**

Section 1.1 Inductive and Deductive Reasoning

Excursion: The Game of Sprouts by John H. Conway

Section 1.2 Problem Solving with Patterns

Excursion: Polygonal Numbers

Section 1.3 Problem-Solving Strategies

Excursion: Routes on a Probability Demonstrator

**2. Sets**

Section 2.1 Basic Properties of Sets

Excursion: Fuzzy Sets

Section 2.2 Subsets

Excursion: Subsets and Complements of Fuzzy Sets

Section 2.3 Set Operations

Excursion: Union and Intersection of Fuzzy Sets

Section 2.4 Applications of Sets

Excursion: Voting Systems

Section 2.5 Infinite Sets

Excursion: Transfinite Arithmetic

**3. Logic**

Section 3.1 Logic Statements and Quantifiers

Excursion: Switching Networks

Section 3.2 Truth Tables and Applications

Excursion: Switching Networks--Part II

Section 3.3 The Conditional and the Biconditional

Excursion: Logic Gates

Section 3.4 The Conditional and Related Statements

Excursion: Sheffer's Stroke and the NAND Gate

Section 3.5 Arguments

Excursion: Fallacies

Section 3.6 Euler Diagrams

Excursion: Use Logic to Solve Puzzles

**4. Numeration Systems and Topics from Number Theory**

Section 4.1 Early Numeration Systems

Excursion: A Rosetta Tablet for the Traditional Chinese Numeration System

Section 4.2 Place-Value Systems

Excursion: Subtraction via the Nines Complement and the End-Around Carry

Section 4.3 Different Base Systems

Excursion: Information Retrieval via a Binary Search

Section 4.4 Arithmetic in Different Bases

Excursion: Subtraction in Base Two via the Ones Complement and the End-Around Carry

Section 4.5 Prime Numbers and Selected Topics from Number Theory

Excursion: The Distribution of the Primes

Section 4.6 Additional Topics from Number Theory

Excursion: A Sum of the Divisors Formula

**5. Applications of Equations**

Section 5.1 First-Degree Equations

Excursion: Body Mass Index

Section 5.2 Rate, Ratio, and Proportion

Excursion: Earned Run Average

Section 5.3 Percent

Excursion: Federal Income Tax

Section 5.4 Second-Degree Equations

Excursion: The Sum and Product of the Solutions of Quadratic Equations

**6. Applications of Functions**

Section 6.1 Rectangular Coordinates and Functions

Excursion: Dilations of a Geometric Figure

Section 6.2 Properties of Linear Functions

Excursion: Negative Velocity

Section 6.3 Finding Linear Models

Excursion: A Linear Business Model

Section 6.4 Quadratic Functions

Excursion: Reflective Properties of a Parabola

Section 6.5 Exponential Functions and Their Applications

Excursion: Chess and Exponential Functions

Section 6.6 Logarithmic Functions and Their Applications

Excursion: Benford's Law

**7. Mathematical Systems**

Section 7.1 Modular Arithmetic

Excursion: Computing the Day of the Week

Section 7.2 Applications of Modular Arithmetic

Excursion: Public Key Cryptography

Section 7.3 Introduction to Group Theory

Excursion: Wallpaper Groups

**8. Geometry**

Section 8.1 Basic Concepts of Euclidean Geometry

Excursion: Preparing a Circle Graph

Section 8.2 Perimeter and Area of Plane Figures

Excursion: Slicing Polygons into Triangles

Section 8.3 Similar Triangles

Excursion: Topology

Section 8.4 Volume and Surface Area

Excursion: Water Displacement

Section 8.5 Non-Euclidean Geometry

Excursion: Find Geodesics

Section 8.6 Fractals

Excursion: The Heighway Dragon Fractal

**9. The Mathematics of Graphs**

Section 9.1 Traveling Roads and Visiting Cities

Excursion: Pen-Tracing Puzzles

Section 9.2 Efficient Routes

Excursion: Extending the Greedy Algorithm

Section 9.3 Planarity and Euler's Formula

Excursion: The Five Regular Convex Polyhedra

Section 9.4 Map Coloring and Graphs

Excursion: Modeling Traffic Lights with Graphs

**10. The Mathematics of Finance**

Section 10.1 Simple Interest

Excursion: Treasury Bills

Section 10.2 Compound Interest

Excursion: Consumer Price Index

Section 10.3 Consumer Loans

Excursion: Leasing versus Buying a Car

Section 10.4 Home Ownership

Excursion: Home Ownership Issues

**11. Combinatorics and Probability**

Section 11.1 The Counting Principle

Excursion: Decision Trees

Section 11.2 Permutations and Combinations

Excursion: Choosing Numbers in Keno

Section 11.3 Probability and Odds

Excursion: The Value of Pi by Simulation

Section 11.4 Addition and Complement Rules

Excursion: Keno Revisited

Section 11.5 Conditional Probability

Excursion: Sharing Birthdays

Section 11.6 Expectation

Excursion: Chuck-a-luck

**12. Statistics**

Section 12.1 Measures of Central Tendency

Excursion: Linear Interpolation and Animation

Section 12.2 Measures of Dispersion

Excursion: A Geometric View of Variance and Standard Deviation

Section 12.3 Measures of Relative Position

Excursion: Stem-and-Leaf Diagrams

Section 12.4 Normal Distributions

Excursion: Cut-Off Scores

Section 12.5 Linear Regression and Correlation

Excursion: An Application of Linear Regression

**13. Apportionment and Voting**

Section 13.1 Introduction to Apportionment

Excursion: Apportioning the 1790 House of Representatives

Section 13.2 Introduction to Voting

Excursion: Variations of the Borda Count Method

Section 13.3 Weighted Voting Systems

Excursion: Blocking Coalitions and the Banzhaf Power Index