by Richard Aufmann, Joanne Lockwood, Richard Nation and Daniel Clegg

ISBN13: 978-0618736829

ISBN10: 0618736824

Cover type:

Edition/Copyright: 04

Publisher: Houghton Mifflin Harcourt

Published: 2004

International: No

ISBN10: 0618736824

Cover type:

Edition/Copyright: 04

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.

**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 a 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 Place Figures

Excursion: Slicing Polygons into Triangles

Section 8.3 Similar Triangles

Excursion: Topology

Section 8.4 Surface Area and Volume

Excursion: Water Displacement

Section 8.5 Non-Euclidean Geometry

Excursion: Find Geodesics

Section 8.6 Fractals

Excursion: The Heightway 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: Compounding Continuously

Section 10.3 Consumer Loans

Excursion: Consumer Price Index

Section 10.4 Home Ownership

Excursion: The Periodic Payment Formula

**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, Animation, and Morphing

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: Voting Paradoxes

Section 13.3 Weighted Voting Systems

Excursion: Blocking Coalitions and the Banzhaf Power Index

Richard Aufmann, Joanne Lockwood, Richard Nation and Daniel Clegg

ISBN13: 978-0618736829ISBN10: 0618736824

Cover type:

Edition/Copyright: 04

Publisher: Houghton Mifflin Harcourt

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.

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 a 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 Place Figures

Excursion: Slicing Polygons into Triangles

Section 8.3 Similar Triangles

Excursion: Topology

Section 8.4 Surface Area and Volume

Excursion: Water Displacement

Section 8.5 Non-Euclidean Geometry

Excursion: Find Geodesics

Section 8.6 Fractals

Excursion: The Heightway 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: Compounding Continuously

Section 10.3 Consumer Loans

Excursion: Consumer Price Index

Section 10.4 Home Ownership

Excursion: The Periodic Payment Formula

**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, Animation, and Morphing

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: Voting Paradoxes

Section 13.3 Weighted Voting Systems

Excursion: Blocking Coalitions and the Banzhaf Power Index

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