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Mathematical Excursions-Package

Mathematical Excursions-Package - 04 edition

Mathematical Excursions-Package - 04 edition

ISBN13: 9780618736829

ISBN10: 0618736824

Mathematical Excursions-Package by Richard Aufmann, Joanne Lockwood, Richard Nation and Daniel Clegg - ISBN 9780618736829
Edition: 04
Copyright: 2004
Publisher: Houghton Mifflin Harcourt
International: No
Mathematical Excursions-Package by Richard Aufmann, Joanne Lockwood, Richard Nation and Daniel Clegg - ISBN 9780618736829

ISBN13: 9780618736829

ISBN10: 0618736824

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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.

Table of Contents

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