Mathematical Excursions - With Cd - 04 edition

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