Cover
Frontmatter
Introduction and Welcome: To Know the End from the Beginning…
Chapter 1: Reasoning and Resources: Tools for Life
1.0 Introduction and Objectives
1.1 Analytical Reasoning: A Tool for Life
Project: Pascal’s Famous Triangle
1.2 Math Classics and Applied Reasoning
Project: Guards and Prisoners
Project: Cross-number Puzzle
1.3 Resources for the Present and the Future
Project: MERLOT and You
Chapter 2: Patterns and Reasoning: Fun with Math!
2.0 Introduction and Objectives
2.1 Deductive and Inductive Reasoning
Project: A Riddling Good Time
2.2 Pattern Recognition: Searching for Connections
Project: The Curious Date: 7-14-98
Project: Another Curious Date: 10-1-01
2.3 The nth Term: The Power of Generalization
Project: Sequence Creations
Project: Generalization—A Powerful Tool
2.4 Logical Thinking and Reasoning Backwards
Project: Puzzle Constructions
2.5 Magic Squares: Sum Fun!
Project: Magic Squares
Project: Magic Square Extensions
Chapter 3: Math from Other Times and Places: Historical Investigations
3.0 Introduction and Objectives
3.1 The Greeks: Students and Investigators
Project: Polygonal Numbers—A Geometric View
3.2 Pascal’s Amazing Triangle: Simple yet Profound
Project: Pascal’s Triangle
3.3 Number Systems through the Ages: Stylistic and Diverse
Project: The Abacus
Project: Numeration in Other Cultures
Chapter 4: Number Bases: Surprising Versatility
4.0 Introduction and Objectives
4.1 Understanding Other Number Bases: Places of Value
Project: The Banker’s Dilemma
4.2 The Binary System: Secret Language of Computers
Project: Chinese Trigrams and Binary Numbers
Project: The ASCII Code
Project: Course Logo: A Hidden Message
4.3 Number Base Applications: More Fun with Math!
Project: Hexadecimals
Chapter 5: Modulus Arithmetic and Its Many Uses
5.0 Introduction and Objectives
5.1 Clock Systems: The Cycles of Life
Project: Perpetual Calendar
5.2 The Modulus in Action: Check Digits and Error Detection
Project: ISBN Numbers and Modulus Arithmetic
Project: ISMN Numbers and Modulus Arithmetic
5.3 Cryptography: The Mathematics of Privacy
Project: Cryptograms—A Popular Pastime
Project: Cryptoquotes—Another Favorite
Chapter 6: Mathematics and Music: Inseparable Partners
6.0 Introduction and Objectives
6.1 The Nature of Sound and Musical Scales: Good Vibrations
Project: Creating Good Vibrations
Project: Famous Math Quotes
6.2 The Mathematics of Stringed Instruments: Structured Harmony
Project: Guitar Analysis
6.3 Digital Music and CD’s: Applied Mathematics
Project: Digital Music and Mathematics
Chapter 7: Mathematics in Art, Architecture and Nature
7.0 Introduction and Objectives
7.1 Mathematical Perspective in Art: A Renaissance Breakthrough
Project: Mathematical Perspective
7.2 Symmetry and Tilings: Mathematical Beauty and Artistry
Project: Tilings in your Home
Project: Symmetry and Tilings
Project: The Mathematical Art of M.C. Escher
7.3 Mathematics in Architecture and Nature: The Golden Section and Fibonacci
Project: The Amazing Rabbit Population
Project: Golden Rectangles in your Home
Project: Fibonacci Numbers in Nature and the Arts
Project: Logarithmic Spirals—Seashell Design
7.4 Long-term Projects
Project: Webliography Report
Project: Term Report
Project: Stock Market Investment Report
Chapter 8: Fractals: New Structures in Mathematics
8.0 Introduction and Objectives
8.1 Mathematical Fractals: A Natural Geometry
Project: Introduction to Fractals
8.2 Fractal Applications
Project: Fractals in Nature
Project: Fractal Music
Project: Fractal Art
8.3 Famous Triangles: Sierpinski Meets Pascal
Project: Triangle Connections
Chapter 9: Linear Relationships: Straight as an Arrow
9.0 Introduction and Objectives
9.1 Mathematical Relationships and Functions: “Vary-ables” in Action
Project: The Shape of Daylight
9.2 Linear Functions: A Deeper Look
9.3 Linear Models: Analytic and Predictive
Project: How Does your Lawn Grow?
Project: How Does your Garden Grow?
Chapter 10: Exponential Growth: Drama and Suspense
10.0 Introduction and Objectives
10.1 Doubling Power: An Amazing Phenomenon
10.2 The Exponential Function: A Deeper Look
Project: World Population Growth
10.3 Exponential Models and Applications
Project: U.S. Population Growth
Project: The Fastest Growing State in the U.S.?
Project: Population Growth in Florida
Chapter 11: Financial Planning: Mathematical Secrets to Acquiring Wealth
11.0 Introduction and Objectives
11.1 Compound Interest: Strategies for Wealth
Project: The Long-Term Results of Compound Interest
11.2 Savings Plans: Don’t Leave Home Without One!
Project: Intro to Savings and Investment
11.3 Stocks, Bonds and Mutual Funds
Project: Intro to Stocks, Bonds and Mutual Funds
Project: Investment Strategies
Project: A True and Amazing Story
Project: Stock Market Investment Report
11.4 Home Mortgages: Mathematical Revelations
Project: The All-Powerful Interest Rate
11.5 Credit Card Economics
Project: Credit Reports and Ratings: An Inside Look
Project: The Truth about Credit Card Debt
Appendices
Appendix A: Helps and Hints for Exercises and Projects
Appendix B: Cross-number Puzzle Terminology
Appendix C: Guide to Correlation Coefficients
Appendix D: Fractal Structures: Italian Parsley