The Heart of Mathematics: An Invitation to Effective Thinking
by Edward B. Burger (Williams College); Michael Starbird ( The University of Texas at Austin )Edition: 2nd
Format: Hardcover
Pub. Date: 2008-06-01
Publisher(s): WILEY
Other versions by this Author
-
This Item Qualifies for Free Shipping!*
*Excludes marketplace orders.
List Price: $187.90
Rent Textbook
Select for Price
New Textbook
We're Sorry
Sold Out
Used Textbook
We're Sorry
Sold Out
eTextbook
We're Sorry
Not Available
How Marketplace Works:
- This item is offered by an independent seller and not shipped from our warehouse
- Item details like edition and cover design may differ from our description; see seller's comments before ordering.
- Sellers much confirm and ship within two business days; otherwise, the order will be cancelled and refunded.
- Marketplace purchases cannot be returned to eCampus.com. Contact the seller directly for inquiries; if no response within two days, contact customer service.
- Additional shipping costs apply to Marketplace purchases. Review shipping costs at checkout.
Summary
The Heart of Mathematics: An invitation to effective thinking --now in its second edition--succeeds at reaching non-math, non-science-oriented readers and encourages them to discover the mathematics inherent in the world around them. Infused throughout with the authors' humor and enthusiasm, The Heart of Mathematics introduces readers to the most important and interesting ideas in mathematics while inspiring them to actively engage in mathematical thinking.
Table of Contents
| But First, a Word from our Sponsors | p. ix |
| Welcome! | p. xi |
| Surfing the Book | p. xv |
| Fun and Games: An Introduction to Rigorous Thought | p. 2 |
| Silly Stories Each with a Moral | p. 4 |
| Conundrums that Evoke Techniques of Effective Thinking | |
| Nudges | p. 4 |
| Leading Questions and Hints for Resolving the Stories | |
| The Punch Lines | p. 18 |
| Solutions and Further Commentary | |
| From Play to Power | p. 27 |
| Discovering Strategies of Thought for Life | |
| Number Contemplation | p. 38 |
| Counting | p. 40 |
| How the Pigeonhole Principle Leads to Precision Through Estimation | |
| Numberical Patterns in Nature | p. 49 |
| Discovering the Beauty of the Fibonacci Numbers | |
| Prime Cuts of Numbers | p. 64 |
| How the Primes Numbers are the Building Blocks of All Natural Numbers | |
| Crazy Clocks and Checking Out Bars | p. 82 |
| Cyclical Clock Arithmetic and Bar Codes | |
| Public Secret Codes adn How to Become a Spy | p. 95 |
| Encrypting Information Using Modula Arithmetic and Primes | |
| The Irrational Side of Numbers | p. 110 |
| Are There Numbers Beyond Fractions? | |
| Get Real | p. 121 |
| The Point of Decimals and Pinpointing Numbers on the Real Line | |
| Infinity | p. 136 |
| Beyond Numbers | p. 138 |
| What Does Infinity Mean? | |
| Comparing the Infinite | p. 145 |
| Pairing Up Collections via a One-to-One Corerspondence | |
| The Missing Member | p. 162 |
| Georg Cantor Answers: Are Some Infinities Larger Than Others? | |
| Geometric Gems | p. 206 |
| Pythagoras and His Hypotenuse | p. 208 |
| How a Puzzle Leads to the Proof of one of the Gems of Mathematics | |
| A View of an Art Gallery | p. 218 |
| Using Computational Geometry to Place Security Cameras in Musuems | |
| The Sexiest Rectangle | p. 232 |
| Finding Aesthetics in Life, Art, and Math Through the Golden Rectangle | |
| Soothing Symmetry and Spinning Pinwheels | p. 249 |
| Can a Floor be Tiled without any Repeating Pattern? | |
| The Platonic Solids Turn Amorous | p. 269 |
| Discovering the Symmetry and Interconnections Among the Platonic Solds | |
| The Shape of Reality? | p. 289 |
| How Straight Lines Can Bend in Non-Euclidean Geometries | |
| The Fouther Dimension | p. 307 |
| Can You See It? | |
| Contortions of Space | p. 326 |
| Rubger Sheet Geometry | p. 328 |
| Discovering the Topological Idea of Equivalence by Distortion | |
| The Band That Wouldn't Stop Playing | p. 46 |
| Experimenting with the Mobius Band and Klein Bottle | |
| Feeling Edgy? | p. 359 |
| Exploring Relationships Among Vertices, Edges, and Faces | |
| Knots and Links | p. 374 |
| Untangling Ropes and Rings | |
| Fixed Points, Hot Loops, and Rainy Days | p. 389 |
| How the Certainty of Fixed Points Implies Certain Weather Phenomena | |
| Chaos and Fractals | p. 402 |
| Images | p. 404 |
| Viewing a Gallery of Fractals | |
| The Dynamics of Change | p. 412 |
| Can Change be Modeled by Repeated Applications of Simple Processes? | |
| The Infinitely Detailed Beuty of Fractals | p. 430 |
| How to Create Workds of Ifinite Intricacy THrough Repeated PRocesses | |
| The Mysterious Art of Imaginary Fractals | p. 458 |
| Creating Juila and Mandelbrot Sets by Stepping Out in the Complex Plane | |
| Predetermined Chase | p. 482 |
| How Repeated SImple Processes Result in Utter Chaos | |
| Between Dimnsions | p. 503 |
| Can the Dimensions of Fractals Fall Through the Cracks? | |
| Taming Uncertainty | p. 514 |
| Chance Surprises | p. 516 |
| Some Scenarioos Involving Chance that Confound our Intuition | |
| Table of Contents provided by Publisher. All Rights Reserved. |
An electronic version of this book is available through VitalSource.
This book is viewable on PC, Mac, iPhone, iPad, iPod Touch, and most smartphones.
By purchasing, you will be able to view this book online, as well as download it, for the chosen number of days.
Digital License
You are licensing a digital product for a set duration. Durations are set forth in the product description, with "Lifetime" typically meaning five (5) years of online access and permanent download to a supported device. All licenses are non-transferable.
More details can be found here.
A downloadable version of this book is available through the eCampus Reader or compatible Adobe readers.
Applications are available on iOS, Android, PC, Mac, and Windows Mobile platforms.
Please view the compatibility matrix prior to purchase.