The Heart of Mathematics: An Invitation to Effective Thinking / Edition 2

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This text is an unbound, binder-ready edition.

Transform your mathematics course into an engaging and mind-opening experience for even your most math-phobic students. Now in its Fourth Edition, The Heart of Mathematics: An Invitation to Effective Thinking succeeds at reaching non-math, non-science-oriented majors, encouraging them to discover the mathematics inherent in the world around them. Infused with the authors’ humor and enthusiasm throughout, The Heart of Mathematics introduces students to the most important and interesting ideas in mathematics while inspiring them to actively engage in mathematical thinking.

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Product Details

  • ISBN-13: 9780470412879
  • Publisher: Wiley
  • Publication date: 6/10/2008
  • Edition description: Older Edition
  • Edition number: 2
  • Pages: 784
  • Product dimensions: 7.50 (w) x 9.60 (h) x 1.30 (d)

Meet the Author

Edward B. Burger is professor of mathematics in the Department of Mathematics and Statistics at Williams College. He graduated from Connecticut College in 1985, where he earned B.A. Summa Cum Laude with Distinction in Mathematics, and received his Ph.D. in mathematics from the University of Texas at Austin. He did his postdoctoral work at the University of Waterloo in Canada. Dr. Burger has received numerous awards including:  the Award of Excellence, for "educational mathematics videos that break new ground from the Technology & Learning magazine, and the Distinguished Achievement Award, for Educational Video Technology from The Association of Educational Publishers.  He was honored as one of the "100 Best of America", Listed in Reader's Digest's Annual Special Issue as Best Math Teacher.  He also received the Residence Life Academic Teaching Award, University of Colorado at Boulder and the Robert W. Hamilton Book Award, for "The Heart of Mathematics".

Michael Starbird Michael Starbird is a University Distinguished Teaching Professor of Mathematics at The University of Texas at Austin. He has received more than a dozen teaching awards including the Mathematical Association of America’s 2007 national teaching award and several university-wide teaching awards based largely on his course in mathematics for liberal arts students. Starbird brings intriguing mathematics to general audiences through his classes, lectures, books, and video courses. In 1989, Starbird was UT’s Recreational Sports Super Racquets Champion.

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Table of Contents

CHAPTER ONE: Fun and Games: An introduction to rigorous thought

CHAPTER TWO: Number Contemplation
Section 2.1. Counting [Pigeonhole principle].
Section 2.2. Numerical Patterns in Nature: [Fibonacci numbers].
Section 2.3. Prime cuts of numbers [Prime numbers].
Section 2.4. Crazy clocks and checking out bars [Modular arithmetic].
Section 2.5. Secret Codes and How to Become a Spy [RSA public key cryptography].
Section 2.6. The irrational side of numbers [Irrational numbers].
Section 2.7. Get real [The real number line].

Section 3.1. Beyond Numbers [An introduction to one-to-one correspondence].
Section 3.2. Comparing the Infinite [Examples of one-to-one correspondences].
Section 3.3. The Missing Member [Cantor's diagonalization proof that |N|<|R|].
Section 3.4. Travels Toward the Stratosphere of Infinities [Power set theorem].
Section 3.5. Straightening up the circle [Geometrical correspondences].

CHAPTER FOUR: Geometric Gems
Section 4.1. Pythagoras and his hypotenuse [Blaskara's elegant proof].
Section 4.2. A view of an art gallery [A view-obstruction question from computational geometry].
Section 4.3. The sexiest rectangle [The Golden Rectangle].
Section 4.4. Soothing symmetry and spinning pinwheels [Aperiodic tilings].
Section 4.5. The Platonic Solids Turn Amorous [Symmetry and duality in the Platonic Solids].
Section 4.6. The shape of reality? [Non-Euclidean geometries].
Section 4.7. The Fourth Dimension [Geometry through analogy].

CHAPTER FIVE: Contortions of Space
Section 5.1. Rubber sheet geometry [Topological equivalence by distortion].
Section 5.2. The Band That Wouldn't Stop Playing [Möbius Band and Klein Bottle].
Section 5.3. Circuit training. [The Euler circuit theorem].
Section 5.4. Feeling edgy? [The Euler characteristic].
Section 5.5. Knots and links [A little knot theory].
Section 5.6. Fixed Points, Hot Loops, and Rainy Days [The Brouwer Fixed Point Theorem].

CHAPTER SIX: Fractals and Chaos
Section 6.1. Images [A gallery of fractals].
Section 6.2. The infinitely detailed beauty of fractals [Creating fractals through repeated processes].
Section 6.3. Between dimensions [Fractal dimension].
Section 6.4. The mysterious art of imaginary fractals [Julia and Mandelbrot Sets].
Section 6.5. The Dynamics of Change [Repeated applications of simple processes].
Section 6.6. Predetermined chaos [Deterministic chaos].

CHAPTER SEVEN: Taming Uncertainty
Section 7.1. Chance surprises [Unexpected scenarios involving chance].
Section 7.2. Predicting the future in an uncertain world [Probability].
Section 7.3. Random thoughts [Coincidences].
Section 7.4. Down for the count [Systematic counting].
Section 7.5. Dizzling, Defending, and Doctoring [Probability of Precipitation, game theory, Bayesian probability]

CHAPTER EIGHT: Meaning from Data
Section 8.1. Stumbling Through a Minefield of Data [Pitfalls of statistics].
Section 8.2. Getting Your Data to Shape Up [Organizing, describing, and summarizing data]
Section 8.3. Looking at Super Models [Mathematically described distributions]
Section 8.4. Go Figure [Making inferences from data, hypothesis testing]
Section 8.5. War, Sports, and Tigers [Cause and effect and correlation, Simpson's Paradox, famous applications of inference]

CHAPTER NINE: Deciding Wisely
Section 9.1. Great Expectations [Expected value]
Section 9.2. Risk [Deciding personal and public safety]
Section 9.3. Money Matters [Compound interest]
Section 9.4. Peril at the polls [voting]
Section 9.5. Cutting cake for greedy people [fair division]

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