{"product_id":"the-heart-of-mathematics-isbn-9781118235706","title":"The Heart of Mathematics","description":"\u003cp\u003e\u003cb\u003eThis text is an unbound, binder-ready edition\u003c\/b\u003e.\u003cbr\u003e\u003cbr\u003eTransform your mathematics course into an engaging and mind-opening experience for even your most math-phobic students. Now in its Fourth Edition, \u003cb\u003e\u003ci\u003eThe Heart of Mathematics: An Invitation to Effective Thinking\u003c\/i\u003e\u003c\/b\u003e succeeds at reaching non-math, non-science-oriented majors, encouraging them to discover the mathematics inherent in the world around them. Infused with the author’s humor and enthusiasm throughout, \u003cb\u003e\u003ci\u003eThe Heart of Mathematics\u003c\/i\u003e\u003c\/b\u003e introduces students to the most important and interesting ideas in mathematics while inspiring them to actively engage in mathematical thinking.\u003c\/p\u003e \u003cb\u003e1.     \u003c\/b\u003e\u003cb\u003eFUN AND GAMES\u003c\/b\u003e \u003cp\u003e\u003ci\u003eAn Introduction to Rigorous Thought\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e1.1  Silly Stories, Each with a Moral\u003c\/p\u003e \u003cp\u003e\u003ci\u003eConundrums that Evoke Techniques of Effective Thinking\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e1.2  Nudges\u003c\/p\u003e \u003cp\u003e\u003ci\u003eLeading Questions and Hints for Resolving the Stories\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e1.3  The Punch Lines\u003c\/p\u003e \u003cp\u003e\u003ci\u003eSolutions and Further Commentary\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e1.4  From Play to Power\u003c\/p\u003e \u003cp\u003e\u003ci\u003eDiscovering Strategies of Thought for Life\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003e \u003c\/i\u003e\u003c\/p\u003e \u003cb\u003e2.     \u003c\/b\u003e\u003cb\u003eNUMBER CONTEMPLATION\u003c\/b\u003e \u003cp\u003e2.1  Counting\u003c\/p\u003e \u003cp\u003e\u003ci\u003eHow the Pigeonhole Principle Leads to Precision Through Estimation\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.2  Numerical Patterns in Nature\u003c\/p\u003e \u003cp\u003e\u003ci\u003eDiscovering the Beauty of the Fibonacci Numbers\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.3  Prime Cuts of Numbers\u003c\/p\u003e \u003cp\u003e\u003ci\u003eHow the Prime Numbers Are the Building Blocks of All Natural Numbers\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.4  Crazy Clocks and Checking Out Bars\u003c\/p\u003e \u003cp\u003e\u003ci\u003eCyclical Clock Arithmetic and Bar Codes\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.5  Public Secret Codes and How to Become a Spy\u003c\/p\u003e \u003cp\u003e\u003ci\u003eEncrypting Information Using Modular Arithmetic and Primes\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.6  The Irrational Side of Numbers\u003c\/p\u003e \u003cp\u003e\u003ci\u003eAre There Numbers Beyond Fractions?\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e2.7  Get Real\u003c\/p\u003e \u003cp\u003e\u003ci\u003eThe Point of Decimals and Pinpointing Numbers on the Real Line\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cb\u003e3.     \u003c\/b\u003e\u003cb\u003eINFINITY\u003c\/b\u003e \u003cp\u003e3.1  Beyond Numbers\u003c\/p\u003e \u003cp\u003e\u003ci\u003eWhat Does Infinity Mean?\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e3.2  Comparing the Infinite\u003c\/p\u003e \u003cp\u003e\u003ci\u003ePairing Up Collections via a One-to-One Correspondence\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e3.3  The Missing Member\u003c\/p\u003e \u003cp\u003e\u003ci\u003eGeorg Cantor Answers: Are Some Infinities Larger than Others?\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e3.4  Travels Toward the Stratosphere of Infinities\u003c\/p\u003e \u003cp\u003e\u003ci\u003eThe Power Set and the Question of an Infinite Galaxy of Infinities\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e3.5 Straightening Up the Circle\u003c\/p\u003e \u003cp\u003e\u003ci\u003eExploring the Infinite Within Geometrical Objects\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cb\u003e4.     \u003c\/b\u003e\u003cb\u003eGEOMETRIC GEMS\u003c\/b\u003e \u003cp\u003e4.1  Pythagoras and His Hypotenuse\u003c\/p\u003e \u003cp\u003e\u003ci\u003eHow a Puzzle Leads to the Proof of One of the Gems of Mathematics\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e4.2  A View of an Art Gallery\u003c\/p\u003e \u003cp\u003e\u003ci\u003eUsing Computational Geometry to Place Security Cameras in Museums\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e4.3  The Sexiest Rectangle\u003c\/p\u003e \u003cp\u003e\u003ci\u003eFinding Aesthetics in Life, Art, and Math Through the Golden Rectangle\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e4.4  Soothing Symmetry and Spinning Pinwheels\u003c\/p\u003e \u003cp\u003e\u003ci\u003eCan a Floor Be Tiled Without Any Repeating Pattern?\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e4.5  The Platonic Solids Turn Amorous\u003c\/p\u003e \u003cp\u003e\u003ci\u003eDiscovering the Symmetry and Interconnections Among the Platonic Solids\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e4.6  The Shape of Reality?\u003c\/p\u003e \u003cp\u003e\u003ci\u003eHow Straight Lines Can Bend in Non-Euclidean Geometries\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e4.7  The Fourth Dimension\u003c\/p\u003e \u003cp\u003e\u003ci\u003eCan You See It?\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cb\u003e5.     \u003c\/b\u003e\u003cb\u003eCONTORTIONS OF SPACE\u003c\/b\u003e \u003cp\u003e5.1  Rubber Sheet Geometry\u003c\/p\u003e \u003cp\u003e\u003ci\u003eDiscovering the Topological Idea of Equivalence by Distortion\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.2  The Band That Wouldn�t Stop Playing\u003c\/p\u003e \u003cp\u003e\u003ci\u003eExperimenting with the Möbius Band and Klein Bottle\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.3  Knots and Links\u003c\/p\u003e \u003cp\u003e\u003ci\u003eUntangling Ropes and Rings\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e5.4  Fixed Points, Hot Loops and Rainy Days\u003c\/p\u003e \u003cp\u003e\u003ci\u003eHow the Certainty of Fixed Points Implies Certain Weather Phenomena\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cb\u003e6.     \u003c\/b\u003e\u003cb\u003eMODELING OUR WORLD THROUGH GRAPHS\u003c\/b\u003e \u003cp\u003e6.1  Circuit Training\u003c\/p\u003e \u003cp\u003e\u003ci\u003eFrom the Königsberg Bridge Puzzle to Graphs\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e6.2  Feeling Edgy?\u003c\/p\u003e \u003cp\u003e\u003ci\u003eExploring Relationships Among Vertices, Edges, and Faces\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e6.3  Plane Old Graphs\u003c\/p\u003e \u003cp\u003e\u003ci\u003eDrawing in the Plane and Coloring Maps\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e6.4  Networking\u003c\/p\u003e \u003cp\u003e\u003ci\u003eUsing Graphical Models to Find the Shortest, Closest, and Cheapest\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cb\u003e7.     \u003c\/b\u003e\u003cb\u003eFRACTALS AND CHAOS\u003c\/b\u003e \u003cp\u003e7.1  Images\u003c\/p\u003e \u003cp\u003e\u003ci\u003eViewing a Gallery of Fractals\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.2 The Infinitely Detailed Beauty of Fractals\u003c\/p\u003e \u003cp\u003e\u003ci\u003eHow to Create Works of Infinite Intricacy Through Repeated Processes\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.3  Between Dimensions\u003c\/p\u003e \u003cp\u003e\u003ci\u003eCan the Dimensions of Fractals Fall Through the Cracks?\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.4  Mysterious Art of Imaginary Fractals\u003c\/p\u003e \u003cp\u003e\u003ci\u003eCreating Julia and Mandelbrot Sets by Stepping Out in the Complex Plane\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.5  They Dynamics of Change\u003c\/p\u003e \u003cp\u003e\u003ci\u003eCan Change Be Modeled by Repeated Applications of Simple Processes?\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e7.6  Predetermined Chaos\u003c\/p\u003e \u003cp\u003e\u003ci\u003eHow Repeated Simple Processes Result in Utter Chaos\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cb\u003e8.     \u003c\/b\u003e\u003cb\u003eTAMING UNCERTAINTY\u003c\/b\u003e \u003cp\u003e8.1  Chance Surprises\u003c\/p\u003e \u003cp\u003e\u003ci\u003eSome Scenarios Involving Chance That Confound Our Intuition\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e8.2  Predicting the Future in an Uncertain World\u003c\/p\u003e \u003cp\u003e\u003ci\u003eHow to Measure Uncertainty Using the Idea of Probability\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e8.3  Random Thoughts\u003c\/p\u003e \u003cp\u003e\u003ci\u003eAre Coincidences as Truly Amazing as They First Appear?\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e8.4  Down for the Count\u003c\/p\u003e \u003cp\u003e\u003ci\u003eSystematically Counting All Possible Outcomes\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e8.5  Drizzling, Defending, and Doctoring\u003c\/p\u003e \u003cp\u003e\u003ci\u003eProbability in Our World and Our Lives\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cbr\u003e\u003cb\u003e9.     \u003c\/b\u003e\u003cb\u003eMEANING FROM DATA\u003c\/b\u003e \u003cp\u003e9.1  Stumbling Through a Minefield of Data\u003c\/p\u003e \u003cp\u003e\u003ci\u003eInspiring Statistical Concepts Through Pitfalls\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e9.2  Getting Your Data to Shape Up\u003c\/p\u003e \u003cp\u003e\u003ci\u003eOrganizing, Describing, and Summarizing Data\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e9.3  Looking at Super Models\u003c\/p\u003e \u003cp\u003e\u003ci\u003eMathematically Described Distributions\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e9.4  Go Figure\u003c\/p\u003e \u003cp\u003e\u003ci\u003eMaking Inferences from Data\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e9.5  War, Sports, and Tigers\u003c\/p\u003e \u003cp\u003e\u003ci\u003eStatistics Throughout Our Lives\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e\u003cb\u003e10.  \u003c\/b\u003e\u003cb\u003eDECIDING WISELY\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eApplications of Rigorous Thinking\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.1        Great Expectations\u003c\/p\u003e \u003cp\u003e\u003ci\u003eDeciding How to Weigh the Unknown Future\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.2        Risk\u003c\/p\u003e \u003cp\u003e\u003ci\u003eDeciding Personal and Public Policy\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.3        Money Matters\u003c\/p\u003e \u003cp\u003e\u003ci\u003eDeciding Between Faring Well and Welfare\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.4        Peril at the Polls\u003c\/p\u003e \u003cp\u003e\u003ci\u003eDeciding Who Actually Wins an Election\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e10.5        Cutting Cake for Greedy People\u003c\/p\u003e \u003cp\u003e\u003ci\u003e                                    Deciding How to Slice Up Scarce Resources\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eDr. Edward Burger\u003c\/b\u003e is a professor mathematics at Williams College in Williamstown, MA. He received his BA from Connecticut College and his PhD from University of Texas at Austin.\u003cbr\u003eHe has received numerous awards including: the \u003ci\u003eNelson Bushnell Prize\u003c\/i\u003e, for Scholarship and Teaching, Williams College, being listed among the top 100 best Math Teachers in the \"\u003ci\u003e100 Best of America\",\u003c\/i\u003e Reader's Digest's Annual Special Issue. He has also received the \u003ci\u003eAward of Excellence\u003c\/i\u003e, for \"educational mathematics videos that break new ground\", from \u003ci\u003eTechnology \u0026amp; Learning\u003c\/i\u003e magazine.\u003cbr\u003eHis research interests include Algebraic Number Theory, Diophantine Analysis, \u003ci\u003ep\u003c\/i\u003eadic Analysis, Geometry of Numbers, and the Theory of Continued Fractions.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47990256992485,"sku":"NP9781118235706","price":111.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118235706.jpg?v=1761787091","url":"https:\/\/k12savings.com\/es\/products\/the-heart-of-mathematics-isbn-9781118235706","provider":"K12savings","version":"1.0","type":"link"}