{"product_id":"the-heart-of-mathematics-isbn-9781118156599","title":"The Heart of Mathematics","description":"\u003cp\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\u003esucceeds 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, \u003ci\u003eThe Heart of Mathematics\u003c\/i\u003e introduces students to the most important and interesting ideas in mathematics while inspiring them to actively engage in mathematical thinking.\u003c\/p\u003e 1.1 FUN AND GAMES \u003cp\u003eAn Introduction to Rigorous Thought\u003c\/p\u003e \u003cp\u003e1.1 Silly Stories, Each with a Moral\u003c\/p\u003e \u003cp\u003eConundrums that Evoke Techniques of Effective Thinking\u003c\/p\u003e \u003cp\u003e1.2 Nudges\u003c\/p\u003e \u003cp\u003eLeading Questions and Hints for Resolving the Stories\u003c\/p\u003e \u003cp\u003e1.3 The Punch Lines\u003c\/p\u003e \u003cp\u003eSolutions and Further Commentary\u003c\/p\u003e \u003cp\u003e1.4 From Play to Power\u003c\/p\u003e \u003cp\u003eDiscovering Strategies of Thought for Life\u003c\/p\u003e \u003cp\u003e2. NUMBER CONTEMPLATION\u003c\/p\u003e \u003cp\u003e2.1 Counting\u003c\/p\u003e \u003cp\u003eHow the Pigeonhole Principle Leads to Precision Through Estimation\u003c\/p\u003e \u003cp\u003e2.2 Numerical Patterns in Nature\u003c\/p\u003e \u003cp\u003eDiscovering the Beauty of the Fibonacci Numbers\u003c\/p\u003e \u003cp\u003e2.3 Prime Cuts of Numbers\u003c\/p\u003e \u003cp\u003eHow the Prime Numbers Are the Building Blocks of All Natural Numbers\u003c\/p\u003e \u003cp\u003e2.4 Crazy Clocks and Checking Out Bars\u003c\/p\u003e \u003cp\u003eCyclical Clock Arithmetic and Bar Codes\u003c\/p\u003e \u003cp\u003e2.5 Public Secret Codes and How to Become a Spy\u003c\/p\u003e \u003cp\u003eEncrypting Information Using Modular Arithmetic and Primes\u003c\/p\u003e \u003cp\u003e2.6 The Irrational Side of Numbers\u003c\/p\u003e \u003cp\u003eAre There Numbers Beyond Fractions?\u003c\/p\u003e \u003cp\u003e2.7 Get Real\u003c\/p\u003e \u003cp\u003eThe Point of Decimals and Pinpointing Numbers on the Real Line\u003c\/p\u003e \u003cp\u003e3. INFINITY\u003c\/p\u003e \u003cp\u003e3.1 Beyond Numbers\u003c\/p\u003e \u003cp\u003eWhat Does Infinity Mean?\u003c\/p\u003e \u003cp\u003e3.2 Comparing the Infinite\u003c\/p\u003e \u003cp\u003ePairing Up Collections via a One-to-One Correspondence\u003c\/p\u003e \u003cp\u003e3.3 The Missing Member\u003c\/p\u003e \u003cp\u003eGeorg Cantor Answers: Are Some Infinities Larger than Others?\u003c\/p\u003e \u003cp\u003e3.4 Travels Toward the Stratosphere of Infinities\u003c\/p\u003e \u003cp\u003eThe Power Set and the Question of an Infinite Galaxy of Infinities\u003c\/p\u003e \u003cp\u003e3.5 Straightening Up the Circle\u003c\/p\u003e \u003cp\u003eExploring the Infinite Within Geometrical Objects\u003c\/p\u003e \u003cp\u003e4. GEOMETRIC GEMS\u003c\/p\u003e \u003cp\u003e4.1 Pythagoras and His Hypotenuse\u003c\/p\u003e \u003cp\u003eHow a Puzzle Leads to the Proof of One of the Gems of Mathematics\u003c\/p\u003e \u003cp\u003e4.2 A View of an Art Gallery\u003c\/p\u003e \u003cp\u003eUsing Computational Geometry to Place Security Cameras in Museums\u003c\/p\u003e \u003cp\u003e4.3 The Sexiest Rectangle\u003c\/p\u003e \u003cp\u003eFinding Aesthetics in Life, Art, and Math Through the Golden Rectangle\u003c\/p\u003e \u003cp\u003e4.4 Soothing Symmetry and Spinning Pinwheels\u003c\/p\u003e \u003cp\u003eCan a Floor Be Tiled Without Any Repeating Pattern?\u003c\/p\u003e \u003cp\u003e4.5 The Platonic Solids Turn Amorous\u003c\/p\u003e \u003cp\u003eDiscovering the Symmetry and Interconnections Among the Platonic Solids\u003c\/p\u003e \u003cp\u003e4.6 The Shape of Reality?\u003c\/p\u003e \u003cp\u003eHow Straight Lines Can Bend in Non-Euclidean Geometries\u003c\/p\u003e \u003cp\u003e4.7 The Fourth Dimension\u003c\/p\u003e \u003cp\u003eCan You See It?\u003c\/p\u003e \u003cp\u003e5. CONTORTIONS OF SPACE\u003c\/p\u003e \u003cp\u003e5.1 Rubber Sheet Geometry\u003c\/p\u003e \u003cp\u003eDiscovering the Topological Idea of Equivalence by Distortion\u003c\/p\u003e \u003cp\u003e5.2 The Band That Wouldn’t Stop Playing\u003c\/p\u003e \u003cp\u003eExperimenting with the Möbius Band and Klein Bottle\u003c\/p\u003e \u003cp\u003e5.3 Knots and Links\u003c\/p\u003e \u003cp\u003eUntangling Ropes and Rings\u003c\/p\u003e \u003cp\u003e5.4 Fixed Points, Hot Loops and Rainy Days\u003c\/p\u003e \u003cp\u003eHow the Certainty of Fixed Points Implies Certain Weather Phenomena\u003c\/p\u003e \u003cp\u003e6. MODELING OUR WORLD THROUGH GRAPHS\u003c\/p\u003e \u003cp\u003e6.1 Circuit Training\u003c\/p\u003e \u003cp\u003eFrom the Königsberg Bridge Puzzle to Graphs\u003c\/p\u003e \u003cp\u003e6.2 Feeling Edgy?\u003c\/p\u003e \u003cp\u003eExploring Relationships Among Vertices, Edges, and Faces\u003c\/p\u003e \u003cp\u003e6.3 Plane Old Graphs\u003c\/p\u003e \u003cp\u003eDrawing in the Plane and Coloring Maps\u003c\/p\u003e \u003cp\u003e6.4 Networking\u003c\/p\u003e \u003cp\u003eUsing Graphical Models to Find the Shortest, Closest, and Cheapest\u003c\/p\u003e \u003cp\u003e7. FRACTALS AND CHAOS\u003c\/p\u003e \u003cp\u003e7.1 Images\u003c\/p\u003e \u003cp\u003eViewing a Gallery of Fractals\u003c\/p\u003e \u003cp\u003e7.2 The Infinitely Detailed Beauty of Fractals\u003c\/p\u003e \u003cp\u003eHow to Create Works of Infinite Intricacy Through Repeated Processes\u003c\/p\u003e \u003cp\u003e7.3 Between Dimensions\u003c\/p\u003e \u003cp\u003eCan the Dimensions of Fractals Fall Through the Cracks?\u003c\/p\u003e \u003cp\u003e7.4 Mysterious Art of Imaginary Fractals\u003c\/p\u003e \u003cp\u003eCreating Julia and Mandelbrot Sets by Stepping Out in the Complex Plane\u003c\/p\u003e \u003cp\u003e7.5 They Dynamics of Change\u003c\/p\u003e \u003cp\u003eCan Change Be Modeled by Repeated Applications of Simple Processes?\u003c\/p\u003e \u003cp\u003e7.6 Predetermined Chaos\u003c\/p\u003e \u003cp\u003eHow Repeated Simple Processes Result in Utter Chaos\u003c\/p\u003e \u003cp\u003e8. TAMING UNCERTAINTY\u003c\/p\u003e \u003cp\u003e8.1 Chance Surprises\u003c\/p\u003e \u003cp\u003eSome Scenarios Involving Chance That Confound Our Intuition\u003c\/p\u003e \u003cp\u003e8.2 Predicting the Future in an Uncertain World\u003c\/p\u003e \u003cp\u003eHow to Measure Uncertainty Using the Idea of Probability\u003c\/p\u003e \u003cp\u003e8.3 Random Thoughts\u003c\/p\u003e \u003cp\u003eAre Coincidences as Truly Amazing as They First Appear?\u003c\/p\u003e \u003cp\u003e8.4 Down for the Count\u003c\/p\u003e \u003cp\u003eSystematically Counting All Possible Outcomes\u003c\/p\u003e \u003cp\u003e8.5 Drizzling, Defending, and Doctoring\u003c\/p\u003e \u003cp\u003eProbability in Our World and Our Lives\u003c\/p\u003e \u003cp\u003e9. MEANING FROM DATA\u003c\/p\u003e \u003cp\u003e9.1 Stumbling Through a Minefield of Data\u003c\/p\u003e \u003cp\u003eInspiring Statistical Concepts Through Pitfalls\u003c\/p\u003e \u003cp\u003e9.2 Getting Your Data to Shape Up\u003c\/p\u003e \u003cp\u003eOrganizing, Describing, and Summarizing Data\u003c\/p\u003e \u003cp\u003e9.3 Looking at Super Models Mathematically Described Distributions\u003c\/p\u003e \u003cp\u003eMathematically Described Distributions\u003c\/p\u003e \u003cp\u003e9.4 Go Figure\u003c\/p\u003e \u003cp\u003eMaking Inferences from Data\u003c\/p\u003e \u003cp\u003e9.5 War, Sports, and Tigers\u003c\/p\u003e \u003cp\u003eStatistics Throughout Our Lives\u003c\/p\u003e \u003cp\u003e10. DECIDING WISELY\u003c\/p\u003e \u003cp\u003eApplications of Rigorous Thinking\u003c\/p\u003e \u003cp\u003e10.1 Great Expectations\u003c\/p\u003e \u003cp\u003eDeciding How to Weigh the Unknown Future\u003c\/p\u003e \u003cp\u003e10.2 Risk\u003c\/p\u003e \u003cp\u003eDeciding Personal and Public Policy\u003c\/p\u003e \u003cp\u003e10.3 Money Matters\u003c\/p\u003e \u003cp\u003eDeciding Between Faring Well and Welfare\u003c\/p\u003e \u003cp\u003e10.4 Peril at the Polls\u003c\/p\u003e \u003cp\u003eDeciding Who Actually Wins an Election\u003c\/p\u003e \u003cp\u003e10.5 Cutting Cake for Greedy People\u003c\/p\u003e \u003cp\u003eDeciding How to Slice Up Scarce Resources\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  \u003cp\u003e\u003cb\u003eWhat mathematics can offer students: an enriched and transformed life.\u003c\/b\u003e \u003ci\u003e—A note from the authors, Edward B. Burger and Michael Starbird\u003c\/i\u003e \u003c\/p\u003e\u003cp\u003eMathematicians encounter surprising and fascinating ideas such as infinity, chaos, fractals, the fourth dimension, rubber sheet geometry, coincidences, and other intriguing topics on a daily basis. These ideas portray effective strategies in everyday thinking that add value to how people make real-life decisions in areas of love and business to art and politics. We wrote \u003cb\u003eThe Heart of Mathematics: An Invitation to Effective Thinking\u003c\/b\u003e to make truly big and beautiful ideas accessible to all students and to give instructors the chance to offer their students delectable math morsels. \u003c\/p\u003e\u003cp\u003eReactions to \u003cb\u003eThe Heart of Mathematics: An Invitation to Effective Thinking\u003c\/b\u003e: \u003c\/p\u003e\u003cp\u003eFROM FACULTY: \u003c\/p\u003e\u003cul\u003e \u003cli\u003e\"\u003cb\u003eHeart of Mathematics\u003c\/b\u003e is easily the best liberal arts math textbook I've ever used.\" \u003ci\u003e—Shippensburg University\u003c\/i\u003e\n\u003c\/li\u003e \u003cli\u003e\"This is very possibly the best mathematics for the non-mathematician book that I've seen.\" \u003ci\u003e\t—American Mathematical Monthly\u003c\/i\u003e\n\u003c\/li\u003e \u003cli\u003e\"For me this book has changed our 'liberal arts math class' from a dreaded assignment to something that is lively and interesting every time.\" \u003ci\u003e—Buffalo State College\u003c\/i\u003e\n\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eFROM STUDENTS: \u003c\/p\u003e\u003cul\u003e\t \u003cli\u003e\"This is far and away the best mathematics textbook I've ever used.\"\u003c\/li\u003e \u003cli\u003e\"This class was not like any other math class. It allowed me to become creative and imaginative.\" \u003c\/li\u003e \u003cli\u003e\"This math book is incredible. It teaches you math in the purest sense of the word. Also, it was funny and challenging.\" \t\t\t\t\t\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThe goal of education is to improve students' ability to think, and \u003cb\u003eThe Heart of Mathematics\u003c\/b\u003e does just that—inviting students to think about how mind-changing ideas can transform lives.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"New","offer_id":44813391986917,"sku":"NP9781118156599","price":173.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118156599.jpg?v=1761780868","url":"https:\/\/k12savings.com\/products\/the-heart-of-mathematics-isbn-9781118156599","provider":"K12savings","version":"1.0","type":"link"}