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The Fate of Schrodinger's Cat

Can we correctly predict the flip of a fair coin more than half the time — or the decay of a single radioactive atom? Our intuition, based on a lifetime of experience, tells us that we cannot, as these are classic examples of what are known to be 50–50 guesses.But mathematics is filled with counterintuitive results — and this book discusses some surprising and entertaining examples. It is possible to devise experiments in which a flipped coin lands heads completely at random half the time, but we can also correctly predict when it will land heads more than half the time. The Fate of Schrodinger's Cat shows how high-school algebra and basic probability theory, with the invaluable assistance of computer simulations, can be used to investigate both the intuitive and the counterintuitive.This book explores fascinating and controversial questions involving prediction, decision-making, and statistical analysis in a number of diverse areas, ranging from whether there is such a thing as a 'hot hand' in shooting a basketball, to how we can successfully predict, more than half the time, the decay of the radioactive atom that determines the fate of Schrodinger's Cat.Contents: <ul><li>Preface</li><li>Introduction — Mathematics, Intuition, and Computers</li><li>The Realm of the Counterintuitive:<ul><li>The Monty Hall Problem</li><li>How Probabilistic Entanglement Connects Almost Everything</li><li>Blackwell's Bet</li><li>A Stop at Willoughby — Mathematics in the Twilight Zone</li><li>The Fate of Schrodinger's Cat</li><li>Coins and Camels</li></ul></li><li>The Monday Morning Quarterback:<ul><li>The Joy of Simulation</li><li>Numbed by Numbers</li><li>Losing the Battle, Winning the War</li></ul></li><li>Getting It Right; A Synergy of Mathematics, Intuition and Computers:<ul><li>The Hot Hand</li><li>The Bent Coin and the Hot Hand</li></ul></li><li>The Last Hurrah:<ul><li>Using Combinatorics to Improve Advertising — For Everyone</li></ul></li><li>Appendix — Basic Probability Theory:<ul><li>Computational Rules for Probability</li><li>Conditional Probability</li><li>Independent Events</li><li>Expected Value (a.k.a. Expectation)</li><li>Bernoulli Trials</li><li>Means and Medians</li></ul></li><li>Annotated Bibliography<li>Index</ul> Readership: General Public, undergraduate math teachers and students in mathematics, computer programming, quantum mechanics, sports or the advertising business.Computer Programming;Sports Betting;Advertising;Prediction;Mathematics;Statistics;Bernoulli Trials;Coin Flip;Expectation;Quantum Mechanics;Mathematical Model;Gambling;Hidden Variables;Random Walk;Random Variable;Math Education;Sports Statistics;Arrow's Impossibility Theorem;Radioactive Decay;50–50;Paradox;Random Number Generator;Intuition;Monty Hall Problem;Chaos Theory;lackwell's Bet;David Blackwell;Butterfly Effect;Connectedness;Postdiction;Blackjack;Sportsmanlike Dumping0Key Features:<ul><li>Much of the material is either new or has not seen in a book of this type — in some cases because it has only appeared in journals or books within the last year or so</li><li>It is a unique blend of probability, statistics, computer modeling, sports, decision-making, quantum mechanics and the advertising business</li></ul>

Mathematical Muffin Morsels

William Gasarch

Suppose you have five muffins that you want to divide and give to Alice, Bob, and Carol. You want each of them to get 5/3. You could cut each muffin into 1/3-1/3-1/3 and give each student five 1/3-sized pieces. But Alice objects! She has large hands! She wants everyone to have pieces larger than 1/3.Is there a way to divide five muffins for three students so that everyone gets 5/3, and all pieces are larger than 1/3? Spoiler alert: Yes! In fact, there is a division where the smallest piece is 5/12. Is there a better division? Spoiler alert: No.In this book we consider THE MUFFIN PROBLEM: what is the best way to divide up m muffins for s students so that everyone gets m/s muffins, with the smallest pieces maximized. We look at both procedures for the problem and proofs that these procedures are optimal.This problem takes us through much mathematics of interest, for example, combinatorics and optimization theory. However, the math is elementary enough for an advanced high school student.Contents: <ul><li>Preface</li><li>About the Authors</li><li>Acknowledgments</li><li>Five Muffins, Three Students; Three Muffins, Five Students</li><li>One Student! Two Students! Some Basic Theorems!</li><li>Our Plan</li><li>Three Students! Four Students! The Floor–Ceiling Theorem!</li><li>Finding Procedures</li><li>The Half Method</li><li>A Formula for ƒ(m,5)</li><li>The Interval Method</li><li>The Midpoint Method</li><li>The Easy Buddy–Match Method</li><li>The Hard Buddy–Match Method</li><li>The Gap and Train Methods</li><li>Scott Huddleston's Method</li><li>Appendices:<ul><li>Math Notation</li><li>Fair Division</li><li>ƒ(m,s) Exists! ƒ(m,s) is Rational! ƒ(m,s) is Computable!</li></ul></li><li>References</li><li>Index</li></ul> Readership: High school and undergraduate students, computer scientists, mathematicians, and anyone interested in recreational mathematics. Fair Division;Muffins;Combinatorics0Key Features:<ul><li>Fun mathematics for high school students</li><li>Material on Muffin Mathematics appears here for the first time</li><li>Unique book, since most other recreational math books are essays on separate topics</li></ul>

Engaging Young Students in Mathematics through Competitions — World Perspectives and Practices

Отсутствует

The two volumes of 'Engaging Young Students in Mathematics through Competitions' present a wide scope of aspects relating to mathematics competitions and their meaning in the world of mathematical research, teaching and entertainment. Volume II contains background information on connections between the mathematics of competitions and the organization of such competitions, their interplay with research, teaching and more. It will be of interest to anyone involved with mathematics competitions at any level, be they researchers, competition participants, teachers or theoretical educators. The various chapters were written by the participants of the 8th Congress of the World Federation of National Mathematics Competitions in Austria in 2018. Contents: Mathematics Competitions and Research: From the Lifting-the-Exponent-Lemma to Elliptic Curves with Isomorphic Groups of Points: How Olympiad Mathematics Influences Mathematical Research (Clemens Heuberger) Examples of Mathematics and Competitions Influencing Each Other (Peter Taylor and Kevin McAvaney) University Mathematics in the Polish Mathematical Olympiad (Krzysztof Ciesielski) Building Bridges Between Olympiads and Mathematics: Three Long-Distance Trains of Thought (Alexander Soifer) Mathematics Competitions and Teaching: Beyond the Rainbow — Thoughts on the Potential of Mathematics Competition Problems in the Classroom (Robert Geretschläger) How to Create and Solve: Analysis of Items from the Mathematical Kangaroo from Two Perspectives (Lukas Andritsch, Evita Hauke and Jakob Kelz) The Special Role of Mathematics Competitions in Certain Countries: The Impact of Mathematical Olympiads on the Mathematics Community of Colombia (María Falk de Losada) The Impact of Mathematical Olympiads on the Mathematics Community of Venezuela (Rafael Sánchez Lamoneda) Mathematical Olympiads in Cabo Verde: Genesis, History and Comments (Natália Furtado) Special Mathematics Competitions: Some Selected Problems from the Mediterranean Mathematics Competition after its First 20 Years (Francisco Bellot-Rosado) Náboj: A Somehow Different Competition (Erich Fuchs, Bettina Kreuzer, Alexander Slávik and Martina Vaváčková) The CompMath Competition: Solving Math Problems with Computer Algebra Systems (Stoyan Kapralov, Penka Ivanova and Stefka Bouyuklieva) Evolving Ideas in Problem Series of the Chernorizec Hrabar Math Tournament (Borislav Yordanov Lazarov) The Julia Robinson Mathematics Festival: A Complement and Alternative to Competitions (Mark Saul) The Flavor of the Colorado Mathematical Olympiad: A Concerto in Four Movements (Alexander Soifer) Computational Thinking Hackathon (Yahya Tabesh and Shaya Zarkesh) Readership: Students, teachers, researchers, and general public interested in mathematics competition problems.Mathematics Competitions;Mathematics Education;Mathematical Puzzles00