The Monty Hall Problem

Author: Jason Rosenhouse
Publisher: Oxford University Press
ISBN: 9780199709908
Format: PDF, ePub, Docs
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Mathematicians call it the Monty Hall Problem, and it is one of the most interesting mathematical brain teasers of recent times. Imagine that you face three doors, behind one of which is a prize. You choose one but do not open it. The host--call him Monty Hall--opens a different door, always choosing one he knows to be empty. Left with two doors, will you do better by sticking with your first choice, or by switching to the other remaining door? In this light-hearted yet ultimately serious book, Jason Rosenhouse explores the history of this fascinating puzzle. Using a minimum of mathematics (and none at all for much of the book), he shows how the problem has fascinated philosophers, psychologists, and many others, and examines the many variations that have appeared over the years. As Rosenhouse demonstrates, the Monty Hall Problem illuminates fundamental mathematical issues and has abiding philosophical implications. Perhaps most important, he writes, the problem opens a window on our cognitive difficulties in reasoning about uncertainty.

Mit Werkzeugen Mathematik und Stochastik lernen Using Tools for Learning Mathematics and Statistics

Author: Thomas Wassong
Publisher: Springer-Verlag
ISBN: 3658031042
Format: PDF, ePub
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Dieser Band mit Beiträgen aus der nationalen und internationalen Forschung zum 60. Geburtstag von Prof. Dr. Rolf Biehler (Universität Paderborn) präsentiert wissenschaftliche Arbeiten zum Werkzeugeinsatz beim Lehren und Lernen von Mathematik im Allgemeinen sowie von Statistik und Stochastik im Besonderen. Wie ein roter Faden durchzieht den Festband, wie auch schon das wissenschaftliche Oeuvre von Rolf Biehler, ein breites Verständnis des Begriffs „Werkzeug“ (engl. „tools“). Die Themen decken das komplette Spektrum der Mathematikdidaktik auf allen Schulstufen sowie auf dem tertiären Sektor ab. Es gibt Beiträge zum Einsatz von Tools in der Grundschule, ebenso wie aus den Sekundarstufen, der Hochschule und der Lehreraus- und -weiterbildung. Im Band werden sowohl Beispiele zum konkreten Einsatz von Werkzeugen im Unterricht aufgezeigt, als auch Studien zur Wirksamkeit von Werkzeugen im Kontext von Mathematiklernen, theoretische Artikel zum Einsatz von Werkzeugen und Neuentwicklungen von Werkzeug-Software vorgelegt.

Discrete Mathematics with Ducks

Author: Sarah-marie Belcastro
Publisher: CRC Press
ISBN: 1351683683
Format: PDF
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Discrete Mathematics with Ducks, Second Edition is a gentle introduction for students who find the proofs and abstractions of mathematics challenging. At the same time, it provides stimulating material that instructors can use for more advanced students. The first edition was widely well received, with its whimsical writing style and numerous exercises and materials that engaged students at all levels. The new, expanded edition continues to facilitate effective and active learning. It is designed to help students learn about discrete mathematics through problem-based activities. These are created to inspire students to understand mathematics by actively practicing and doing, which helps students better retain what they’ve learned. As such, each chapter contains a mixture of discovery-based activities, projects, expository text, in-class exercises, and homework problems. The author’s lively and friendly writing style is appealing to both instructors and students alike and encourages readers to learn. The book’s light-hearted approach to the subject is a guiding principle and helps students learn mathematical abstraction. Features: The book’s Try This! sections encourage students to construct components of discussed concepts, theorems, and proofs Provided sets of discovery problems and illustrative examples reinforce learning Bonus sections can be used by instructors as part of their regular curriculum, for projects, or for further study

Taking Sudoku Seriously

Author: Jason Rosenhouse
Publisher: Oxford University Press
ISBN: 0199913153
Format: PDF, ePub, Mobi
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Packed with more than a hundred color illustrations and a wide variety of puzzles and brainteasers, Taking Sudoku Seriously uses this popular craze as the starting point for a fun-filled introduction to higher mathematics. How many Sudoku solution squares are there? What shapes other than three-by-three blocks can serve as acceptable Sudoku regions? What is the fewest number of starting clues a sound Sudoku puzzle can have? Does solving Sudoku require mathematics? Jason Rosenhouse and Laura Taalman show that answering these questions opens the door to a wealth of interesting mathematics. Indeed, they show that Sudoku puzzles and their variants are a gateway into mathematical thinking generally. Among many topics, the authors look at the notion of a Latin square--an object of long-standing interest to mathematicians--of which Sudoku squares are a special case; discuss how one finds interesting Sudoku puzzles; explore the connections between Sudoku, graph theory, and polynomials; and consider Sudoku extremes, including puzzles with the maximal number of vacant regions, with the minimal number of starting clues, and numerous others. The book concludes with a gallery of novel Sudoku variations--just pure solving fun! Most of the puzzles are original to this volume, and all solutions to the puzzles appear in the back of the book or in the text itself. A math book and a puzzle book, Taking Sudoku Seriously will change the way readers look at Sudoku and mathematics, serving both as an introduction to mathematics for puzzle fans and as an exploration of the intricacies of Sudoku for mathematics buffs.

50 Visions of Mathematics

Author: Dara O' Briain
Publisher: OUP Oxford
ISBN: 0191005339
Format: PDF, ePub
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Relax: no one understands technical mathematics without lengthy training but we all have an intuitive grasp of the ideas behind the symbols. To celebrate the 50th anniversary of the founding of the Institute of Mathematics and its Applications (IMA), this book is designed to showcase the beauty of mathematics - including images inspired by mathematical problems - together with its unreasonable effectiveness and applicability, without frying your brain. The book is a collection of 50 original essays contributed by a wide variety of authors. It contains articles by some of the best expositors of the subject (du Sautoy, Singh and Stewart for example) together with entertaining biographical pieces and articles of relevance to our everyday lives (such as Spiegelhalter on risk and Elwes on medical imaging). The topics covered are deliberately diverse and involve concepts from simple numerology to the very cutting edge of mathematics research. Each article is designed to be read in one sitting and to be accessible to a general audience. There is also other content. There are 50 pictorial 'visions of mathematics' which were supplied in response to an open call for contributions from IMA members, Plus readers and the worldwide mathematics community. You'll also find a series of "proofs " of Phythagoras's Theorem - mathematical, literary and comedy - after this, you'll never think of Pythagoras the same way again.

Among the Creationists

Author: Jason Rosenhouse
Publisher: Oxford University Press
ISBN: 0199911096
Format: PDF, Mobi
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Why do so many Americans reject the modern theory of evolution? Why does creationism, thoroughly refuted by scientists, retain such popularity among the public? Is the perceived conflict between evolution and Christianity genuine, or is it merely an illusion peculiar to Protestant fundamentalism? Seeking answers to these questions, mathematician Jason Rosenhouse became a regular attendee at creationist conferences and other gatherings. After ten years of attending events like the giant Creation Mega-Conference in Lynchburg, Virginia, and visiting sites like the Creation Museum in Petersburg, Kentucky, and after hundreds of surprisingly friendly conversations with creationists of varying stripes, he has emerged with a story to tell, a story that goes well beyond the usual stereotypes of Bible-thumping fanatics railing against coldly rational scientists. Through anecdotes, personal reflections, and scientific and philosophical discussion, Rosenhouse presents a more down-to-earth picture of modern creationism and the people who espouse it. He is neither polemical nor insulting, but he does not pull punches when he spots an error in the logical or scientific reasoning of creationists, especially when they wander into his own field, mathematics. Along the way, he also tells the story of his own nonbeliever's attempt to understand a major aspect of American religion. Forced to wrestle with his views about God and evolution, Rosenhouse found himself drawn into a new world of ideas previously unknown to him, arriving at a sharper understanding of the reality of science-versus-religion disputes, and how these debates look to those beyond the ivory tower. A personal memoir of one scientist's attempt to come to grips with this controversy-by immersing himself in the culture of the anti-evolutionists-Among the Creationists is a fair, fresh, and insightful account of the modern American debate over Darwinism.

Four Lives

Author: Raymond M. Smullyan
Publisher: Courier Corporation
ISBN: 048649067X
Format: PDF, Kindle
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" This 'best of' collection of works by Raymond Smullyan features excerpts from his published writings, including logic puzzles, explorations of mathematical logic and paradoxes, retrograde analysis chess problems, jokes and anecdotes, and meditations on the philosophy of religion. In addition, numerous personal tributes salute this celebrated professor, author, and logic scholar who is also a magician and musician. "--