Magic Tricks, Card Shuffling and Dynamic Computer Memories
Magic Tricks, Card Shuffling, and Dynamic Computer Memories is a book that explores the fascinating interconnections between these seemingly unrelated topics. It is written for undergraduate mathematics, computer science, and electrical engineering majors, but it is accessible to motivated high school math students and magicians who want to understand the mathematics of card shuffling. It is a fun book that stands alone, but it could nicely supplement classes in discrete mathematics,...
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The maths of card tricks; how to do magic without maths. AAAS, Sciences Books and Films "An excellent stand-alone volume.... Could be used as a supplementary text in a finite mathematics course.... Unquestionably well done, and I recommend it without reservation for undergraduate college students and anyone with a mathematical bent who wants to be thoroughly entertained by the poetry of combinatorial mathematics."
AcknowledgmentsIntroduction1. The Perfect ShuffleThe Origins of the Perfect ShuffleThe Faro Dealer's ShuffleA Mathematical Model of the Perfect ShuffleThe Stay-Stack PrincipleTrick: "The Seekers," Paul Swinford 2. The Order of ShufflesThe Order of ShufflesThe Product of ShufflesMoving a Card in a DeckTrick: "A Spelling Bee" 3. Shuffle GroupsRandomizing a Deck of CardsShuffles and Cuts in Even DecksShuffles and Cuts in Odd DecksOut- and In-Shuffles in an Even DeckTrick: "A Challenge Poker Deal" 4. Generalizing the Perfect ShuffleOut-Shuffling Several Packets of CardsLooking for a Neat FormulaPermutation MatricesGeneralizing TheoremsGeneralized Shuffle GroupsGeneralizing the In-ShuffleTrick: "The Triple Seekers" 5. Dynamic Computer MemoriesThe Shift-Register MemoryData Accessing Algorithm for a Shift-Register MemoryThe Perfect-Shuffle MemoryThe Shift-Shuffle MemoryDetails, Details, DetailsThe Perfect-Shuffle Memory for N=2"Random Accessing Algorithm for a Perfect-Shuffle MemorySequential Accessing in a Perfect-Shuffle Memory of Size N=2"Properties of ToursEpilogueTrick: "Unshuffled" by Paul Getner Appendix 1. The Order of ShufflesAppendix 2. How to Do the Faro ShuffleThe Double or Ordinary Faro ShuffleThe Triple Faro ShuffleAppendix 3. Tours on Decks of Size 8, 16, 32, and 64Appendix 4. A LagniappeThe Book of TheoremsThe Mathematician, the Psychic, and the MagicianA Constant FunctionBibliography: Selected Perfect Shuffle References
\ AAAS, Sciences Books and Films"An excellent stand-alone volume.... Could be used as a supplementary text in a finite mathematics course.... Unquestionably well done, and I recommend it without reservation for undergraduate college students and anyone with a mathematical bent who wants to be thoroughly entertained by the poetry of combinatorial mathematics."\ \ \ \ \ The Mathematics Teacher"One of the more satisfying occurrences in teaching is to put the right book in the hands of the right student at the right time. At best the result can open up a new area of learning, introducing the student to the challenge of self-directed study and to an author with something different to share...I can think of half a dozen students-and a few teachers- for whom [this books] would be a remarkable workout, an insight into how several mathematical areas can apply, and a recognition of some "parlor magic" as mathematically relevant and good fun."\ \ \ Zentralblatt fur Mathematik"It is a fun book that stand alone, but it could nicely supplement classes in discrete mathematics, combinatorics, algorithms, and computer networks. This book looks at the mathematics of the perfect shuffle and develops the algorithms for controlling dynamic memories (and doing some clever card tricks). Each chapter begins with the description of a card trick and ends with its explanation, usually using mathematics developed in the chapter. The book itself is designed as a prop for a trick, but you don't nee dot use or understand any of its mathematics to do some magic."\ \ \ \ \ BooknewsThis is a lively exploration of the interconnections between mathematics and card tricks, for undergraduates in mathematics, computer science, and electrical engineering majors, as well as motivated high school students and magicians. Each chapter begins with a card trick and ends with an explanation, delving into the mathematics of the perfect shuffle, for example, and algorithms for controlling dynamic memories. Includes b&w illustrations. Can be used as a supplement in classes in discrete mathematics, combinatorics, algorithms, and computer networks. Annotation c. by Book News, Inc., Portland, Or.\ \
