This is an exciting if not rambling account of events of Raymond Smullyan's four lives — as a mathematical logician, musician, magician, and author — together with thoughts that come to his mind as he recalls them. This book includes topics from some of Smullyan's twenty-six books, as well as many of his favorite anecdotes and jokes. It also presents some generalizations of theorems of the great logicians Gödel and Tarski, and discusses logic in general, and how he won his wife with a logic trick! Smullyan also relates some of his teaching experiences, and expresses his views on mathematical education, and how our present textbooks are primarily responsible for its decline! About his life as a pianist, Smullyan relates a good deal about his experiences with the Piano Society — a wonderful organization to which he is a staunch contributor, and how he has had such delightful relations with many of its members. Last but not least, Smullyan recounts how he has known some lovely ladies over the years. Contents:Early ChildhoodLater ChildhoodHigh SchoolBeginning CollegeUniversity of Chicago, Music, MagicDartmouth, PrincetonAfter GraduationDiagonalization, Love, Logic, a LetterThe Piano SocietyLovely Ladies I Have Known Readership: Music enthusiasts, piano society, math and logic enthusiasts, people interested in magic, people interested in Taoist philosophy, etc. Keywords:Logic;Magic;Mathematics;Gödel;Tarski;Piano Society;JokesReview: “We read of Smullyan's recollections of incidents in his past that support the images of a man who enjoys logic, music, mathematics, puns etc. If you have enjoyed any of Smullyan's books and wish to know more about the author, you will enjoy this breezy set of reflections as well.” Mathematical Association of America
This is an exciting if not rambling account of events of Raymond Smullyan's four lives -- as a mathematical logician, musician, magician, and author -- together with thoughts that come to his mind as he recalls them. This book includes topics from some of Smullyan's twenty-six books, as well as many of his favorite anecdotes and jokes. It also presents some generalizations of theorems of the great logicians GOdel and Tarski, and discusses logic in general, and how he won his wife with a logic trick! Smullyan also relates some of his teaching experiences, and expresses his views on mathematical education, and how our present textbooks are primarily responsible for its decline! About his life as a pianist, Smullyan relates a good deal about his experiences with the Piano Society -- a wonderful organization to which he is a staunch contributor, and how he has had such delightful relations with many of its members. Last but not least, Smullyan recounts how he has known some lovely ladies over the years.
Combines two previously published works, resulting in ninety-three brain-teasing puzzles, riddles, and questions with an emphasis on humor.
The noted expert and longtime author of Scientific American's Mathematical Games column selects 70 of his favorite "short" puzzles. Enthusiasts can challenge their skills with such mind-bogglers as The Returning Explorer, The Mutilated Chessboard, Scrambled Box Tops, Bronx vs. Brooklyn, and dozens more involving logic and basic math. Complete solutions included.
In his new book, Raymond Smullyan, grand vizier of the logic puzzle, joins Scheherazade, a charming young woman of “fantastic logical ingenuity,” to give us 1001 hours of brain-teasing fun. Scheherazade, we find, has gotten back into hot water with the king, and is once more in danger of losing her head at down. But, thinking quickly, she tempts the king to stay her execution by posing him the most delightfully devious mathematical and logic puzzle ever invented. They keep him guessing for many more nights until the fatal hour has passed, and she keeps her head. The Riddle of Scheherazade includes several wonderful old chestnuts and many fiendishly original puzzles, 225 in all. There are logic tricks and number games, metapuzzles (puzzles about puzzles), liar/truth-teller exercises, Gödelian brian twisters, baffling paradoxes, and an excursion, under Scheherazade’s expert guidance, into an amusing new field invented by Smullyan, called “coercive” logic, in which the answer to a problem can actually change the fate of the puzzler! An absolute must for all puzzle fans—from the middle-school whiz to the sophisticated mathematician or computer scientist.
Forever Undecided is the most challenging yet of Raymond Smullyan’s puzzle collections. It is, at the same time, an introduction—ingenious, instructive, entertaining—to Gödel’s famous theorems. With all the wit and charm that have delighted readers of his previous books, Smullyan transports us once again to that magical island where knights always tell the truth and knaves always lie. Here we meet a new and amazing array of characters, visitors to the island, seeking to determine the natives’ identities. Among them: the census-taker McGregor; a philosophical-logician in search of his flighty bird-wife, Oona; and a regiment of Reasoners (timid ones, normal ones, conceited, modest, and peculiar ones) armed with the rules of propositional logic (if X is true, then so is Y). By following the Reasoners through brain-tingling exercises and adventures—including journeys into the “other possible worlds” of Kripke semantics—even the most illogical of us come to understand Gödel’s two great theorems on incompleteness and undecidability, some of their philosophical and mathematical implications, and why we, like Gödel himself, must remain Forever Undecided!
This "best of" hardcover collection of works by Raymond Smullyan features logic puzzles, musings on mathematical logic and paradoxes, chess problems, and thoughts on the philosophy of religion, plus personal tributes to the author.
Hofstadter’s collection of quirky essays is unified by its primary concern: to examine the way people perceive and think.
Includes reminiscences, a festschrift, and the final annotations Gardner made to the Alice books post 'definitive edition,' and an authoritative bibliography of his Carroll-related writings.
This book serves both as a completely self-contained introduction and as an exposition of new results in the field of recursive function theory and its application to formal systems.
Magical Mathematics reveals the secrets of fun-to-perform card tricks—and the profound mathematical ideas behind them—that will astound even the most accomplished magician. Persi Diaconis and Ron Graham provide easy, step-by-step instructions for each trick, explaining how to set up the effect and offering tips on what to say and do while performing it. Each card trick introduces a new mathematical idea, and varying the tricks in turn takes readers to the very threshold of today’s mathematical knowledge. Diaconis and Graham tell the stories—and reveal the best tricks—of the eccentric and brilliant inventors of mathematical magic. The book exposes old gambling secrets through the mathematics of shuffling cards, explains the classic street-gambling scam of three-card Monte, traces the history of mathematical magic back to the oldest mathematical trick—and much more.
Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems. The level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists.
Murderous Maths: The Magic of Maths is full of incredible tricks to wow children and teachers alike. Brand new for the relaunch of the primary national curriculum in autumn 2014, children can discover how to use the power of maths to beat the calculator, perform amazing card tricks and even read minds! Illustrated by Philip Reeve and presented in a bold, funky and accessible way so children can find out why maths is marvellous, a new generation of Kjartan Poskitt fans will be able to discover the world of MURDEROUS MATHS. Get ready to be amazed!
Second collection of amusing, thought-provoking problems and puzzles from the "Cyclopedia." Arithmetic, algebra, speed and distance problems, game theory, counter and sliding block problems, similar topics. 166 problems. 150 original drawings, diagrams.
This book is more than a mathematics textbook. It discusses various kinds of numbers and curious interconnections between them. Without getting into hardcore and difficult mathematical technicalities, the book lucidly introduces all kinds of numbers that mathematicians have created. Interesting anecdotes involving great mathematicians and their marvelous creations are included. The reader will get a glimpse of the thought process behind the invention of new mathematics. Starting from natural numbers, the book discusses integers, real numbers, imaginary and complex numbers and some special numbers like quaternions, dual numbers and p-adic numbers. Real numbers include rational, irrational and transcendental numbers. Iterations on real numbers are shown to throw up some unexpected behavior, which has given rise to the new science of "Chaos". Special numbers like e, pi, golden ratio, Euler's constant, Gauss's constant, amongst others, are discussed in great detail. The origin of imaginary numbers and the use of complex numbers constitute the next topic. It is shown why modern mathematics cannot even be imagined without imaginary numbers. Iterations on complex numbers are shown to generate a new mathematical object called 'Fractal', which is ubiquitous in nature. Finally, some very special numbers, not mentioned in the usual textbooks, and their applications, are introduced at an elementary level. The level of mathematics discussed in this book is easily accessible to young adults interested in mathematics, high school students, and adults having some interest in basic mathematics. The book concentrates more on the story than on rigorous mathematics.
From Ancient Greek times, music has been seen as a mathematical art, and the relationship between mathematics and music has fascinated generations. This collection of wide ranging, comprehensive and fully-illustrated papers, authorized by leading scholars, presents the link between these two subjects in a lucid manner that is suitable for students of both subjects, as well as the general reader with an interest in music. Physical, theoretical, physiological, acoustic, compositional and analytical relationships between mathematics and music are unfolded and explored with focus on tuning and temperament, the mathematics of sound, bell-ringing and modern compositional techniques.
A lucid, elegant, and complete survey of set theory, this three-part treatment explores axiomatic set theory, the consistency of the continuum hypothesis, and forcing and independence results. 1996 edition.
Literary Nonfiction. Memoir. Humor. Music. Of all of Raymond Smullyan's many books, A MIXED BAG: JOKES, PUZZLES, RIDDLES AND MEMORABILIA perhaps best captures the timeless delight of the casual conversation of this American polymath. A seamless continuum of jokes, stories, puzzles, and reflections, caught in an deliciously unpremeditated arc that nonetheless is remarkably cohesive, it is sparkling and charming proof that cheerfulness need not be incompatible with intelligence, nor pleasure with wisdom.
Astronomer John Barrow takes an intriguing look at the limits of science, who argues that there are things that are ultimately unknowable, undoable, or unreachable.