A clear-headed command of logic can make the mind powerful enough to outmaneuver the devil himself, according to these intriguing stories. More than 200 puzzles, problems, and paradoxes await within these pages, woven together by a wizard's captivating narrative. The Sorcerer—so skilled in the ... read more
My Best Mathematical and Logic Puzzles by Martin Gardner The noted expert selects 70 of his favorite "short" puzzles, including such mind-bogglers as The Returning Explorer, The Mutilated Chessboard, Scrambled Box Tops, and dozens more involving logic and basic math. Solutions.
First-Order Logic by Raymond M. Smullyan This self-contained study is both an introduction to quantification theory and an exposition of new results and techniques in "analytic" or "cut free" methods. The focus is on the tableau point of view. Includes 144 illustrations.
Introduction to Elementary Mathematical Logic by A. A. Stolyar Lucid, accessible exploration of propositional logic, propositional calculus, and predicate logic. Topics include computer science and systems analysis, linguistics, and problems in the foundations of mathematics. 1970 edition.
Undecidable Theories: Studies in Logic and the Foundation of Mathematics by Alfred Tarski, Andrzej Mostowski, Raphael M. Robinson This well-known book by the famed logician consists of three treatises: "A General Method in Proofs of Undecidability," "Undecidability and Essential Undecidability in Mathematics," and "Undecidability of the Elementary Theory of Groups." 1953 edition.
First Course in Mathematical Logic by Patrick Suppes, Shirley Hill Rigorous introduction is simple enough in presentation and context for wide range of students. Symbolizing sentences; logical inference; truth and validity; truth tables; terms, predicates, universal quantifiers; universal specification and laws of identity; more.
King Arthur in Search of His Dog and Other Curious Puzzles by Raymond M. Smullyan This fanciful, original collection for readers of all ages features arithmetic puzzles, logic problems related to crime detection, and logic and arithmetic puzzles involving King Arthur and his Dogs of the Round Table.
Set Theory and the Continuum Problem by Raymond M. Smullyan, Melvin Fitting 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.
The Lady or the Tiger?: and Other Logic Puzzles by Raymond M. Smullyan Created by a renowned puzzle master, these whimsically themed challenges involve paradoxes about probability, time, and change; metapuzzles; and self-referentiality. Nineteen chapters advance in difficulty from relatively simple to highly complex. 1982 edition.
Logic for Mathematicians by J. Barkley Rosser Examination of essential topics and theorems assumes no background in logic. "Undoubtedly a major addition to the literature of mathematical logic." — Bulletin of the American Mathematical Society. 1978 edition.
Professor Hoffmann's Best Math and Logic Puzzles by Louis Hoffmann These pleasantly perplexing highlights from the classic 1893 puzzle book abound in Victorian charm. They include both arithmetic problems and challenges involving words and letters. Complete solutions.
Mathematical Logic: A First Course by Joel W. Robbin This self-contained text will appeal to readers from diverse fields and varying backgrounds. Topics include 1st-order recursive arithmetic, 1st- and 2nd-order logic, and the arithmetization of syntax. Numerous exercises; some solutions. 1969 edition.
The Elements of Mathematical Logic by Paul C. Rosenbloom This excellent introduction to mathematical logic provides a sound knowledge of the most important approaches, stressing the use of logical methods. "Reliable." — The Mathematical Gazette. 1950 edition.
Essays in Experimental Logic by John Dewey 14 of the American philosopher's most influential essays appear here, offering profound reflections on many different aspects of knowledge, reality, and epistemology, including the relationship of thought and its subject matter; the antecedents and stimuli of thought, data, and meanings; the objects of thought; and control of ideas by facts.
A Profile of Mathematical Logic by Howard DeLong This introduction to mathematical logic explores philosophical issues and Gödel's Theorem. Its widespread influence extends to the author of Gödel, Escher, Bach, whose Pulitzer Prize–winning book was inspired by this work.
Basic Concepts of Mathematics and Logic by Michael C. Gemignani Intended as a first look at mathematics at the college level, this text emphasizes logic and set theory — counting, numbers, functions, ordering, probabilities, and other components of higher mathematics.
Mathematical Logic by Stephen Cole Kleene Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more.
Introduction to Logic by Patrick Suppes Part I of this coherent, well-organized text deals with formal principles of inference and definition. Part II explores elementary intuitive set theory, with separate chapters on sets, relations, and functions. Ideal for undergraduates.
Flatland: A Romance of Many Dimensions by Edwin A. Abbott Classic of science (and mathematical) fiction — charmingly illustrated by the author — describes the adventures of A. Square, a resident of Flatland, in Spaceland (three dimensions), Lineland (one dimension), and Pointland (no dimensions).
Mathematics and Logic by Mark Kac, Stanislaw M. Ulam Fascinating study of the origin and nature of mathematical thought, including relation of mathematics and science, 20th-century developments, impact of computers, more. Includes 34 illustrations. 1968 edition.
The Moscow Puzzles: 359 Mathematical Recreations by Boris A. Kordemsky Most popular Russian puzzle book ever published. Brain teasers range from simple "catch" riddles to difficult problems. Lavishly illustrated. First English translation. Introduction. Solutions.
First Order Mathematical Logic by Angelo Margaris Well-written undergraduate-level introduction begins with symbolic logic and set theory, followed by presentation of statement calculus and predicate calculus. Also covers first-order theories, completeness theorem, Godel's incompleteness theorem, much more. Exercises. Bibliography.
Mathematics for the Nonmathematician by Morris Kline Erudite and entertaining overview follows development of mathematics from ancient Greeks to present. Topics include logic and mathematics, the fundamental concept, differential calculus, probability theory, much more. Exercises and problems.
Test Your Logic by George J. Summers Fifty logic puzzles range in difficulty from the simple to the more complex. Mostly set in story form, some problems involve establishing identities from clues, while others are based on cryptarithmetic.
Puzzles in Math and Logic by Aaron J. Friedland 100 original problems in math and logic, featuring permutations, combinations, properties of numbers, algebra, solid and plane geometry, logic, and probability. Even accomplished mathematicians are likely to find some surprises here. 31 drawings.
Symbolic Logic and the Game of Logic by Lewis Carroll Over 350 ingenious problems involving classical logic: logic expressed in symbols; syllogisms and the sorites diagrammed; logic as a game played with 2 diagrams and a set of counters.
101 Puzzles in Thought and Logic by C. R. Wylie, Jr. Solve murder problems and robberies, see which fishermen are liars and how a blind man can identify color — purely by reasoning! Hours of mind-strengthening entertainment.
Alice in Puzzle-Land: A Carrollian Tale for Children Under Eighty by Raymond M. Smullyan, Martin Gardner, Greer Fitting Characters from Wonderland and Through the Looking-Glass populate these 88 puzzles involving word play, logic and metalogic, and philosophical paradoxes. The charmingly illustrated challenges range from easy to difficult and include solutions.
A clear-headed command of logic can make the mind powerful enough to outmaneuver the devil himself, according to these intriguing stories. More than 200 puzzles, problems, and paradoxes await within these pages, woven together by a wizard's captivating narrative. The Sorcerer—so skilled in the art of logic that his reasoning seems like magic—takes a puzzle-based perspective on the principles underlying the works of mathematician Georg Cantor. His fascinating riddles involve probability, certainty, time, and infinity, and they unfold amid a landscape populated by honorable knights, lying knaves, quick-witted robots, and other fanciful characters. Amusing and enlightening, the Sorcerer's guided tour of infinity is geared toward the most dedicated puzzle-solvers. Although many of the solutions require only common sense, equations appear in several of the stories, and a familiarity with algebra is essential. The author of several imaginative books on recreational mathematics, Raymond Smullyan is a well-known mathematician and logician. He provides solutions within text, rather than at the end or in footnotes, offering readers a natural progression on a puzzle-filled path through the wonders of logic.
Reprint of the Alfred A. Knopf, New York, 1992 edition.
Raymond Smullyan (1919– ), mathematician, logician, magician, creator of extraordinary puzzles, philosopher, pianist, and man of many parts. The first Dover book by Raymond Smullyan was First-Order Logic (1995). Recent years have brought a number of his magical books of logic and math puzzles: The Lady or the Tiger (2009); Satan, Cantor and Infinity (2009); an original, never-before-published collection, King Arthur in Search of His Dog and Other Curious Puzzles (2010); and Set Theory and the Continuum Problem (with Melvin Fitting, also reprinted by Dover in 2010). More will be coming in subsequent years. In the Author's Own Words: "Recently, someone asked me if I believed in astrology. He seemed somewhat puzzled when I explained that the reason I don't is that I'm a Gemini."
"Some people are always critical of vague statements. I tend rather to be critical of precise statements: they are the only ones which can correctly be labeled 'wrong.'" — Raymond Smullyan Critical Acclaim for The Lady or the Tiger: "Another scintillating collection of brilliant problems and paradoxes by the most entertaining logician and set theorist who ever lived." — Martin Gardner
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