Practical, scientific, philosophical, and artistic problems have caused men to investigate mathematics. But there is one other motive which is as strong as any of these—the search for beauty. Mathematics is an art, and as such affords the pleasures which all the arts afford." In this erudite, e... read more
Calculus: An Intuitive and Physical Approach (Second Edition) by Morris Kline Application-oriented introduction relates the subject as closely as possible to science with explorations of the derivative; differentiation and integration of the powers of x; theorems on differentiation, antidifferentiation; the chain rule; trigonometric functions; more. Examples. 1967 edition.
Mathematics and the Physical World by Morris Kline Stimulating account of development of mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations, and non-Euclidean geometries. Also describes how math is used in optics, astronomy, and other phenomena.
Mathematics and the Imagination by Edward Kasner, James Newman With wit and clarity, the authors progress from simple arithmetic to calculus and non-Euclidean geometry. Their subjects: geometry, plane and fancy; puzzles that made mathematical history; tantalizing paradoxes; more. Includes 169 figures.
Mathematician's Delight by W. W. Sawyer "Recommended with confidence" by The Times Literary Supplement, this lively survey was written by a renowned teacher. It starts with arithmetic and algebra, gradually proceeding to trigonometry and calculus. 1943 edition.
Prelude to Mathematics by W. W. Sawyer This lively, stimulating account of non-Euclidean geometry by a noted mathematician covers matrices, determinants, group theory, and many other related topics, with an emphasis on the subject's novel, striking aspects. 1955 edition.
Introduction to Proof in Abstract Mathematics by Andrew Wohlgemuth This undergraduate text teaches students what constitutes an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights. 1990 edition.
Theory of Sets by E. Kamke Introductory treatment emphasizes fundamentals, covering rudiments; arbitrary sets and their cardinal numbers; ordered sets and their ordered types; and well-ordered sets and their ordinal numbers. "Exceptionally well written." — School Science and Mathematics.
A Concept of Limits by Donald W. Hight An exploration of conceptual foundations and the practical applications of limits in mathematics, this text offers a concise introduction to the theoretical study of calculus. Many exercises with solutions. 1966 edition.
Mathematics: The Man-Made Universe by Sherman K. Stein Highly readable volume covers number theory, topology, set theory, geometry, algebra, and analysis, plus the primes, fundamental theory of arithmetic, probability, and more. Solutions manual available upon request. 1994 edition.
Newton's Philosophy of Nature: Selections from His Writings by Sir Isaac Newton, H. S. Thayer A wide, accessible representation of the interests, problems, and philosophic issues that preoccupied the great 17th-century scientist, this collection is grouped according to methods, principles, and theological considerations. 1953 edition.
A Short Account of the History of Mathematics by W. W. Rouse Ball This standard text treats hundreds of figures and schools instrumental in the development of mathematics, from the Phoenicians to such 19th-century giants as Grassman, Galois, and Riemann.
Playing with Infinity by Rózsa Péter Popular account ranges from counting to mathematical logic and covers many concepts related to infinity: graphic representation of functions; pairings, other combinations; prime numbers; logarithms, circular functions; more. 216 illustrations.
Group Theory by W. R. Scott Here is a clear, well-organized coverage of the most standard theorems, including isomorphism theorems, transformations and subgroups, direct sums, abelian groups, and more. This undergraduate-level text features more than 500 exercises.
Geometry from Euclid to Knots by Saul Stahl This text provides a historical perspective on plane geometry and covers non-neutral Euclidean geometry, circles and regular polygons, projective geometry, symmetries, inversions, informal topology, and more. Includes 1,000 practice problems. Solutions available. 2003 edition.
Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise by Manfred Schroeder A fascinating exploration of the connections between chaos theory, physics, biology, and mathematics, this book abounds in award-winning computer graphics, optical illusions, and games that clarify memorable insights into self-similarity. 1992 edition.
Satan, Cantor and Infinity: Mind-Boggling Puzzles by Raymond M. Smullyan A renowned mathematician tells stories of knights and knaves in an entertaining look at the logical precepts behind infinity, probability, time, and change. Requires a strong background in mathematics. Complete solutions.
The Art of Mathematics by Jerry P. King Clear, concise, and superbly written, this book reveals the beauty at the heart of mathematics, illustrating the fundamental connection between aesthetics and mathematics. "Witty, trenchant, and provocative." — Mathematical Association of America.
Descartes' Dream: The World According to Mathematics by Philip J. Davis, Reuben Hersh These provocative essays take a modern look at the 17th-century thinker's dream, examining the influences of mathematics on society, particularly in light of technological advances. 1987 edition.
The World of Mathematics: A Four-Volume Set by James R. Newman Save 10% when you order the complete set! A monumental 4-volume reference, 15 years in the making, The World of Mathematics was specially designed to make mathematics more accessible to the inexperienced.
A Refresher Course in Mathematics by F. J. Camm Readers wishing to extend their mathematical skills will find this volume a practical companion. Easy-to-follow explanations cover fractions, decimals, square roots, metric system, algebra, more. 195 figures. 1943 edition.
Problem Solving Through Recreational Mathematics by Bonnie Averbach, Orin Chein Fascinating approach to mathematical teaching stresses use of recreational problems, puzzles, and games to teach critical thinking. Logic, number and graph theory, games of strategy, much more. Includes answers to selected problems. 1980 edition.
Intriguing Mathematical Problems by Oswald Jacoby, William H. Benson Treasury of challenging brainteasers includes puzzles involving numbers, letters, probability, reasoning, more: The Enterprising Snail, The Fly and the Bicycles, The Lovesick Cockroaches, many others. No advanced math needed. Solutions.
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.
Introduction to Mathematical Philosophy by Bertrand Russell Seminal work focuses on concepts of number, order, relations, limits and continuity, propositional functions, descriptions and classes, more. Clear, accessible excursion into realm where mathematics and philosophy meet.
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).
Mathographics by Robert Dixon Stimulating, unique book explores mathematical drawing through compass constructions and computer graphics. Over 100 full-page drawings: five-point egg, golden ratio, plughole vortex, blancmange curve, more. Exercises. 1987 edition.
Excursions in Geometry by C. Stanley Ogilvy A straightedge, compass, and a little thought are all that's needed to discover the intellectual excitement of geometry. Harmonic division and Apollonian circles, inversive geometry, hexlet, Golden Section, more. 132 illustrations.
Perplexing Puzzles and Tantalizing Teasers by Martin Gardner Ninety-three riddles, mazes, illusions, tricky questions, word and picture puzzles, and other challenges offer hours of entertainment for youngsters. Richly illustrated with rib-tickling drawings by Laszlo Kubinyi. Includes solutions.
Taxicab Geometry: An Adventure in Non-Euclidean Geometry by Eugene F. Krause Fascinating, accessible introduction to unusual mathematical system in which distance is not measured by straight lines. Illustrated topics include applications to urban geography and comparisons to Euclidean geometry. Selected answers to problems.
Famous Problems of Geometry and How to Solve Them by Benjamin Bold Delve into the development of modern mathematics and match wits with Euclid, Newton, Descartes, and others. Each chapter explores an individual type of challenge, with commentary and practice problems. Solutions.
Geometry, Relativity and the Fourth Dimension by Rudolf Rucker Exposition of fourth dimension, concepts of relativity as Flatland characters continue adventures. Topics include curved space time as a higher dimension, special relativity, and shape of space-time. Includes 141 illustrations.
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.
The Divine Proportion by H. E. Huntley Discussion ranges from theories of biological growth to intervals and tones in music, Pythagorean numerology, conic sections, Pascal's triangle, the Fibonnacci series, and much more. Excellent bridge between science and art. Features 58 figures.
Mathematics, Magic and Mystery by Martin Gardner Famed puzzle expert explains math behind a multitude of mystifying tricks: card tricks, stage "mind reading," coin and match tricks, counting out games, geometric dissections, etc. More than 400 tricks. 135 illustrations.
How to Calculate Quickly: Full Course in Speed Arithmetic by Henry Sticker Many useful procedures explained and taught: 2-column addition, left-to-right subtraction, mental division of large numbers, more. Also numerous helpful shortcuts. More than 8,000 problems, with solutions. 1945 edition.
Practical, scientific, philosophical, and artistic problems have caused men to investigate mathematics. But there is one other motive which is as strong as any of these—the search for beauty. Mathematics is an art, and as such affords the pleasures which all the arts afford." In this erudite, entertaining college-level text, Morris Kline, Professor Emeritus of Mathematics at New York University, provides the liberal arts student with a detailed treatment of mathematics in a cultural and historical context. The book can also act as a self-study vehicle for advanced high school students and laymen. Professor Kline begins with an overview, tracing the development of mathematics to the ancient Greeks, and following its evolution through the Middle Ages and the Renaissance to the present day. Subsequent chapters focus on specific subject areas, such as "Logic and Mathematics," "Number: The Fundamental Concept," "Parametric Equations and Curvilinear Motion," "The Differential Calculus," and "The Theory of Probability." Each of these sections offers a step-by-step explanation of concepts and then tests the student's understanding with exercises and problems. At the same time, these concepts are linked to pure and applied science, engineering, philosophy, the social sciences or even the arts. In one section, Professor Kline discusses non-Euclidean geometry, ranking it with evolution as one of the "two concepts which have most profoundly revolutionized our intellectual development since the nineteenth century." His lucid treatment of this difficult subject starts in the 1800s with the pioneering work of Gauss, Lobachevsky, Bolyai and Riemann, and moves forward to the theory of relativity, explaining the mathematical, scientific and philosophical aspects of this pivotal breakthrough. Mathematics for the Nonmathematician exemplifies Morris Kline's rare ability to simplify complex subjects for the nonspecialist.
Reprint of Mathematics for Liberal Arts, Addison-Wesley Publishing Company, Reading, 1967.
Morris Kline (1908–1992) had a strong and forceful personality which he brought both to his position as Professor at New York University from 1952 until his retirement in 1975, and to his role as the driving force behind Dover's mathematics reprint program for even longer, from the 1950s until just a few years before his death. Professor Kline was the main reviewer of books in mathematics during those years, filling many file drawers with incisive, perceptive, and always handwritten comments and recommendations, pro or con. It was inevitable that he would imbue the Dover math program ― which he did so much to launch ― with his personal point of view that what mattered most was the quality of the books that were selected for reprinting and the point of view that stressed the importance of applications and the usefulness of mathematics. He urged that books should concentrate on demonstrating how mathematics could be used to solve problems in the real world, not solely for the creation of intellectual structures of theoretical interest to mathematicians only.
Morris Kline was the author or editor of more than a dozen books, including Mathematics in Western Culture (Oxford, 1953), Mathematics: The Loss of Certainty (Oxford, 1980), and Mathematics and the Search for Knowledge (Oxford, 1985). His Calculus, An Intuitive and Physical Approach, first published in 1967 and reprinted by Dover in 1998, remains a widely used text, especially by readers interested in taking on the sometimes daunting task of studying the subject on their own. His 1985 Dover book, Mathematics for the Nonmathematician could reasonably be regarded as the ultimate math for liberal arts text and may have reached more readers over its long life than any other similarly directed text. In the Author's Own Words: "Mathematics is the key to understanding and mastering our physical, social and biological worlds."
"Logic is the art of going wrong with confidence."
"Statistics: the mathematical theory of ignorance."
"A proof tells us where to concentrate our doubts." ― Morris Kline
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