Morris Kline

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.

Mathematics for the Nonmathematician

Application-oriented introduction relates the subject as closely as possible to science. In-depth explorations of the derivative, the differentiation and integration of the powers of x, and theorems on differentiation and antidifferentiation lead to a definition of the chain rule and examinations of trigonometric functions, logarithmic and exponential functions, techniques of integration, polar coordinates, much more. Clear-cut explanations, numerous drills, illustrative examples. 1967 edition. Solution guide available upon request.

An Intuitive and Physical Approach

Calculus

Refuting the accepted belief that mathematics is exact and infallible, the author examines the development of conflicting concepts of mathematics and their implications for the physical, applied, social, and computer sciences

The Loss of Certainty

Mathematics

Mathematical Thought From Ancient to Modern Times, Volume 2

Mathematical Thought From Ancient to Modern Times, Volume 3

Professor of Mathematics Emeritus Courant Institute of Mathematical Sciences Morris Kline

Explains why mathematics has become more and more important in scientific research, looks at quantum and relativity theory, and considers why mathematics works

Mathematics and the Search for Knowledge

"Kline is a first-class teacher and an able writer. . . . This is an enlarging and a brilliant book." ? Scientific American "Dr. Morris Kline has succeeded brilliantly in explaining the nature of much that is basic in math, and how it is used in science." ? San Francisco Chronicle Since the major branches of mathematics grew and expanded in conjunction with science, the most effective way to appreciate and understand mathematics is in terms of the study of nature. Unfortunately, the relationship of mathematics to the study of nature is neglected in dry, technique-oriented textbooks, and it has remained for Professor Morris Kline to describe the simultaneous growth of mathematics and the physical sciences in this remarkable book. In a manner that reflects both erudition and enthusiasm, the author provides a stimulating account of the development of basic mathematics from arithmetic, algebra, geometry, and trigonometry, to calculus, differential equations, and the non-Euclidean geometries. At the same time, Dr. Kline shows how mathematics is used in optics, astronomy, motion under the law of gravitation, acoustics, electromagnetism, and other phenomena. Historical and biographical materials are also included, while mathematical notation has been kept to a minimum. This is an excellent presentation of mathematical ideas from the time of the Greeks to the modern era. It will be of great interest to the mathematically inclined high school and college student, as well as to any reader who wants to understand ? perhaps for the first time ? the true greatness of mathematical achievements.

Mathematics and the Physical World

This book gives a remarkably fine account of the influences mathematics has exerted on the development of philosophy, the physical sciences, religion, and the arts in Western life.

Mathematics in Western Culture

Scritto con uno stile colloquiale e brillante, questo volume non è una storia tecnica della matematica. L’intento dell’autore è quello di ricondurre alla matematica – tra le manifestazioni più tipiche e tra gli strumenti più preziosi della civiltà umana – quei lettori che ne sono stati allontanati da un insegnamento scolastico arido e tedioso, codificato in formule fossilizzate e ormai prive di vita. Percorrendo l’intera storia della civiltà occidentale, Kline sceglie alcuni temi significativi per mettere in luce i legami tra matematica e forze sociali, politiche, artistiche, culturali, religiose, etiche, economiche. La matematica e i suoi problemi – dalla concezione di un ordine ideale dell’universo, propria della tradizione platonico-pitagorica, all’attuale visione di un universo “disordinato”, cui le scienze statistiche impongono un ordine di tipo laico – sono illuminati dal loro interno, nelle loro motivazioni, nel loro divenire, e si ritrasformano prodigiosamente in quell’organismo vivo di cui spesso gli studenti non riescono a ricostruire il funzionamento.

La matematica nella cultura occidentale

Storia di un amore infinito

Most intelligent people today still believe that mathematics is a body of unshakable truths about the physical world and that mathematical reasoning is exact and infallible. Mathematics: The Loss of Certainty refutes that myth.

Mathematics, the Loss of Certainty

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.

Briefly discusses the traditional mathematics formerly taught in American schools and views the language and weaknesses of the modern math curriculum

The Failure of the New Math

Why Johnny Can't Add

The Theory of Electromagnetic Waves

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.

An Intuitive and Physical Approach (Second Edition)

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.

This comprehensive history traces the development of mathematical ideas and the careers of the men responsible for them. Volume 1 looks at the disciplines origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the 19th century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Godel on recent mathematical study.

Mathematical Thought From Ancient to Modern Times

Durante los últimos quince años se ha impuesto en las escuelas norteamericanas un plan de enseñanza de matemáticas modernas o de nueva matemática. Se han escrito cientos de nuevos textos, y millones de niños y jóvenes han sido y están siendo enseñados con este nuevo material. Además se han publicado docenas de libros que explican el nuevo plan a padres y maestros. El dinero, tiempo energías e ideas invertidos en este programa han sido enormes. Y los resultados -según el profesor Kline- totalmente negativos: una generación de analfabetos en matemáticas, con un temor sin precedentes a este campo de la enseñanza, es la prueba más palpable del fracaso de la matemática moderna. La razón está clara: las nuevas matemáticas están dirigidas a una reducida fracción de estudiantes que algún día serán matemáticos de profesión. Los demás se quedan con una formación matemática apenas suficiente para realizar simples operaciones aritméticas, y sin duda insuficiente para rellenar un impreso de declaración de impuestos. El autor reconoce que los antiguos métodos de enseñanza de matemáticas eran imperfectos, pero arguye que una enseñanza que excluya los números en beneficio de unos conjuntos bastante vacíos, no satisface los deseos ni las necesidades de la abrumadora mayoría del estudiantado. El profesor Kline ha escrito una incisiva y razonada refutación de la nueva matemática, unida a un persuasivo alegato acerca de la necesidad de que los educadores admitan su error y busquen un remedio eficaz.

¿por qué Juanito no sabe sumar?

El Fracaso de la matemática moderna

Traces the development of mathematics from its beginnings in Babylonia and ancient Egypt to the work of Riemann and Godel in modern times

Morris Kline

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