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Mathematics for the Nonmathematicianby Morris Kline
Synopses & ReviewsPublisher Comments: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 collegelevel 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 selfstudy 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 stepbystep 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 nonEuclidean 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. Synopsis: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. Synopsis:Erudite and entertaining overview follows development of mathematics from ancient Greeks, through Middle Ages and Renaissance to the present. Chapters focus on Logic and Mathematics, the Number, the Fundamental Concept, Differential Calculus, the Theory of Probability and much more. Exercises and pr
Synopsis: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.
About the AuthorMorris Kline: Mathematics for the Masses Morris Kline (19081992) 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 Table of Contents1 Why Mathematics?
2 A Historical Orientation 21 Introduction 22 Mathematics in early civilizations 23 The classical Greek period 24 The Alexandrian Greek period 25 The Hindus and Arabs 26 Early and medieval Europe 27 The Renaissance 28 Developments from 1550 to 1800 29 Developments from 1800 to the present 210 The human aspect of mathematics 3 Logic and Mathematics 31 Introduction 32 The concepts of mathematics 33 Idealization 34 Methods of reasoning 35 Mathematical proof 36 Axioms and definitions 37 The creation of mathematics 4 Number: the Fundamental Concept 41 Introduction 42 Whole numbers and fractions 43 Irrational numbers 44 Negative numbers 45 The axioms concerning numbers * 46 Applications of the number system 5 "Algebra, the Higher Arithmetic" 51 Introduction 52 The language of algebra 53 Exponents 54 Algebraic transformations 55 Equations involving unknowns 56 The general seconddegree equation * 57 The history of equations of higher degree 6 The Nature and Uses of Euclidean Geometry 61 The beginnings of geometry 62 The content of Euclidean geometry 63 Some mundane uses of Euclidean geometry * 64 Euclidean geometry and the study of light 65 Conic sections * 66 Conic sections and light * 67 The cultural influence of Euclidean geometry 7 Charting the Earth and Heavens 71 The Alexandrian world 72 Basic concepts of trigonometry 73 Some mundane uses of trigonometric ratios * 74 Charting the earth * 75 Charting the heavens * 76 Further progress in the study of light 8 The Mathematical Order of Nature 81 The Greek concept of nature 82 PreGreek and Greek views of nature 83 Greek astronomical theories 84 The evidence for the mathematical design of nature 85 The destruction of the Greek world * 9 The Awakening of Europe 91 The medieval civilization of Europe 92 Mathematics in the medieval period 93 Revolutionary influences in Europe 94 New doctrines of the Renaissance 95 The religious motivation in the study of nature * 10 Mathematics and Painting in the Renaissance 101 Introduction 102 Gropings toward a scientific system of perspective 103 Realism leads to mathematics 104 The basic idea of mathematical perspective 105 Some mathematical theorems on perspective drawing 106 Renaissance paintings employing mathematical perspective 107 Other values of mathematical perspective 11 Projective Geometry 111 The problem suggested by projection and section 112 The work of Desargues 113 The work of Pascal 114 The principle of duality 115 The relationship between projective and Euclidean geometries 12 Coordinate Geometry 121 Descartes and Fermat 122 The need for new methods in geometry 123 The concepts of equation and curve 124 The parabola 125 Finding a curve from its equation 126 The ellipse * 127 The equations of surfaces * 128 Fourdimensional geometry 129 Summary 13 The Simplest Formulas in Action 131 Mastery of nature 132 The search for scientific method 133 The scientific method of Galileo 134 Functions and formulas 135 The formulas describing the motion of dropped objects 136 The formulas describing the motion of objects thrown downward 137 Formulas for the motion of bodies projected upward 14 Parametric Equations and Curvillinear Motion 141 Introduction 142 The concept of parametric equations 143 The motion of a projectile dropped from an airplane 144 The motion of projectiles launched by cannons * 145 The motion of projectiles fired at an arbitrary angle 146 Summary 15 The Application of Formulas to Gravitation 151 The revolution in astronomy 152 The objections to a heliocentric theory 153 The arguments for the heliocentric theory 154 The problem of relating earthly and heavenly motions 155 A sketch of Newton's life 156 Newton's key idea 157 Mass and weight 158 The law of gravitation 159 Further discussion of mass and weight 1510 Some deductions from the law of gravitation * 1511 The rotation of the earth * 1512 Gravitation and the Keplerian laws * 1513 Implications of the theory of gravitation * 16 The Differential Calculus 161 Introduction 162 The problem leading to the calculus 163 The concept of instantaneous rate of change 164 The concept of instantaneous speed 165 The method of increments 166 The method of increments applied to general functions 167 The geometrical meaning of the derivative 168 The maximum and minimum values of functions * 17 The Integral Calculus 171 Differential and integral calculus compared 172 Finding the formula from the given rate of change 173 Applications to problems of motion 174 Areas obtained by integration 175 The calculation of work 176 The calculation of escape velocity 177 The integral as the limit of a sum 178 Some relevant history of the limit concept 179 The Age of Reason 18 Trigonometric Functions and Oscillatory Motion 181 Introduction 182 The motion of a bob on a spring 183 The sinusoidal functions 184 Acceleration in sinusoidal motion 185 The mathematical analysis of the motion of the bob 186 Summary * 19 The Trigonometric Analysis of Musical Sounds 191 Introduction 192 The nature of simple sounds 193 The method of addition of ordinates 194 The analysis of complex sounds 195 Subjective properties of musical sounds 20 NonEuclidean Geometries and Their Significance 201 Introduction 202 The historical background 203 The mathematical content of Gauss's nonEuclidean geometry 204 Riemann's nonEuclidean geometry 205 The applicability of nonEuclidean geometry 206 The applicability of nonEuclidean geometry under a new interpretation of line 207 NonEuclidean geometry and the nature of mathematics 208 The implications of nonEuclidean geometry for other branches of our culture 21 Arithmetics and Their Algebras 211 Introduction 212 The applicability of the real number system 213 Baseball arithmetic 214 Modular arithmetics and their algebras 215 The algebra of sets 216 Mathematics and models * 22 The Statistical Approach to the Social and Biological Sciences 221 Introduction 222 A brief historical review 223 Averages 224 Dispersion 225 The graph and normal curve 226 Fitting a formula to data 227 Correlation 228 Cautions concerning the uses of statistics * 23 The Theory of Probability 231 Introduction 232 Probability for equally likely outcomes 233 Probability as relative frequency 234 Probability in continuous variation 235 Binomial distributions 236 The problems of sampling 24 The Nature and Values of Mathem 244 The aesthetic and intellectual values 245 Mathematics and rationalism 246 The limitations of mathematics Table of Trigonometric Ratios Answers to Selected and Review Exercises Additional Answers and Solutions Index What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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