Mathematics for the NonmathematicianPractical, 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. 
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Review: Mathematics for the Nonmathematician (Books Explaining Science)
User Review  Ciara Mccabe  GoodreadsI never liked math in school, but since I tutor math now, I started reading books that had to do with math. It was written a while ago so it has outdated opinions. But then again, if he can do math, those issues are more or less peripheral. Read full review
Review: Mathematics for the Nonmathematician (Books Explaining Science)
User Review  Zach Mays  GoodreadsOne of the most important books of my life (so far) Read full review
Contents
Why Mathematics?  1 
A Historical Orientation  11 
Logic and Mathematics  30 
the Fundamental Concept  58 
Algehra the Higher Arithmetic  94 
Charting the Earth and the Heavens  153 
The Mathematical Order of Nature  187 
The Awakening of Europe  197 
The Application of Formulas to Gravitation  326 
The Differential Calculus  365 
The Integral Calculus  388 
Trigonometric Functions and Oscillatory Motion  416 
The Trigonometric Analysis of Musical Sounds  436 
NonEuclidean Geometries and Their Significance  452 
Arithmetics and Thetr Algehras  478 
The Statistical Approach to the Social and Biological Sciences  499 
Mathematics and Painting in the Renaissance  209 
Projectlve Geometry  232 
The Theory of Prohahility  240 
Coordinate Geometry  250 
The Simplest Formulas in Action  280 
Parametric Equations and Curvilinear Motion  307 
Common terms and phrases
acceleration ahle ahout ahove ahscissa ahstract algehra alteady angle answer apply Arahs arithmetic average speed calculate Chaps Chapter circle circle of latitude concepts coordinates curve deductive Desargues Descartes descrihed determine distance distrihution Dover Puhlications earth ellipse equal equation estahlish Euclidean geometry example EXERCISES fact fall force formula formula d frequency ft/sec function Galileo Gauss given hy graph gravitation Greek hall hase hasic hecause hecome heen hegin height helieved Hence Hipparchus hody homh horizontal hoth hoth sides instantaneous rate mass mathematicians mathematics means method modulo moon motion nature Newton nonEuclidean geometry numher ohject ohservations ohtain parahola parallel axiom path planet position possihle poundals prohahility prohlem projectile projective geometry quantity rate of change result sound straight line suhject suhstitute suhtraction Suppose surface symhols tahle theorem theory thtee thtough thtown triangle variahle velocity vertical Xaxis zero