The Good, the Bad, and the Hungry Sale
 
 

Recently Viewed clear list


The Powell's Playlist | June 18, 2014

Daniel H. Wilson: IMG The Powell’s Playlist: Daniel H. Wilson



Like many writers, I'm constantly haunting coffee shops with a laptop out and my headphones on. I listen to a lot of music while I write, and songs... Continue »

spacer
Qualifying orders ship free.
$6.95
List price: $16.95
Used Trade Paper
Ships in 1 to 3 days
Add to Wishlist
Qty Store Section
3 Hawthorne Mathematics- General

Mathematics for the Nonmathematician

by

Mathematics for the Nonmathematician Cover

 

Synopses & Reviews

Publisher 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 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.

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 Author

Morris Kline: Mathematics for the Masses

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

Table of Contents

1 Why Mathematics?

2 A Historical Orientation

  2-1 Introduction

  2-2 Mathematics in early civilizations

  2-3 The classical Greek period

  2-4 The Alexandrian Greek period

  2-5 The Hindus and Arabs

  2-6 Early and medieval Europe

  2-7 The Renaissance

  2-8 Developments from 1550 to 1800

  2-9 Developments from 1800 to the present

  2-10 The human aspect of mathematics

3 Logic and Mathematics

  3-1 Introduction

  3-2 The concepts of mathematics

  3-3 Idealization

  3-4 Methods of reasoning

  3-5 Mathematical proof

  3-6 Axioms and definitions

  3-7 The creation of mathematics

4 Number: the Fundamental Concept

  4-1 Introduction

  4-2 Whole numbers and fractions

  4-3 Irrational numbers

  4-4 Negative numbers

  4-5 The axioms concerning numbers

  * 4-6 Applications of the number system

5 "Algebra, the Higher Arithmetic"

  5-1 Introduction

  5-2 The language of algebra

  5-3 Exponents

  5-4 Algebraic transformations

  5-5 Equations involving unknowns

  5-6 The general second-degree equation

  * 5-7 The history of equations of higher degree

6 The Nature and Uses of Euclidean Geometry

  6-1 The beginnings of geometry

  6-2 The content of Euclidean geometry

  6-3 Some mundane uses of Euclidean geometry

  * 6-4 Euclidean geometry and the study of light

  6-5 Conic sections

  * 6-6 Conic sections and light

  * 6-7 The cultural influence of Euclidean geometry

7 Charting the Earth and Heavens

  7-1 The Alexandrian world

  7-2 Basic concepts of trigonometry

  7-3 Some mundane uses of trigonometric ratios

  * 7-4 Charting the earth

  * 7-5 Charting the heavens

  * 7-6 Further progress in the study of light

8 The Mathematical Order of Nature

  8-1 The Greek concept of nature

  8-2 Pre-Greek and Greek views of nature

  8-3 Greek astronomical theories

  8-4 The evidence for the mathematical design of nature

  8-5 The destruction of the Greek world

* 9 The Awakening of Europe

  9-1 The medieval civilization of Europe

  9-2 Mathematics in the medieval period

  9-3 Revolutionary influences in Europe

  9-4 New doctrines of the Renaissance

  9-5 The religious motivation in the study of nature

* 10 Mathematics and Painting in the Renaissance

  10-1 Introduction

  10-2 Gropings toward a scientific system of perspective

  10-3 Realism leads to mathematics

  10-4 The basic idea of mathematical perspective

  10-5 Some mathematical theorems on perspective drawing

  10-6 Renaissance paintings employing mathematical perspective

  10-7 Other values of mathematical perspective

11 Projective Geometry

  11-1 The problem suggested by projection and section

  11-2 The work of Desargues

  11-3 The work of Pascal

  11-4 The principle of duality

  11-5 The relationship between projective and Euclidean geometries

12 Coordinate Geometry

  12-1 Descartes and Fermat

  12-2 The need for new methods in geometry

  12-3 The concepts of equation and curve

  12-4 The parabola

  12-5 Finding a curve from its equation

  12-6 The ellipse

  * 12-7 The equations of surfaces

  * 12-8 Four-dimensional geometry

  12-9 Summary

13 The Simplest Formulas in Action

  13-1 Mastery of nature

  13-2 The search for scientific method

  13-3 The scientific method of Galileo

  13-4 Functions and formulas

  13-5 The formulas describing the motion of dropped objects

  13-6 The formulas describing the motion of objects thrown downward

  13-7 Formulas for the motion of bodies projected upward

14 Parametric Equations and Curvillinear Motion

  14-1 Introduction

  14-2 The concept of parametric equations

  14-3 The motion of a projectile dropped from an airplane

  14-4 The motion of projectiles launched by cannons

  * 14-5 The motion of projectiles fired at an arbitrary angle

  14-6 Summary

15 The Application of Formulas to Gravitation

  15-1 The revolution in astronomy

  15-2 The objections to a heliocentric theory

  15-3 The arguments for the heliocentric theory

  15-4 The problem of relating earthly and heavenly motions

  15-5 A sketch of Newton's life

  15-6 Newton's key idea

  15-7 Mass and weight

  15-8 The law of gravitation

  15-9 Further discussion of mass and weight

  15-10 Some deductions from the law of gravitation

  * 15-11 The rotation of the earth

  * 15-12 Gravitation and the Keplerian laws

  * 15-13 Implications of the theory of gravitation

* 16 The Differential Calculus

  16-1 Introduction

  16-2 The problem leading to the calculus

  16-3 The concept of instantaneous rate of change

  16-4 The concept of instantaneous speed

  16-5 The method of increments

  16-6 The method of increments applied to general functions

  16-7 The geometrical meaning of the derivative

  16-8 The maximum and minimum values of functions

* 17 The Integral Calculus

  17-1 Differential and integral calculus compared

  17-2 Finding the formula from the given rate of change

  17-3 Applications to problems of motion

  17-4 Areas obtained by integration

  17-5 The calculation of work

  17-6 The calculation of escape velocity

  17-7 The integral as the limit of a sum

  17-8 Some relevant history of the limit concept

  17-9 The Age of Reason

18 Trigonometric Functions and Oscillatory Motion

  18-1 Introduction

  18-2 The motion of a bob on a spring

  18-3 The sinusoidal functions

  18-4 Acceleration in sinusoidal motion

  18-5 The mathematical analysis of the motion of the bob

  18-6 Summary

* 19 The Trigonometric Analysis of Musical Sounds

  19-1 Introduction

  19-2 The nature of simple sounds

  19-3 The method of addition of ordinates

  19-4 The analysis of complex sounds

  19-5 Subjective properties of musical sounds

20 Non-Euclidean Geometries and Their Significance

  20-1 Introduction

  20-2 The historical background

  20-3 The mathematical content of Gauss's non-Euclidean geometry

  20-4 Riemann's non-Euclidean geometry

  20-5 The applicability of non-Euclidean geometry

  20-6 The applicability of non-Euclidean geometry under a new interpretation of line

  20-7 Non-Euclidean geometry and the nature of mathematics

  20-8 The implications of non-Euclidean geometry for other branches of our culture

21 Arithmetics and Their Algebras

  21-1 Introduction

  21-2 The applicability of the real number system

  21-3 Baseball arithmetic

  21-4 Modular arithmetics and their algebras

  21-5 The algebra of sets

  21-6 Mathematics and models

* 22 The Statistical Approach to the Social and Biological Sciences

  22-1 Introduction

  22-2 A brief historical review

  22-3 Averages

  22-4 Dispersion

  22-5 The graph and normal curve

  22-6 Fitting a formula to data

  22-7 Correlation

  22-8 Cautions concerning the uses of statistics

* 23 The Theory of Probability

  23-1 Introduction

  23-2 Probability for equally likely outcomes

  23-3 Probability as relative frequency

  23-4 Probability in continuous variation

  23-5 Binomial distributions

  23-6 The problems of sampling

24 The Nature and Values of Mathem

  24-4 The aesthetic and intellectual values

  24-5 Mathematics and rationalism

  24-6 The limitations of mathematics

  Table of Trigonometric Ratios

  Answers to Selected and Review Exercises

  Additional Answers and Solutions

  Index

Product Details

ISBN:
9780486248233
Author:
Kline, Morris
Publisher:
Dover Publications
Author:
Kline
Location:
New York :
Subject:
General
Subject:
General science
Subject:
Mathematics
Subject:
Math anxiety
Subject:
General Science
Subject:
Mathematics - General
Subject:
History
Copyright:
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
no. 134
Publication Date:
19850231
Binding:
TRADE PAPER
Grade Level:
General/trade
Language:
English
Illustrations:
Yes
Pages:
672
Dimensions:
8.5 x 5.38 in 1.5 lb

Other books you might like

  1. The Story of Mathematics Used Mass Market $5.95
  2. How To Lie With Statistics Used Trade Paper $4.50
  3. Why Do Buses Come in Threes?: The... Used Trade Paper $7.50
  4. Time Travel & Other Mathematical... Used Hardcover $7.95
  5. A Source Book in Mathematics New Trade Paper $29.95
  6. History of Mathematics 2ND Edition Used Trade Paper $14.95

Related Subjects


Reference » Science Reference » General
Science and Mathematics » Energy » General
Science and Mathematics » Mathematics » Games and Puzzles
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » History
Science and Mathematics » Mathematics » Popular Surveys and Recreational

Mathematics for the Nonmathematician Used Trade Paper
0 stars - 0 reviews
$6.95 In Stock
Product details 672 pages Dover Publications - English 9780486248233 Reviews:
"Synopsis" by ,
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" by , 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" by , 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.
spacer
spacer
  • back to top
Follow us on...




Powell's City of Books is an independent bookstore in Portland, Oregon, that fills a whole city block with more than a million new, used, and out of print books. Shop those shelves — plus literally millions more books, DVDs, and gifts — here at Powells.com.