# Mathematics for the Non-mathematician

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## Description

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## Product details

- Paperback | 641 pages
- 138 x 216 x 33mm | 670g
- 01 Aug 1985
- Dover Publications Inc.
- New York, United States
- English
- Illustrations, unspecified
- 0486248232
- 9780486248233
- 68,760

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## Table of contents

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

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## About Morris Kline

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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