Synopses & Reviews
"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 ChronicleSince 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.
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.
Stimulating account of growth of math and physical sciences from arithmetic to calculus and non-Euclidean geometries. 147 illus.
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, other phenomena.
Table of Contents
1: THE WHY AND WHEREFORE
2: DISCOVERY AND PROOF
3: THE SCIENCE OF ARITHMETIC
4: THE DEEPER WATERS OF ARITHMETIC
5: "NUMBERS, KNOWN AND UNKNOWN"
6: THE LAWS OF SPACE AND FORMS
7: THE DIMENSIONS OF THE HEAVENLY SPHERES
8: THE REVOLUTIONS OF THE HEAVENLY SPHERES
9: THE SCIENTIFIC REVOLUTION
10: THE WEDDING OF CURVE AND EQUATION
11: EXPLANATION VERSUS DESCRIPTION
12: VERTICAL MOTION
13: MOTION ON AN INCLINED PLANE
14: THE MOTION OF PROJECTILES
15: FROM PROJECTILE TO PLANET AND SATELLITE
16: DEDUCTIONS FROM THE LAW OF GRAVITATION
17: MORE LIGHT ON LIGHT
18: THE MATHEMATICS OF OSCILLATORY MOTION
19: OSCILLATIONS OF THE AIR
20: OLD FOES WITH NEW FACES
21: MATHEMATICAL OSCILLATIONS OF THE ETHER
22: THE DIFFERENTIAL CALCULUS
23: THE INTEGRAL CALCULUS
24: DIFFERENTIAL EQUATIONS-THE HEART OF ANALYSIS
25: FROM CALCULUS TO COSMIC PLANNING
26: NON-EUCLIDEAN GEOMETRIES
27: MATHEMATICS AND NATURE