The Nature and Power of Mathematics (Dover Books on Mathematics)

In this engaging book, Donald Davis explains some of the most fascinating ideas in mathematics to the nonspecialist, highlighting their philosophical and historical interest, their often surprising applicability, and their beauty. The three main topics discussed are non-Euclidean geometry, with its application to the theory of relativity; number theory, with its application to cryptography; and fractals, which are an application in art, among other areas, of early mathematical work on iteration. Other topics include the influence of Greek mathematics on Kepler's laws of planetary motion, and the theoretical work that led to the development of computers. Assuming the reader has some background in basic algebra and geometry, Davis relies on exercises to develop some of the important concepts. These exercises are designed to improve the reader's ability in logic, and enable him or her actually to experience mathematics at increasingly advanced levels. This captivating book explains some of mathematics' most fascinating ideas to nonspecialists. It explores items of philosophical and historical interest, discusses the often-surprising applicability of mathematics, and reveals the subject's intrinsic beauty. Author Donald M. Davis focuses on three main areas: non-Euclidean geometry, a basis for relativity theory; number theory, a major component of cryptography; and fractals, the key elements of computer-generated art. He also discusses related topics, such as the relevance of Greek mathematics to Kepler's laws of planetary motion, and the theoretical work that led to the development of computers.Only a background in basic algebra and geometry is necessary to appreciate this volume, which features exercises that further develop some of its important concepts. Graded according to difficulty, these exercises are designed to improve readers' skills in logic, and to enable them to experience mathematics at increasingly advanced levels. Supplementary materials at the end of each chapter include intriguing examples of the subjects' applications, as well as biographical sketches of Archimedes, Einstein, Newton, and other luminaries of mathematics. This captivating book explains some of mathematics' most fascinating ideas to nonspecialists. It explores items of philosophical and historical interest, discusses the often-surprising applicability of mathematics, and reveals the subject's intrinsic beauty. Author Donald M. Davis focuses on three main non-Euclidean geometry, a basis for relativity theory; number theory, a major component of cryptography; and fractals, the key elements of computer-generated art. He also discusses related topics, such as the relevance of Greek mathematics to Kepler's laws of planetary motion, and the theoretical work that led to the development of computers. Only a background in basic algebra and geometry is necessary to appreciate this volume, which features exercises that further develop some of its important concepts. Graded according to difficulty, these exercises are designed to improve readers' skills in logic, and to enable them to experience mathematics at increasingly advanced levels. Supplementary materials at the end of each chapter include intriguing examples of the subjects' applications, as well as biographical sketches of Archimedes, Einstein, Newton, and other luminaries of mathematics.

in This Engaging Book, Donald Davis Explains Some Of The Most Fascinating Ideas In Mathematics To The Nonspecialist, Highlighting Their Philosophical And Historical Interest, Their Often Surprising Applicability, And Their Beauty. The Three Main Topics Discussed Are Non-euclidean Geometry, With Its Application To The Theory Of Relativity; Number Theory, With Its Application To Cryptography; And Fractals, Which Are An Application In Art, Among Other Areas, Of Early Mathematical Work On Iteration. Other Topics Include The Influence Of Greek Mathematics On Kepler's Laws Of Planetary Motion, And The Theoretical Work That Led To The Development Of Computers.

assuming The Reader Has Some Background In Basic Algebra And Geometry, Davis Relies On Exercises To Develop Some Of The Important Concepts. These Exercises Are Designed To Improve The Reader's Ability In Logic, And Enable Him Or Her Actually To Experience Mathematics At Increasingly Advanced Levels.

This volume explains ideas in mathematics to the non-specialist, highlighting the field's philosophical and historical interest. The main topics discussed are non-Euclidean geometry, number theory, with its application to cryptography, and fractals. Donald M. Davis. Includes Bibliographical References (p. [379]-382) And Index.