History of Mathematics Series

History of Mathematics, The: Probability and Statistics, the Science of Uncertainty. Facts on File Math Library.

Geometry; The Language of Space and Form. Facts on File Math Library: The History of Mathematics.

Progress has often been slow when it comes to understanding numbers. Numbers provide a rich source of exotic ideas, philosophical and mathematical, but because many of us are so invested in the familiar, we have often resisted ideas about numbers that are new and unfamiliar.

Numbers, Revised Edition deals with numbers from the point of view of computation, beginning with the earliest number concepts from ancient Mesopotamian, Chinese, and Mayan mathematicians. It describes the origin and diffusion of Arabic numerals, and it concludes with a discussion of the way that the number system is represented within computers. A new section describes some of the IEEE standards for floating point arithmetic, and a more detailed discussion of the work of Goedel and Turing has been added to this edition. Irrational numbers and the idea of infinity are also examined in this in-depth guide.

Probability and Statistics

by John Tabak

Published 21 October 2004

Concepts from the fields of probability and statistics pervade our thinking--even those of us who believe in the existence of luck--and we routinely express ourselves using language borrowed from various branches of mathematics. News reports, weather reports, and even sports reports are some examples of the probabilistic and statistical thinking that seeps into our everyday lives.

Probability and Statistics, Revised Edition deals with the history of probability, describing the modern concept of randomness and examining ""pre-probabilistic"" ideas of what most people today would characterize as randomness. This revised book documents some historically important early uses of probability to illustrate some very important probabilistic questions. It goes on to explore statistics and the generations of mathematicians and non-mathematicians who began to address problems in statistical analysis, including the statistical structure of data sets as well as the theory of sampling and the characterization of the nature of variation. The final chapter describes the role of statistics in the development, testing, licensure, and subsequent study of vaccines. A new chapter has been added that gives special attention to vaccines for measles, polio, pertussis, and rubella.\p>

Algebra

by John Tabak

Published 1 January 2004

For thousands of years, algebra consisted solely of expanding the list of problem-solving algorithms-a list of procedures similar in concept to the quadratic formula. But much of contemporary algebra focuses on identifying and describing the logical structures upon which mathematics is built. It is now clear that identifying and exploiting these structures is just as important for mathematical and scientific progress as the development of new algorithms.

Algebra, Revised Edition describes the history of both strands of algebraic thought. This updated resource describes some of the earliest progress in algebra as well as some of the mathematicians in Mesopotamia, Egypt, China, and Greece who contributed to this early period. It goes on to explore the many breakthroughs in algebraic techniques as well as how letters were used to represent numbers. New material has been added to the chapter on ""modern"" algebra, a type of mathematical research that continues to occupy the attention of many mathematicians today.\p>

Mathematics and the Laws of Nature

by John Tabak

Published 1 January 2004

Mathematical methods are useful in understanding nature. Though many people accept this view without question, it is usually an act of faith. History demonstrates that nature's most fundamental and important patterns are neither easy to recognize nor easy to harness for the common good. The development of the concepts and methods necessary to deduce new knowledge of nature from already established results-and the development of methods to separate correct results from incorrect ones-remains a work-in-progress. Attempts to create these methods are documented in the earliest written records, and efforts to refine these methods and develop new ones continue to this day.

Mathematics and the Laws of Nature, Revised Edition describes the evolution of the idea that nature can be described in the language of mathematics. Colorful chapters explore the earliest attempts to apply deductive methods to the study of the natural world. This revised resource goes on to examine the development of classical conservation laws, including the conservation of momentum, the conservation of mass, and the conservation of energy. Chapters have been updated and revised to reflect recent information, including the mathematical pioneers who introduced new ideas about what it meant to solve an equation and the influential efforts of the mathematicians of the former Soviet Union.\p>

Geometry

by John Tabak

Published 22 June 2004

Greek ideas about geometry, straight-edge and compass constructions, and the nature of mathematical proof dominated mathematical thought for about 2,000 years. Projective geometry began its development in the Renaissance as artists like da Vinci and Durer explored methods for representing 3-dimensional objects on 2-dimensional surfaces. These ideas were refined and made increasingly abstract in the 19th and 20th centuries. Late in the 20th century, ideas from projective geometry found widespread application in the area of computer graphics. Similarly, Descartes's ideas about coordinate geometry led to progress in finding mathematical representations for shapes of increasing complexity, including the shape of the universe and other areas considered by mathematicians today. Covering the many aspects of geometry, this volume of the History of Mathematics series presents a compelling look at mathematical theories alongside historical occurrences. The engaging and informative text, complemented by photographs and illustrations, introduces students to the fascinating story of how geometry has developed.
Biographical information on key figures, a look at different applications of geometry over time, and the groundbreaking discoveries related to geometry are comprehensively covered.