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Traces development of arithmetic, algebra, geometry, and trigonometry in ancient world; influence of Hindu and Arabic mathematicians on medieval Europe; and trends that led to modern mathematics. 1917 edition.
Includes section "Recent publications."
Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.
In Infinite Ascent, David Berlinski, the acclaimed author of The Advent of the Algorithm, A Tour of the Calculus, and Newton’s Gift, tells the story of mathematics, bringing to life with wit, elegance, and deep insight a 2,500-year-long intellectual adventure. Berlinski focuses on the ten most important breakthroughs in mathematical history–and the men behind them. Here are Pythagoras, intoxicated by the mystical significance of numbers; Euclid, who gave the world the very idea of a proof; Leibniz and Newton, co-discoverers of the calculus; Cantor, master of the infinite; and Gödel, who in one magnificent proof placed everything in doubt. The elaboration of mathematical knowledge has meant nothing less than the unfolding of human consciousness itself. With his unmatched ability to make abstract ideas concrete and approachable, Berlinski both tells an engrossing tale and introduces us to the full power of what surely ranks as one of the greatest of all human endeavors.
Quantitative analysis is a fundamental mode of thought in the modern world, and quantitative reasoning is one of the most powerful tools available for the study and interpretation of historical events. By using examples from published historical works,ÊUnderstanding Quantitative HistoryÊprovides historians and nonhistorians with an introductory guide to descriptive statistics, sampling and multivariate analysis, and formal reasoning. The book will prepare readers to understand and critique quantitative analysis in history and related disciplines such as sociology and political science. More broadly it will allow readers to participate more effectively in a wide range of public-policy discussions that use - or misuse numbers. One of the best ways to gain proficiency as a reader of quantitative history is to practice on published books and articles.ÊUnderstanding Quantitative HistoryÊreprints brief examples from a wide range of published works in American history, covering such topics as black women's, labor, and family history from early colonial times to the post-World War II era. Each chapter includes thirty to fifty questions with answers provided at the end of the chapter. The authors rely on ordinary language rather than mathematical terminology and emphasize the underlying logic of quantitative arguments rather than the details of the calculations. Understanding Quantitative HistoryÊwas sponsored by the Alfred P. Sloan Foundation.
Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.
Covering a span of almost 4000 years, from the ancient Babylonians to the eighteenth century, this collection chronicles the enormous changes in mathematical thinking over this time as viewed by distinguished historians of mathematics from the past and the present. Each of the four sections of the book (Ancient Mathematics, Medieval and Renaissance Mathematics, The Seventeenth Century, The Eighteenth Century) is preceded by a Foreword, in which the articles are put into historical context, and followed by an Afterword, in which they are reviewed in the light of current historical scholarship. In more than one case, two articles on the same topic are included to show how knowledge and views about the topic changed over the years. This book will be enjoyed by anyone interested in mathematics and its history - and, in particular, by mathematics teachers at secondary, college, and university levels.