Priestley W.M. Calculus: A Liberal Art

Springer, 1986. - 339 Pages. This book originated with a series of lectures on nineteenth-century analysis which I gave at the University of Calabria in 1977- 79. The study of nineteenth-century mathematics presents an extraordinarily rich and fertile field for historical research, particularly when we realize that the production of mathematics in the last century was greater than in all the preceding centuries put together, and that many contem...

Springer, 1994. - 368 Pages. This is a lucid account of the highlights in the historical development of the calculus from ancient to modern times from the beginnings of geometry in antiquity to the nonstandard analysis of the twentieth century. It emphasizes the genesis and evolution of both fundamental concepts and computational techniques. The intended audience includes not only students of the history of mathematics, but also the wider mathem...

Springer, 2011. - 478 pages. This book offers an accessible and in-depth look at some of the most important episodes of two thousand years of mathematical history. Beginning with trigonometry and moving on through logarithms, complex numbers, infinite series, and calculus, this book profiles some of the lesser known but crucial contributors to modern day mathematics. It is unique in its use of primary sources as well as its accessibility; a kno...

Cambridge University Press, 2003. - 244 pages. Guicciardini presents a comprehensive survey of both the research and teaching of Newtonian calculus, the calculus of "fluxions", over the period between 1700 and 1810. Although Newton was one of the inventors of calculus, the developments in Britain remained separate from the rest of Europe for over a century. While it is usually maintained that after Newton there was a period of decline in British...

Springer, 2008. - 377 pages. This book presents first-year calculus roughly in the order in which it first was discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. The text is...

Springer, 2004. - 158 Pages. What is the relationship between modern mathematics - more precisely computational mathematics - and mathematical education? It is this controversal topic that the authors address with an in-depth analysis. In fact, what they present in an extremely well-reasoned account of the development of mathematics and its culture giving concrete recommendation for a much-needed reform of the teaching of mathematics. The book i...

Birkhauser Basel, 2009. - 207 pages. Galileo and Newton’s work towards the mathematisation of the physical world; Leibniz’s universal logical calculus; the Enlightenment’s math?matique sociale. John von Neumann inherited all these aims and philosophical intuitions, together with an idea that grew up around the Vienna Circle of an ethics in the form of an exact science capable of guiding individuals to make correct decisions. With the help of his...

Princeton University Press, 1994. - 223 pages. The story of pi has been told many times, both in scholarly works and in popular books. But its close relative, the number e, has fared less well. Despite the central role it plays in mathematics, its history has never before been written for a general audience. The present work fills this gap. Geared to the reader with only a modest background in mathematics, the book describes the story of e from...

Sterling, 2009. - 528 pages. Math’s infinite mysteries and beauty unfold in this follow-up to the best-selling The Science Book. Beginning millions of years ago with ancient ant odometers and moving through time to our modern-day quest for new dimensions, it covers 250 milestones in mathematical history. Among the numerous delights readers will learn about as they dip into this inviting anthology: cicada-generated prime numbers, magic squares fr...

AMS, 2006. - 302 Pages. Euler is one of the greatest and most prolific mathematicians of all time. He wrote the first accessible books on calculus, created the theory of circular functions, and discovered new areas of research such as elliptic integrals, the calculus of variations, graph theory, divergent series, and so on. It took hundreds of years for his successors to develop in full the theories he began, and some of his themes are still at...