What Is Mathematics

Author: Richard Courant
Publisher: Oxford University Press, USA
ISBN: 0195105192
Size: 11.81 MB
Format: PDF
View: 64

A discussion of fundamental mathematical principles from algebra to elementary calculus designed to promote constructive mathematical reasoning.


Author: Timothy Gowers
Publisher: Sterling Publishing Company, Inc.
ISBN: 1402768974
Size: 16.45 MB
Format: PDF, ePub, Docs
View: 78

Mathematics is a subject we are all exposed to in our daily lives, but one that many of us fear. Timothy Gowers’s entertaining overview of the topic explains the differences between what we learn at school and advanced mathematics, and helps the math phobic emerge with a clearer understanding of such paradoxical-sounding concepts as “infinity,” “curved space,” and “imaginary numbers.” From basic ideas to philosophical queries to common sociological questions about the mathematical community, this book unravels the mysteries of space and numbers.

Philosophy Of Mathematics

Author: Paul Benacerraf
Publisher: Cambridge University Press
ISBN: 052129648X
Size: 20.54 MB
Format: PDF, Kindle
View: 16

The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.

What Is Mathematics Really

Author: Reuben Hersh
Publisher: Oxford University Press, USA
ISBN: 0195130871
Size: 10.92 MB
Format: PDF
View: 95

Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos. What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.

A History Of Mathematics

Author: Florian Cajori
Publisher: American Mathematical Soc.
ISBN: 0821821024
Size: 15.47 MB
Format: PDF, Mobi
View: 73

Originally published in 1893, this book was significantly revised and extended by the author (second edition, 1919) to cover the history of mathematics from antiquity to the end of World War I. Since then, three more editions were published, and the current volume is a reproduction of the fifth edition (1991). The book covers the history of ancient mathematics (Babylonian, Egyptian, Roman, Chinese, Japanese, Mayan, Hindu, and Arabic, with a major emphasis on ancient Greek mathematics). The chapters that follow explore European mathematics in the Middle Ages and the mathematics of the sixteenth, seventeenth, and eighteenth centuries (Vieta, Decartes, Newton, Euler, and Lagrange). The last and longest chapter discusses major mathematics events of the nineteenth and early twentieth centuries. Topics discussed in this chapter include synthetic and analytic geometry, algebra, analysis, the theory of functions, the theory of numbers, and others. In one concise volume, the author presents an interesting and reliable account of mathematics history. Cajori has mastered the art of incorporating an enormous amount of material into a smoothly flowing narrative. The review of the volume's third edition in Mathematical Reviews ends with the following words: "Chaque mathematicien devrait lire ce livre!"