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Author: W.S. Anglin
Publisher: Springer Science & Business Media
ISBN: 1461208750
Category : Science
Languages : en
Pages : 253
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Book Description
This is a concise introductory textbook for a one-semester (40-class) course in the history and philosophy of mathematics. It is written for mathemat ics majors, philosophy students, history of science students, and (future) secondary school mathematics teachers. The only prerequisite is a solid command of precalculus mathematics. On the one hand, this book is designed to help mathematics majors ac quire a philosophical and cultural understanding of their subject by means of doing actual mathematical problems from different eras. On the other hand, it is designed to help philosophy, history, and education students come to a deeper understanding of the mathematical side of culture by means of writing short essays. The way I myself teach the material, stu dents are given a choice between mathematical assignments, and more his torical or philosophical assignments. (Some sample assignments and tests are found in an appendix to this book. ) This book differs from standard textbooks in several ways. First, it is shorter, and thus more accessible to students who have trouble coping with vast amounts of reading. Second, there are many detailed explanations of the important mathematical procedures actually used by famous mathe maticians, giving more mathematically talented students a greater oppor tunity to learn the history and philosophy by way of problem solving.
Author: W.S. Anglin
Publisher: Springer Science & Business Media
ISBN: 1461208750
Category : Science
Languages : en
Pages : 253
Get Book Here
Book Description
This is a concise introductory textbook for a one-semester (40-class) course in the history and philosophy of mathematics. It is written for mathemat ics majors, philosophy students, history of science students, and (future) secondary school mathematics teachers. The only prerequisite is a solid command of precalculus mathematics. On the one hand, this book is designed to help mathematics majors ac quire a philosophical and cultural understanding of their subject by means of doing actual mathematical problems from different eras. On the other hand, it is designed to help philosophy, history, and education students come to a deeper understanding of the mathematical side of culture by means of writing short essays. The way I myself teach the material, stu dents are given a choice between mathematical assignments, and more his torical or philosophical assignments. (Some sample assignments and tests are found in an appendix to this book. ) This book differs from standard textbooks in several ways. First, it is shorter, and thus more accessible to students who have trouble coping with vast amounts of reading. Second, there are many detailed explanations of the important mathematical procedures actually used by famous mathe maticians, giving more mathematically talented students a greater oppor tunity to learn the history and philosophy by way of problem solving.
Author: John Stillwell
Publisher: Cambridge University Press
ISBN: 1108456235
Category : Science
Languages : en
Pages : 77
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Book Description
This Element aims to present an outline of mathematics and its history, with particular emphasis on events that shook up its philosophy. It ranges from the discovery of irrational numbers in ancient Greece to the nineteenth- and twentieth-century discoveries on the nature of infinity and proof. Recurring themes are intuition and logic, meaning and existence, and the discrete and the continuous. These themes have evolved under the influence of new mathematical discoveries and the story of their evolution is, to a large extent, the story of philosophy of mathematics.
Author: Yan Li
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 312
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Book Description
This volume presents a record of mathematical developments in China over a period of more than 2000 years. It goes into greater detail than ever previously available in English. Because the emphasis in Chinese mathematics is on algorithms rather than proofs, readers will find results such as Bezout's theorem and Horner's method appearing in a very different context from the familiar tradition of Euclidean deductive geometry. The Chinese always preferred algebraic methods, and by the 13th century A.D. they were the best algebraists in the world. The original Chinese point of view is retained by the translators. They have supplemented the text with short explanatory comments and references to all relevant reference sources available in the West. An extensive bibliography is included, creating a work which will appeal to general readers interested in Chinese history as well as historians of mathematics.
Author: Dirk Jan Struik
Publisher: Courier Corporation
ISBN: 9780486602554
Category : Mathematics
Languages : en
Pages : 260
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Book Description
This compact, well-written history covers major mathematical ideas and techniques from the ancient Near East to 20th-century computer theory, surveying the works of Archimedes, Pascal, Gauss, Hilbert, and many others. "The author's ability as a first-class historian as well as an able mathematician has enabled him to produce a work which is unquestionably one of the best." — Nature.
Author: Øystein Linnebo
Publisher: Princeton University Press
ISBN: 069120229X
Category : Mathematics
Languages : en
Pages : 214
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Book Description
A sophisticated, original introduction to the philosophy of mathematics from one of its leading thinkers Mathematics is a model of precision and objectivity, but it appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic, accessible introduction to the field that is trying to answer that question: the philosophy of mathematics. Øystein Linnebo, one of the world's leading scholars on the subject, introduces all of the classical approaches to the field as well as more specialized issues, including mathematical intuition, potential infinity, and the search for new mathematical axioms. Sophisticated but clear and approachable, this is an essential book for all students and teachers of philosophy and of mathematics.
Author: Stephen P. Schwartz
Publisher: John Wiley & Sons
ISBN: 1118271726
Category : Philosophy
Languages : en
Pages : 367
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Book Description
A Brief History of Analytic Philosophy: From Russell to Rawls presents a comprehensive overview of the historical development of all major aspects of analytic philosophy, the dominant Anglo-American philosophical tradition in the twentieth century. Features coverage of all the major subject areas and figures in analytic philosophy - including Wittgenstein, Bertrand Russell, G.E. Moore, Gottlob Frege, Carnap, Quine, Davidson, Kripke, Putnam, and many others Contains explanatory background material to help make clear technical philosophical concepts Includes listings of suggested further readings Written in a clear, direct style that presupposes little previous knowledge of philosophy
Author: Mark Colyvan
Publisher: Cambridge University Press
ISBN: 0521826020
Category : Mathematics
Languages : en
Pages : 199
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Book Description
A fascinating journey through intriguing mathematical and philosophical territory - a lively introduction to this contemporary topic.
Author: David Bostock
Publisher: John Wiley & Sons
ISBN: 1405189924
Category : Mathematics
Languages : en
Pages : 345
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Book Description
Philosophy of Mathematics: An Introduction provides a critical analysis of the major philosophical issues and viewpoints in the concepts and methods of mathematics - from antiquity to the modern era. Offers beginning readers a critical appraisal of philosophical viewpoints throughout history Gives a separate chapter to predicativism, which is often (but wrongly) treated as if it were a part of logicism Provides readers with a non-partisan discussion until the final chapter, which gives the author's personal opinion on where the truth lies Designed to be accessible to both undergraduates and graduate students, and at the same time to be of interest to professionals
Author: Jeff Suzuki
Publisher: MAA
ISBN: 9780883855706
Category : Mathematics
Languages : en
Pages : 432
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Book Description
What would Newton see if he looked out his bedroom window? This book describes the world around the important mathematicians of the past, and explores the complex interaction between mathematics, mathematicians, and society. It takes the reader on a grand tour of history from the ancient Egyptians to the twentieth century to show how mathematicians and mathematics were affected by the outside world, and at the same time how the outside world was affected by mathematics and mathematicians. Part biography, part mathematics, and part history, this book provides the interested layperson the background to understand mathematics and the history of mathematics, and is suitable for supplemental reading in any history of mathematics course.
Author: Stewart Shapiro
Publisher: OUP Oxford
ISBN: 0192893068
Category : Philosophy
Languages : en
Pages : 323
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Book Description
Thinking about Mathematics covers the range of philosophical issues and positions concerning mathematics. The text describes the questions about mathematics that motivated philosophers throughout history and covers historical figures such as Plato, Aristotle, Kant, and Mill. It also presents the major positions and arguments concerning mathematics throughout the twentieth century, bringing the reader up to the present positions and battle lines.
