Mathematics A Concise History And Philosophy

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Mathematics: A Concise History and Philosophy

W.S. Anglin
Mathematics A Concise History and Philosophy Book PDF

Author : W.S. Anglin
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 54,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461208754

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Mathematics: A Concise History and Philosophy by W.S. Anglin Pdf

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.

A Concise History of Mathematics for Philosophers .

John Stillwell
A Concise History of Mathematics for Philosophers Book PDF

Author : John Stillwell
Publisher : Cambridge University Press
Page : 77 pages
File Size : 46,5 Mb
Release : 2019-06-06
Category : Science
ISBN : 9781108456234

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A Concise History of Mathematics for Philosophers . by John Stillwell Pdf

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.

A Concise History of Mathematics

Dirk Jan Struik
A Concise History of Mathematics Book PDF

Author : Dirk Jan Struik
Publisher : Courier Corporation
Page : 260 pages
File Size : 43,9 Mb
Release : 1967
Category : Mathematics
ISBN : 0486602559

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A Concise History of Mathematics by Dirk Jan Struik Pdf

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.

An Introduction to the Philosophy of Mathematics

Mark Colyvan
An Introduction to the Philosophy of Mathematics Book PDF

Author : Mark Colyvan
Publisher : Cambridge University Press
Page : 199 pages
File Size : 55,6 Mb
Release : 2012-06-14
Category : Mathematics
ISBN : 9780521826020

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An Introduction to the Philosophy of Mathematics by Mark Colyvan Pdf

A fascinating journey through intriguing mathematical and philosophical territory - a lively introduction to this contemporary topic.

History and Philosophy of Modern Mathematics

William Aspray,Philip Kitcher
History and Philosophy of Modern Mathematics Book PDF

Author : William Aspray,Philip Kitcher
Publisher : U of Minnesota Press
Page : 396 pages
File Size : 44,6 Mb
Release : 1988
Category : Mathematics
ISBN : 9780816615674

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History and Philosophy of Modern Mathematics by William Aspray,Philip Kitcher Pdf

History and Philosophy of Modern Mathematics was first published in 1988. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. The fourteen essays in this volume build on the pioneering effort of Garrett Birkhoff, professor of mathematics at Harvard University, who in 1974 organized a conference of mathematicians and historians of modern mathematics to examine how the two disciplines approach the history of mathematics. In History and Philosophy of Modern Mathematics, William Aspray and Philip Kitcher bring together distinguished scholars from mathematics, history, and philosophy to assess the current state of the field. Their essays, which grow out of a 1985 conference at the University of Minnesota, develop the basic premise that mathematical thought needs to be studied from an interdisciplinary perspective. The opening essays study issues arising within logic and the foundations of mathematics, a traditional area of interest to historians and philosophers. The second section examines issues in the history of mathematics within the framework of established historical periods and questions. Next come case studies that illustrate the power of an interdisciplinary approach to the study of mathematics. The collection closes with a look at mathematics from a sociohistorical perspective, including the way institutions affect what constitutes mathematical knowledge.

Philosophy of Mathematics

Øystein Linnebo
Philosophy of Mathematics Book PDF

Author : Øystein Linnebo
Publisher : Princeton University Press
Page : 214 pages
File Size : 43,5 Mb
Release : 2020-03-24
Category : Mathematics
ISBN : 9780691202297

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Philosophy of Mathematics by Øystein Linnebo Pdf

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.

Mathematics and Its History

John Stillwell
Mathematics and Its History Book PDF

Author : John Stillwell
Publisher : Springer Nature
Page : 400 pages
File Size : 48,7 Mb
Release : 2020-11-07
Category : Mathematics
ISBN : 9783030551933

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Mathematics and Its History by John Stillwell Pdf

This textbook provides a unified and concise exploration of undergraduate mathematics by approaching the subject through its history. Readers will discover the rich tapestry of ideas behind familiar topics from the undergraduate curriculum, such as calculus, algebra, topology, and more. Featuring historical episodes ranging from the Ancient Greeks to Fermat and Descartes, this volume offers a glimpse into the broader context in which these ideas developed, revealing unexpected connections that make this ideal for a senior capstone course. The presentation of previous versions has been refined by omitting the less mainstream topics and inserting new connecting material, allowing instructors to cover the book in a one-semester course. This condensed edition prioritizes succinctness and cohesiveness, and there is a greater emphasis on visual clarity, featuring full color images and high quality 3D models. As in previous editions, a wide array of mathematical topics are covered, from geometry to computation; however, biographical sketches have been omitted. Mathematics and Its History: A Concise Edition is an essential resource for courses or reading programs on the history of mathematics. Knowledge of basic calculus, algebra, geometry, topology, and set theory is assumed. From reviews of previous editions: “Mathematics and Its History is a joy to read. The writing is clear, concise and inviting. The style is very different from a traditional text. I found myself picking it up to read at the expense of my usual late evening thriller or detective novel.... The author has done a wonderful job of tying together the dominant themes of undergraduate mathematics.” Richard J. Wilders, MAA, on the Third Edition "The book...is presented in a lively style without unnecessary detail. It is very stimulating and will be appreciated not only by students. Much attention is paid to problems and to the development of mathematics before the end of the nineteenth century.... This book brings to the non-specialist interested in mathematics many interesting results. It can be recommended for seminars and will be enjoyed by the broad mathematical community." European Mathematical Society, on the Second Edition

Thinking about Mathematics

Stewart Shapiro
Thinking about Mathematics Book PDF

Author : Stewart Shapiro
Publisher : OUP Oxford
Page : 323 pages
File Size : 42,6 Mb
Release : 2000-07-13
Category : Philosophy
ISBN : 9780192893062

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Thinking about Mathematics by Stewart Shapiro Pdf

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.

A Brief History of Mathematical Thought

Luke Heaton
A Brief History of Mathematical Thought Book PDF

Author : Luke Heaton
Publisher : Oxford University Press
Page : 337 pages
File Size : 54,7 Mb
Release : 2017
Category : History
ISBN : 9780190621766

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A Brief History of Mathematical Thought by Luke Heaton Pdf

Emblazoned on many advertisements for the wildly popular game of Sudoku are the reassuring words, -no mathematical knowledge required.- Anxiety about math plagues many of us, and school memories can still summon intense loathing. In A Brief History of Mathematical Thought, Luke Heaton shows that much of what many think-and fear-about mathematics is misplaced, and to overcome our insecurities we need to understand its history. To help, he offers a lively guide into and through the world of mathematics and mathematicians, one in which patterns and arguments are traced through logic in a language grounded in concrete experience. Heaton reveals how Greek and Roman mathematicians like Pythagoras, Euclid, and Archimedes helped shaped the early logic of mathematics; how the Fibonacci sequence, the rise of algebra, and the invention of calculus are connected; how clocks, coordinates, and logical padlocks work mathematically; and how, in the twentieth century, Alan Turing's revolutionary work on the concept of computation laid the groundwork for the modern world. A Brief History of Mathematical Thought situates mathematics as part of, and essential to, lived experience. Understanding it requires not abstract thought or numbing memorization but an historical imagination and a view to its origins. --

Chinese Mathematics

Yan Li,Shiran Du
Chinese Mathematics Book PDF

Author : Yan Li,Shiran Du
Publisher : Oxford University Press, USA
Page : 312 pages
File Size : 54,7 Mb
Release : 1987
Category : Mathematics
ISBN : UOM:39015017285712

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Chinese Mathematics by Yan Li,Shiran Du Pdf

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.

Mathematics in Historical Context

Jeff Suzuki
Mathematics in Historical Context Book PDF

Author : Jeff Suzuki
Publisher : MAA
Page : 432 pages
File Size : 46,7 Mb
Release : 2009-08-27
Category : Mathematics
ISBN : 0883855704

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Mathematics in Historical Context by Jeff Suzuki Pdf

An exploration of the interaction between mathematics, mathematicians and society. What would Newton see if he looked out his window?

Analysis and Synthesis in Mathematics

Michael Otte,Marco Panza
Analysis and Synthesis in Mathematics Book PDF

Author : Michael Otte,Marco Panza
Publisher : Springer Science & Business Media
Page : 476 pages
File Size : 41,8 Mb
Release : 1997
Category : History
ISBN : 0792345703

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Analysis and Synthesis in Mathematics by Michael Otte,Marco Panza Pdf

The book discusses the main interpretations of the classical distinction between analysis and synthesis with respect to mathematics. In the first part, this is discussed from a historical point of view, by considering different examples from the history of mathematics. In the second part, the question is considered from a philosophical point of view, and some new interpretations are proposed. Finally, in the third part, one of the editors discusses some common aspects of the different interpretations.

More Precisely: The Math You Need to Do Philosophy - Second Edition

Eric Steinhart
More Precisely The Math You Need to Do Philosophy Second Edition Book PDF

Author : Eric Steinhart
Publisher : Broadview Press
Page : 250 pages
File Size : 48,5 Mb
Release : 2017-11-21
Category : Philosophy
ISBN : 9781554813452

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More Precisely: The Math You Need to Do Philosophy - Second Edition by Eric Steinhart Pdf

More Precisely is a rigorous and engaging introduction to the mathematics necessary to do philosophy. Eric Steinhart provides lucid explanations of many basic mathematical concepts and sets out the most commonly used notational conventions. He also demonstrates how mathematics applies to fundamental issues in various branches of philosophy, including metaphysics, philosophy of language, epistemology, and ethics. This second edition adds a substantial section on decision and game theory, as well as a chapter on information theory and the efficient coding of information.

Research in History and Philosophy of Mathematics

Maria Zack,Dirk Schlimm
Research in History and Philosophy of Mathematics Book PDF

Author : Maria Zack,Dirk Schlimm
Publisher : Springer
Page : 203 pages
File Size : 51,7 Mb
Release : 2018-09-14
Category : Mathematics
ISBN : 9783319909837

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Research in History and Philosophy of Mathematics by Maria Zack,Dirk Schlimm Pdf

This volume contains thirteen papers that were presented at the 2017 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/Société canadienne d’histoire et de philosophie des mathématiques, which was held at Ryerson University in Toronto. It showcases rigorously reviewed modern scholarship on an interesting variety of topics in the history and philosophy of mathematics from Ancient Greece to the twentieth century. A series of chapters all set in the eighteenth century consider topics such as John Marsh’s techniques for the computation of decimal fractions, Euler’s efforts to compute the surface area of scalene cones, a little-known work by John Playfair on the practical aspects of mathematics, and Monge’s use of descriptive geometry. After a brief stop in the nineteenth century to consider the culture of research mathematics in 1860s Prussia, the book moves into the twentieth century with an examination of the historical context within which the Axiom of Choice was developed and a paper discussing Anatoly Vlasov’s adaptation of the Boltzmann equation to ionized gases. The remaining chapters deal with the philosophy of twentieth-century mathematics through topics such as an historically informed discussion of finitism and its limits; a reexamination of Mary Leng’s defenses of mathematical fictionalism through an alternative, anti-realist approach to mathematics; and a look at the reasons that mathematicians select specific problems to pursue. Written by leading scholars in the field, these papers are accessible to not only mathematicians and students of the history and philosophy of mathematics, but also anyone with a general interest in mathematics.

Converging Realities

Roland Omnès
Converging Realities Book PDF

Author : Roland Omnès
Publisher : Princeton University Press
Page : 300 pages
File Size : 55,6 Mb
Release : 2005
Category : Mathematics
ISBN : 0691115303

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Converging Realities by Roland Omnès Pdf

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