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Cultures Of Mathematics And Logic
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Download or read book Mathematics and Logic written by Mark Kac and published by Courier Corporation. This book was released on 1992-01-01 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fascinating study of the origin and nature of mathematical thought, including relation of mathematics and science, 20th-century developments, impact of computers, and more.Includes 34 illustrations. 1968 edition."
Book Synopsis Cultures of Mathematics and Logic by : Shier Ju
Download or read book Cultures of Mathematics and Logic written by Shier Ju and published by Birkhäuser. This book was released on 2016-08-10 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers the proceedings of the conference "Cultures of Mathematics and Logic," held in Guangzhou, China. The event was the third in a series of interdisciplinary, international conferences emphasizing the cultural components of philosophy of mathematics and logic. It brought together researchers from many disciplines whose work sheds new light on the diversity of mathematical and logical cultures and practices. In this context, the cultural diversity can be diachronical (different cultures in different historical periods), geographical (different cultures in different regions), or sociological in nature.
Book Synopsis Mathematics Across Cultures by : Helaine Selin
Download or read book Mathematics Across Cultures written by Helaine Selin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics Across Cultures: A History of Non-Western Mathematics consists of essays dealing with the mathematical knowledge and beliefs of cultures outside the United States and Europe. In addition to articles surveying Islamic, Chinese, Native American, Aboriginal Australian, Inca, Egyptian, and African mathematics, among others, the book includes essays on Rationality, Logic and Mathematics, and the transfer of knowledge from East to West. The essays address the connections between science and culture and relate the mathematical practices to the cultures which produced them. Each essay is well illustrated and contains an extensive bibliography. Because the geographic range is global, the book fills a gap in both the history of science and in cultural studies. It should find a place on the bookshelves of advanced undergraduate students, graduate students, and scholars, as well as in libraries serving those groups.
Book Synopsis Mathematics as a Cultural System by : Raymond L. Wilder
Download or read book Mathematics as a Cultural System written by Raymond L. Wilder and published by Elsevier. This book was released on 2014-05-20 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics as a Cultural System discusses the relationship between mathematics and culture. The book is comprised of eight chapters discussing topics that support the concept of mathematics as a cultural system. Chapter I deals with the nature of culture and cultural systems, while Chapter 2 provides examples of cultural patterns observable in the evolution of mechanics. Chapter III treats historical episodes as a laboratory for the illustration of patterns and forces that have been operative in cultural change. Chapter IV covers hereditary stress, and Chapter V discusses consolidation as a force and process. Chapter VI talks about the singularities in the evolution of mechanics, while Chapter 7 deals with the laws governing the evolution of mathematics. Chapter VIII tackles the role and future of mathematics. The book will be of great interest to readers who are curious about how mathematics relates to culture.
Book Synopsis Introduction to Mathematical Logic by : Alonzo Church
Download or read book Introduction to Mathematical Logic written by Alonzo Church and published by . This book was released on 1965 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mathematics in Popular Culture by : Jessica K. Sklar
Download or read book Mathematics in Popular Culture written by Jessica K. Sklar and published by McFarland. This book was released on 2014-01-10 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics has maintained a surprising presence in popular media for over a century. In recent years, the movies Good Will Hunting, A Beautiful Mind, and Stand and Deliver, the stage plays Breaking the Code and Proof, the novella Flatland and the hugely successful television crime series NUMB3RS all weave mathematics prominently into their storylines. Less obvious but pivotal references to the subject appear in the blockbuster TV show Lost, the cult movie The Princess Bride, and even Tolstoy's War and Peace. In this collection of new essays, contributors consider the role of math in everything from films, baseball, crossword puzzles, fantasy role-playing games, and television shows to science fiction tales, award-winning plays and classic works of literature. Revealing the broad range of intersections between mathematics and mainstream culture, this collection demonstrates that even "mass entertainment" can have a hidden depth.
Book Synopsis A Course in Mathematical Logic by : Yu.I. Manin
Download or read book A Course in Mathematical Logic written by Yu.I. Manin and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. This book is above all addressed to mathematicians. It is intended to be a textbook of mathematical logic on a sophisticated level, presenting the reader with several of the most significant discoveries of the last ten or fifteen years. These include: the independence of the continuum hypothe sis, the Diophantine nature of enumerable sets, the impossibility of finding an algorithmic solution for one or two old problems. All the necessary preliminary material, including predicate logic and the fundamentals of recursive function theory, is presented systematically and with complete proofs. We only assume that the reader is familiar with "naive" set theoretic arguments. In this book mathematical logic is presented both as a part of mathe matics and as the result of its self-perception. Thus, the substance of the book consists of difficult proofs of subtle theorems, and the spirit of the book consists of attempts to explain what these theorems say about the mathematical way of thought. Foundational problems are for the most part passed over in silence. Most likely, logic is capable of justifying mathematics to no greater extent than biology is capable of justifying life. 2. The first two chapters are devoted to predicate logic. The presenta tion here is fairly standard, except that semantics occupies a very domi nant position, truth is introduced before deducibility, and models of speech in formal languages precede the systematic study of syntax.
Book Synopsis A First Course in Mathematical Logic and Set Theory by : Michael L. O'Leary
Download or read book A First Course in Mathematical Logic and Set Theory written by Michael L. O'Leary and published by John Wiley & Sons. This book was released on 2015-09-14 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematical introduction to the theory and applications of logic and set theory with an emphasis on writing proofs Highlighting the applications and notations of basic mathematical concepts within the framework of logic and set theory, A First Course in Mathematical Logic and Set Theory introduces how logic is used to prepare and structure proofs and solve more complex problems. The book begins with propositional logic, including two-column proofs and truth table applications, followed by first-order logic, which provides the structure for writing mathematical proofs. Set theory is then introduced and serves as the basis for defining relations, functions, numbers, mathematical induction, ordinals, and cardinals. The book concludes with a primer on basic model theory with applications to abstract algebra. A First Course in Mathematical Logic and Set Theory also includes: Section exercises designed to show the interactions between topics and reinforce the presented ideas and concepts Numerous examples that illustrate theorems and employ basic concepts such as Euclid’s lemma, the Fibonacci sequence, and unique factorization Coverage of important theorems including the well-ordering theorem, completeness theorem, compactness theorem, as well as the theorems of Löwenheim–Skolem, Burali-Forti, Hartogs, Cantor–Schröder–Bernstein, and König An excellent textbook for students studying the foundations of mathematics and mathematical proofs, A First Course in Mathematical Logic and Set Theory is also appropriate for readers preparing for careers in mathematics education or computer science. In addition, the book is ideal for introductory courses on mathematical logic and/or set theory and appropriate for upper-undergraduate transition courses with rigorous mathematical reasoning involving algebra, number theory, or analysis.
Book Synopsis Advances in Experimental Philosophy of Logic and Mathematics by : Andrew Aberdein
Download or read book Advances in Experimental Philosophy of Logic and Mathematics written by Andrew Aberdein and published by Bloomsbury Publishing. This book was released on 2019-05-02 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the results of applying empirical methods to the philosophy of logic and mathematics. Much of the work that has earned experimental philosophy a prominent place in twenty-first century philosophy is concerned with ethics or epistemology. But, as this book shows, empirical methods are just as much at home in logic and the philosophy of mathematics. Chapters demonstrate and discuss the applicability of a wide range of empirical methods including experiments, surveys, interviews, and data-mining. Distinct themes emerge that reflect recent developments in the field, such as issues concerning the logic of conditionals and the role played by visual elements in some mathematical proofs. Featuring leading figures from experimental philosophy and the fields of philosophy of logic and mathematics, this collection reveals that empirical work in these disciplines has been quietly thriving for some time and stresses the importance of collaboration between philosophers and researchers in mathematics education and mathematical cognition.
Book Synopsis The Primary Logic by : Michele Malatesta
Download or read book The Primary Logic written by Michele Malatesta and published by Gracewing Publishing. This book was released on 1997 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Concise Introduction to Mathematical Logic by : Wolfgang Rautenberg
Download or read book A Concise Introduction to Mathematical Logic written by Wolfgang Rautenberg and published by Springer. This book was released on 2010-07-01 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical logic developed into a broad discipline with many applications in mathematics, informatics, linguistics and philosophy. This text introduces the fundamentals of this field, and this new edition has been thoroughly expanded and revised.
Book Synopsis A Mathematical Introduction to Logic by : Herbert B. Enderton
Download or read book A Mathematical Introduction to Logic written by Herbert B. Enderton and published by Elsevier. This book was released on 2001-01-23 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Mathematical Introduction to Logic
Book Synopsis The Mathematical Imagination by : Matthew Handelman
Download or read book The Mathematical Imagination written by Matthew Handelman and published by Fordham Univ Press. This book was released on 2019-03-05 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an archeology of the undeveloped potential of mathematics for critical theory. As Max Horkheimer and Theodor W. Adorno first conceived of the critical project in the 1930s, critical theory steadfastly opposed the mathematization of thought. Mathematics flattened thought into a dangerous positivism that led reason to the barbarism of World War II. The Mathematical Imagination challenges this narrative, showing how for other German-Jewish thinkers, such as Gershom Scholem, Franz Rosenzweig, and Siegfried Kracauer, mathematics offered metaphors to negotiate the crises of modernity during the Weimar Republic. Influential theories of poetry, messianism, and cultural critique, Handelman shows, borrowed from the philosophy of mathematics, infinitesimal calculus, and geometry in order to refashion cultural and aesthetic discourse. Drawn to the austerity and muteness of mathematics, these friends and forerunners of the Frankfurt School found in mathematical approaches to negativity strategies to capture the marginalized experiences and perspectives of Jews in Germany. Their vocabulary, in which theory could be both mathematical and critical, is missing from the intellectual history of critical theory, whether in the work of second generation critical theorists such as Jürgen Habermas or in contemporary critiques of technology. The Mathematical Imagination shows how Scholem, Rosenzweig, and Kracauer’s engagement with mathematics uncovers a more capacious vision of the critical project, one with tools that can help us intervene in our digital and increasingly mathematical present.
Book Synopsis Mathematics: A Very Short Introduction by : Timothy Gowers
Download or read book Mathematics: A Very Short Introduction written by Timothy Gowers and published by Oxford Paperbacks. This book was released on 2002-08-22 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this volume is to explain the differences between research-level mathematics and the maths taught at school. Most differences are philosophical and the first few chapters are about general aspects of mathematical thought.
Download or read book Ethnomathematics written by Marcia Ascher and published by Routledge. This book was released on 2017-12-01 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this truly one-of-a-kind book, Ascher introduces the mathematical ideas of people in traditional, or ""small-scale"", cultures often omitted from discussion of mathematics. Topics such as ""Numbers: Words and Symbols"", ""Tracing Graphs in the Sand"", ""The Logic of Kin Relations"", ""Chance and Strategy in Games and Puzzles"", and ""The Organization and Modeling of Space"" are traced in various cultures including the Inuit, Navajo, and Iroquois of North America; the Inca of South America; the Malekula, Warlpiri, Maori, and Caroline Islanders of Oceania, and the Tshokwe, Bushoong, and Kpelle of Africa. As Ascher explores mathematical ideas involving numbers, logic, spatial configuration, and the organization of these into systems and structures, readers gain both a broader understanding and anappreciation for the idease of other peoples.
Book Synopsis Science and an African Logic by : Helen Verran
Download or read book Science and an African Logic written by Helen Verran and published by University of Chicago Press. This book was released on 2001-12-15 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Does two and two equal four? Ask someone and they should answer yes. An equation such as this seems the very definition of certainty, but is it? In this book, Helen Verran addresses precisely that question.
Book Synopsis The Mathematics of Logic by : Richard W. Kaye
Download or read book The Mathematics of Logic written by Richard W. Kaye and published by Cambridge University Press. This book was released on 2007-07-12 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate textbook covers the key material for a typical first course in logic, in particular presenting a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. Looking at a series of interesting systems, increasing in complexity, then proving and discussing the Completeness Theorem for each, the author ensures that the number of new concepts to be absorbed at each stage is manageable, whilst providing lively mathematical applications throughout. Unfamiliar terminology is kept to a minimum, no background in formal set-theory is required, and the book contains proofs of all the required set theoretical results. The reader is taken on a journey starting with König's Lemma, and progressing via order relations, Zorn's Lemma, Boolean algebras, and propositional logic, to completeness and compactness of first-order logic. As applications of the work on first-order logic, two final chapters provide introductions to model theory and nonstandard analysis.
