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Philosophy Of Mathematics And Deductive Structure In Euclids Elements
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Book Synopsis Philosophy of Mathematics and Deductive Structure in Euclid's Elements by : Ian Mueller
Download or read book Philosophy of Mathematics and Deductive Structure in Euclid's Elements written by Ian Mueller and published by Courier Dover Publications. This book was released on 2006 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of Euclid's Elements, this text provides an understanding of the classical Greek conception of mathematics and its similarities to modern views as well as its differences. It focuses on philosophical, foundational, and logical questions -- rather than focusing strictly on historical and mathematical issues -- and features several helpful appendixes.
Book Synopsis Euclid's Elements (the Thirteen Books) by : Euclid
Download or read book Euclid's Elements (the Thirteen Books) written by Euclid and published by . This book was released on 2017-12-17 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Euclid was a mathematician from the Greek city of Alexandria who lived during the 4th and 3rd century B.C. and is often referred to as the "father of geometry." Within his foundational treatise "Elements," Euclid presents the results of earlier mathematicians and includes many of his own theories in a systematic, concise book that utilized a brief set of axioms and meticulous proofs to solidify his deductions. In addition to its easily referenced geometry, "Elements" also includes number theory and other mathematical considerations. For centuries, this work was a primary textbook of mathematics, containing the only framework for geometry known by mathematicians until the development of "non-Euclidian" geometry in the late 19th century. The extent to which Euclid's "Elements" is of his own original authorship or borrowed from previous scholars is unknown, however despite this fact it was his collation of these basic mathematical principles for which most of the world would come to the study of geometry. Today, Euclid's "Elements" is acknowledged as one of the most influential mathematical texts in history. This volume includes all thirteen books of Euclid's "Elements," is printed on premium acid-free paper, and follows the translation of Thomas Heath.
Book Synopsis Reader's Guide to the History of Science by : Arne Hessenbruch
Download or read book Reader's Guide to the History of Science written by Arne Hessenbruch and published by Routledge. This book was released on 2013-12-16 with total page 965 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Reader's Guide to the History of Science looks at the literature of science in some 550 entries on individuals (Einstein), institutions and disciplines (Mathematics), general themes (Romantic Science) and central concepts (Paradigm and Fact). The history of science is construed widely to include the history of medicine and technology as is reflected in the range of disciplines from which the international team of 200 contributors are drawn.
Book Synopsis Mathematics in Kant's Critical Philosophy by : Lisa Shabel
Download or read book Mathematics in Kant's Critical Philosophy written by Lisa Shabel and published by Routledge. This book was released on 2017-09-25 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 2003. Routledge is an imprint of Taylor & Francis, an informa company.
Book Synopsis Set Theory: The Structure of Arithmetic by : Norman T. Hamilton
Download or read book Set Theory: The Structure of Arithmetic written by Norman T. Hamilton and published by Courier Dover Publications. This book was released on 2018-05-16 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is formulated on the fundamental idea that much of mathematics, including the classical number systems, can best be based on set theory. Beginning with a discussion of the rudiments of set theory, authors Norman T. Hamilton and Joseph Landin lead readers through a construction of the natural number system, discussing the integers and the rational numbers, and concluding with an in-depth examination of the real numbers. Drawn from lecture notes for a course intended primarily for high school mathematics teachers, this volume was designed to answer the question, "What is a number?" and to provide a foundation for the study of abstract algebra, elementary Euclidean geometry, and analysis. Upon completion of this treatment — which is suitable for high school mathematics teachers and advanced high school students — readers should be well prepared for introductory courses in abstract algebra and real variables.
Book Synopsis The Tyranny of Public Discourse by : David Hirsch
Download or read book The Tyranny of Public Discourse written by David Hirsch and published by Casemate Publishers. This book was released on 2019-05-19 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: “The ultimate teacher of fact-based, reasoned rhetoric . . . A nice dose of American history makes learning the groundbreaking technique fun.” —Nerida F. Ellerton and McKenzie A. Clements, authors on writings of Thomas Jefferson and Abraham Lincoln Are you satisfied with the current state of public discourse? The almost unanimous response from people across the nation is a loud and emphatic “No!” The reply is always the same regardless of politics. Today’s public discourse typically starts with a “conclusion” and goes downhill from there. If there are talking heads, argument begins instantly and typically runs in circles. This is a dangerous path for a society that depends upon civility and virtue to survive. The Tyranny of Public Discourse addresses what is one of the most important issues of our time. This book can teach anyone how to use logic and reason to create persuasive writing. A byproduct of this is the civility that will ensue with an elevated public discourse. The Tyranny of Public Discourse establishes the six elements of a proposition as a verbal form of the scientific method—something Abraham Lincoln knew and used routinely. His logic and reason are so well known that he is quoted today more than 150 years after his death. Learning the six elements and how to use them to discuss any topic at any time is not only fascinating, but fairly easy to understand and implement. This book sets it all out, step-by-step and color coded, from beginning to end. The Tyranny of Public Discourse, complete with 21 diagrams on how to structure your logic, is the book you have been waiting for. The time is short, and the hour is now.
Book Synopsis Elements of the Theory of Functions by : Konrad Knopp
Download or read book Elements of the Theory of Functions written by Konrad Knopp and published by Courier Dover Publications. This book was released on 2016-10-05 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Well-known book provides a clear, concise review of complex numbers and their geometric representation; linear functions and circular transformations; sets, sequences, and power series; analytic functions and conformal mapping; and elementary functions. 1952 edition.
Book Synopsis An Introduction to Algebraic Structures by : Joseph Landin
Download or read book An Introduction to Algebraic Structures written by Joseph Landin and published by Courier Corporation. This book was released on 2012-08-29 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained text covers sets and numbers, elements of set theory, real numbers, the theory of groups, group isomorphism and homomorphism, theory of rings, and polynomial rings. 1969 edition.
Book Synopsis Revolutions and Continuity in Greek Mathematics by : Michalis Sialaros
Download or read book Revolutions and Continuity in Greek Mathematics written by Michalis Sialaros and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-04-23 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings together a number of leading scholars working in the field of ancient Greek mathematics to present their latest research. In their respective area of specialization, all contributors offer stimulating approaches to questions of historical and historiographical ‘revolutions’ and ‘continuity’. Taken together, they provide a powerful lens for evaluating the applicability of Thomas Kuhn’s ideas on ‘scientific revolutions’ to the discipline of ancient Greek mathematics. Besides the latest historiographical studies on ‘geometrical algebra’ and ‘premodern algebra’, the reader will find here some papers which offer new insights into the controversial relationship between Greek and pre-Hellenic mathematical practices. Some other contributions place emphasis on the other edge of the historical spectrum, by exploring historical lines of ‘continuity’ between ancient Greek, Byzantine and post-Hellenic mathematics. The terminology employed by Greek mathematicians, along with various non-textual and material elements, is another topic which some of the essays in the volume explore. Finally, the last three articles focus on a traditionally rich source on ancient Greek mathematics; namely the works of Plato and Aristotle.
Book Synopsis Mathematical Methods in the Theory of Queuing by : A. Y. Khinchin
Download or read book Mathematical Methods in the Theory of Queuing written by A. Y. Khinchin and published by Courier Corporation. This book was released on 2013-07-04 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a prominent Russian mathematician, this concise monograph examines aspects of queuing theory as an application of probability. Prerequisites include a familiarity with the theory of probability and mathematical analysis. 1960 edition.
Book Synopsis Mathematizing Space by : Vincenzo De Risi
Download or read book Mathematizing Space written by Vincenzo De Risi and published by Birkhäuser. This book was released on 2015-01-31 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects the papers of the conference held in Berlin, Germany, 27-29 August 2012, on 'Space, Geometry and the Imagination from Antiquity to the Modern Age'. The conference was a joint effort by the Max Planck Institute for the History of Science (Berlin) and the Centro die Ricerca Matematica Ennio De Giorgi (Pisa).
Book Synopsis Method in Ancient Philosophy by : Jyl Gentzler
Download or read book Method in Ancient Philosophy written by Jyl Gentzler and published by Oxford University Press. This book was released on 2001 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Method in Ancient Philosophy brings together fifteen new, specially written essays by leading scholars on a broad subject of central importance. It is characteristic of human beings that they direct their activities by reasoning, but methods of reasoning, even towards the same ends, vary. Self-conscious reflection on the methods of reasoning marks the beginning of philosophy in the West; and the views of the ancient Greeks have had considerable influence upon our own assumptions about the demarcations between different kinds of enquiry and the sorts of methods that are appropriate for them. For this reason, examination of how the ancients reasoned, and how they thought about methods of reasoning, helps us to see how they came to hold the views they did, and how we have come to think as we do. Most of the essays focus on Socrates, Plato, or Aristotle, but earlier and later ancient philosophy is brought into the picture by essays on Eleatic and Epicurean thought.
Book Synopsis Euclid—The Creation of Mathematics by : Benno Artmann
Download or read book Euclid—The Creation of Mathematics written by Benno Artmann and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Euclid presents the essential of mathematics in a manner which has set a high standard for more than 2000 years. This book, an explanation of the nature of mathematics from its most important early source, is for all lovers of mathematics with a solid background in high school geometry, whether they be students or university professors.
Download or read book Graph Theory written by Ronald Gould and published by Courier Corporation. This book was released on 2013-10-03 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory text in graph theory, this treatment covers primary techniques and includes both algorithmic and theoretical problems. Algorithms are presented with a minimum of advanced data structures and programming details. 1988 edition.
Download or read book Proof Theory written by Gaisi Takeuti and published by Courier Corporation. This book was released on 2013-01-01 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on Gentzen-type proof theory, this volume presents a detailed overview of creative works by author Gaisi Takeuti and other twentieth-century logicians. The text explores applications of proof theory to logic as well as other areas of mathematics. Suitable for advanced undergraduates and graduate students of mathematics, this long-out-of-print monograph forms a cornerstone for any library in mathematical logic and related topics. The three-part treatment begins with an exploration of first order systems, including a treatment of predicate calculus involving Gentzen's cut-elimination theorem and the theory of natural numbers in terms of Gödel's incompleteness theorem and Gentzen's consistency proof. The second part, which considers second order and finite order systems, covers simple type theory and infinitary logic. The final chapters address consistency problems with an examination of consistency proofs and their applications.
Book Synopsis Fractional Graph Theory by : Edward R. Scheinerman
Download or read book Fractional Graph Theory written by Edward R. Scheinerman and published by Courier Corporation. This book was released on 2011-01-01 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified treatment of the most important results in the study of fractional graph concepts, this volume explores the various ways in which integer-valued concepts can be modified to derive nonintegral values. It begins with the general fractional theory of hypergraphs and presents in-depth coverage of fundamental and advanced topics. Subjects include fractional matching, fractional coloring, fractional edge coloring, fractional arboricity via matroid methods, and fractional isomorphism. The final chapter examines additional topics such as fractional domination, fractional intersection numbers, and fractional aspects of partially ordered sets. Challenging exercises reinforce the contents of each chapter, and the authors provide substantial references and bibliographic materials. A comprehensive reference for researchers, this volume also constitutes an excellent graduate-level text for students of graph theory and linear programming.
Book Synopsis A Book of Set Theory by : Charles C Pinter
Download or read book A Book of Set Theory written by Charles C Pinter and published by Courier Corporation. This book was released on 2014-07-23 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--
