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The Arche Papers On The Mathematics Of Abstraction
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Book Synopsis The Arché Papers on the Mathematics of Abstraction by : Roy T. Cook
Download or read book The Arché Papers on the Mathematics of Abstraction written by Roy T. Cook and published by Springer Science & Business Media. This book was released on 2007-11-27 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects together a number of important papers concerning both the method of abstraction generally and the use of particular abstraction principles to reconstruct central areas of mathematics along logicist lines. Attention is focused on extending the Neo-Fregean treatment to all of mathematics, with the reconstruction of real analysis from various cut- or cauchy-sequence-related abstraction principles and the reconstruction of set theory from various restricted versions of Basic Law V as case studies.
Book Synopsis A Gateway to Abstract Mathematics by :
Download or read book A Gateway to Abstract Mathematics written by and published by CUP Archive. This book was released on with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Limits of Abstraction by : Kit Fine
Download or read book The Limits of Abstraction written by Kit Fine and published by Clarendon Press. This book was released on 2002 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The Limits of Abstraction breaks new ground both technically and philosophically, and is essential reading for all those working on the philosophy of mathematics."--BOOK JACKET.
Book Synopsis Introducing Philosophy Through Pop Culture by : William Irwin
Download or read book Introducing Philosophy Through Pop Culture written by William Irwin and published by John Wiley & Sons. This book was released on 2022-03-10 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Can Wonder Woman help us understand feminist philosophy? How Does Wakandan technology transcend anti-Blackness? What can Star Trek teach us about the true nature of reality? Introducing Philosophy Through Pop Culture makes important philosophical concepts and the work of major philosophers relevant, fun, and exciting. Using engaging examples from film and television, this easy-to-read book covers everything from basic metaphysics and epistemology to abstract and complex philosophical ideas about ethics and the meaning of life. You don’t have to be a pop culture expert to benefit from this book—even a general awareness of cultural icons like Superman or Harry Potter will be more than enough for you to learn about a wide range of philosophical notions, thinkers, and movements. The expanded second edition offers timely coverage of important topics such as race, gender, personal identity, social justice, and environmental ethics. New essays explore the philosophical underpinnings of The Good Place, Game of Thrones, Black Panther, Star Wars, The Avengers, South Park, The Lego Movie, The Big Bang Theory, and more. This edition is supported by a new website with links to primary philosophical texts, information about all the popular culture discussed, and additional resources for teachers, students, and general readers alike. Features a selection of key essays from the bestselling Blackwell Philosophy and Pop Culture Series Draws on examples from popular media including The Matrix, Lost, Doctor Strange, The Hobbit, Westworld, and Star Trek Explains philosophical concepts such as relativism, skepticism, existentialist ethics, logic, social contract theory, utilitarianism, and mind-body dualism Discusses the ideas of Socrates, Aristotle, Plato, Descartes, Nietzsche, Heidegger, Marx, Mill, Kierkegaard, and other important thinkers Introducing Philosophy Through Pop Culture is an excellent supplementary textbook for introductory philos for introductory philosophy courses and a valuable resource for general readers wanting to learn about philosophy and its connections with pop culture.
Book Synopsis The Joy of Abstraction by : Eugenia Cheng
Download or read book The Joy of Abstraction written by Eugenia Cheng and published by Cambridge University Press. This book was released on 2022-10-13 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: A uniquely accessible introduction to abstract mathematics and category theory written by popular science author of How to Bake Pi.
Book Synopsis Bridge to Abstract Mathematics by : Ralph W. Oberste-Vorth
Download or read book Bridge to Abstract Mathematics written by Ralph W. Oberste-Vorth and published by American Mathematical Society. This book was released on 2020-02-20 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Bridge to Abstract Mathematics will prepare the mathematical novice to explore the universe of abstract mathematics. Mathematics is a science that concerns theorems that must be proved within the constraints of a logical system of axioms and definitions rather than theories that must be tested, revised, and retested. Readers will learn how to read mathematics beyond popular computational calculus courses. Moreover, readers will learn how to construct their own proofs. The book is intended as the primary text for an introductory course in proving theorems, as well as for self-study or as a reference. Throughout the text, some pieces (usually proofs) are left as exercises. Part V gives hints to help students find good approaches to the exercises. Part I introduces the language of mathematics and the methods of proof. The mathematical content of Parts II through IV were chosen so as not to seriously overlap the standard mathematics major. In Part II, students study sets, functions, equivalence and order relations, and cardinality. Part III concerns algebra. The goal is to prove that the real numbers form the unique, up to isomorphism, ordered field with the least upper bound. In the process, we construct the real numbers starting with the natural numbers. Students will be prepared for an abstract linear algebra or modern algebra course. Part IV studies analysis. Continuity and differentiation are considered in the context of time scales (nonempty, closed subsets of the real numbers). Students will be prepared for advanced calculus and general topology courses. There is a lot of room for instructors to skip and choose topics from among those that are presented.
Book Synopsis Introduction to Abstract Mathematics by : Theodore A. Bick
Download or read book Introduction to Abstract Mathematics written by Theodore A. Bick and published by . This book was released on 1971 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proceedings written by Leon Henkin and published by American Mathematical Soc.. This book was released on 1974 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A History of Abstract Algebra by : Jeremy Gray
Download or read book A History of Abstract Algebra written by Jeremy Gray and published by Springer. This book was released on 2018-08-07 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides an accessible account of the history of abstract algebra, tracing a range of topics in modern algebra and number theory back to their modest presence in the seventeenth and eighteenth centuries, and exploring the impact of ideas on the development of the subject. Beginning with Gauss’s theory of numbers and Galois’s ideas, the book progresses to Dedekind and Kronecker, Jordan and Klein, Steinitz, Hilbert, and Emmy Noether. Approaching mathematical topics from a historical perspective, the author explores quadratic forms, quadratic reciprocity, Fermat’s Last Theorem, cyclotomy, quintic equations, Galois theory, commutative rings, abstract fields, ideal theory, invariant theory, and group theory. Readers will learn what Galois accomplished, how difficult the proofs of his theorems were, and how important Camille Jordan and Felix Klein were in the eventual acceptance of Galois’s approach to the solution of equations. The book also describes the relationship between Kummer’s ideal numbers and Dedekind’s ideals, and discusses why Dedekind felt his solution to the divisor problem was better than Kummer’s. Designed for a course in the history of modern algebra, this book is aimed at undergraduate students with an introductory background in algebra but will also appeal to researchers with a general interest in the topic. With exercises at the end of each chapter and appendices providing material difficult to find elsewhere, this book is self-contained and therefore suitable for self-study.
Book Synopsis A History of Abstract Algebra by : Israel Kleiner
Download or read book A History of Abstract Algebra written by Israel Kleiner and published by Springer Science & Business Media. This book was released on 2007-10-02 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the history of abstract algebra. It shows how abstract algebra has arisen in attempting to solve some of these classical problems, providing a context from which the reader may gain a deeper appreciation of the mathematics involved.
Book Synopsis Fuzzy Logic and Mathematics by : Radim Belohlavek
Download or read book Fuzzy Logic and Mathematics written by Radim Belohlavek and published by Oxford University Press. This book was released on 2017-05-03 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: The term "fuzzy logic," as it is understood in this book, stands for all aspects of representing and manipulating knowledge based on the rejection of the most fundamental principle of classical logic---the principle of bivalence. According to this principle, each declarative sentence is required to be either true or false. In fuzzy logic, these classical truth values are not abandoned. However, additional, intermediate truth values between true and false are allowed, which are interpreted as degrees of truth. This opens a new way of thinking---thinking in terms of degrees rather than absolutes. For example, it leads to the definition of a new kind of sets, referred to as fuzzy sets, in which membership is a matter of degree. The book examines the genesis and development of fuzzy logic. It surveys the prehistory of fuzzy logic and inspects circumstances that eventually lead to the emergence of fuzzy logic. The book explores in detail the development of propositional, predicate, and other calculi that admit degrees of truth, which are known as fuzzy logic in the narrow sense. Fuzzy logic in the broad sense, whose primary aim is to utilize degrees of truth for emulating common-sense human reasoning in natural language, is scrutinized as well. The book also examines principles for developing mathematics based on fuzzy logic and provides overviews of areas in which this has been done most effectively. It also presents a detailed survey of established and prospective applications of fuzzy logic in various areas of human affairs, and provides an assessment of the significance of fuzzy logic as a new paradigm.
Book Synopsis A Century of Advancing Mathematics by : Paul Zorn
Download or read book A Century of Advancing Mathematics written by Paul Zorn and published by The Mathematical Association of America. This book was released on 2015-08-23 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: The MAA was founded in 1915 to serve as a home for The American Mathematical Monthly. The mission of the Association-to advance mathematics, especially at the collegiate level-has, however, always been larger than merely publishing world-class mathematical exposition. MAA members have explored more than just mathematics; we have, as this volume tries to make evident, investigated mathematical connections to pedagogy, history, the arts, technology, literature, every field of intellectual endeavor. Essays, all commissioned for this volume, include exposition by Bob Devaney, Robin Wilson, and Frank Morgan; history from Karen Parshall, Della Dumbaugh, and Bill Dunham; pedagogical discussion from Paul Zorn, Joe Gallian, and Michael Starbird, and cultural commentary from Bonnie Gold, Jon Borwein, and Steve Abbott. This volume contains 35 essays by all-star writers and expositors writing to celebrate an extraordinary century for mathematics-more mathematics has been created and published since 1915 than in all of previous recorded history. We've solved age-old mysteries, created entire new fields of study, and changed our conception of what mathematics is. Many of those stories are told in this volume as the contributors paint a portrait of the broad cultural sweep of mathematics during the MAA's first century. Mathematics is the most thrilling, the most human, area of intellectual inquiry; you will find in this volume compelling proof of that claim.
Book Synopsis Handbook of the History and Philosophy of Mathematical Practice by : Bharath Sriraman
Download or read book Handbook of the History and Philosophy of Mathematical Practice written by Bharath Sriraman and published by Springer Nature. This book was released on with total page 3221 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Far East Journal of Mathematical Sciences by :
Download or read book Far East Journal of Mathematical Sciences written by and published by . This book was released on 2007 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Hyperreason written by Mike Hockney and published by Magus Books. This book was released on with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: A sufficiently clever person, sitting alone in their room, could work out all of the principles of existence. No faith and no sensory observations or experiments are required. No one needs to spend billions on a Large Hadron Collider. It's not an atom smasher you need but a bullshit and fallacy smasher. Hyperrationalism differs from rationalism in asserting that all rational truths are mathematical and that the universe is 100% mathematical. "Hyperreason" is the extraordinary story of the attempts of the rational to explain reality via thought alone. Find out about Thomas Aquinas's five rationalist proofs for the existence of God, Leibniz's ontological argument and principle of sufficient reason, Gödel's Incompleteness Theorem, the Riemann hypothesis, the Multiverse theories of science and why the human brain - with its two hemispheres doing radically different types of Fourier mathematics - points the way to a complete understanding of reality. Welcome to the Mind of God!
Book Synopsis An Abstract of the Contents and Utilities of Books, Plans and Mechanical Machinery, ready for publication, by R. Blackburne. Together with an introductory preamble; setting forth the reasons which induced him ... to take this step, etc by : Robert Blackburne (teacher of mathematics at Liverpool.)
Download or read book An Abstract of the Contents and Utilities of Books, Plans and Mechanical Machinery, ready for publication, by R. Blackburne. Together with an introductory preamble; setting forth the reasons which induced him ... to take this step, etc written by Robert Blackburne (teacher of mathematics at Liverpool.) and published by . This book was released on 1777 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Causation and the Principle of Sufficient Reason by : Mike Hockney
Download or read book Causation and the Principle of Sufficient Reason written by Mike Hockney and published by Magus Books. This book was released on with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The cleverest people in the world are those most capable of making the least expected connections between apparently disparate things. This book explains how light, life, mind, souls, causation, motion, energy, ontological mathematics and ontological reason are all synonymous. Are you one of the rare few capable of seeing the light? Can you see the hidden mathematical order beneath the Grand Illusion presented to our senses? Only those on the verge of Enlightenment have any hope of understanding ontological mathematics, the science of the soul, the science of the unseen light of the Universal Mind. It's all in the math. "If then you do not make yourself equal to God, you cannot apprehend God; for like is known by like." - Hermes Trismegistus
