Download or read book Set Theory and the Continuum Hypothesis written by Paul J. Cohen and published by Courier Corporation. This book was released on 2008-12-09 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This exploration of a notorious mathematical problem is the work of the man who discovered the solution. Written by an award-winning professor at Stanford University, it employs intuitive explanations as well as detailed mathematical proofs in a self-contained treatment. This unique text and reference is suitable for students and professionals. 1966 edition. Copyright renewed 1994.
Download or read book Set Theory and the Continuum Problem written by Raymond M. Smullyan and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A lucid, elegant, and complete survey of set theory, this three-part treatment explores axiomatic set theory, the consistency of the continuum hypothesis, and forcing and independence results. 1996 edition.
Download or read book An Introduction to Homological Algebra written by Charles A. Weibel and published by Cambridge University Press. This book was released on 1995-10-27 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: The landscape of homological algebra has evolved over the last half-century into a fundamental tool for the working mathematician. This book provides a unified account of homological algebra as it exists today. The historical connection with topology, regular local rings, and semi-simple Lie algebras are also described. This book is suitable for second or third year graduate students. The first half of the book takes as its subject the canonical topics in homological algebra: derived functors, Tor and Ext, projective dimensions and spectral sequences. Homology of group and Lie algebras illustrate these topics. Intermingled are less canonical topics, such as the derived inverse limit functor lim1, local cohomology, Galois cohomology, and affine Lie algebras. The last part of the book covers less traditional topics that are a vital part of the modern homological toolkit: simplicial methods, Hochschild and cyclic homology, derived categories and total derived functors. By making these tools more accessible, the book helps to break down the technological barrier between experts and casual users of homological algebra.
Download or read book Continuum Mechanics written by D. S. Chandrasekharaiah and published by Elsevier. This book was released on 2014-05-19 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed and self-contained text written for beginners, Continuum Mechanics offers concise coverage of the basic concepts, general principles, and applications of continuum mechanics. Without sacrificing rigor, the clear and simple mathematical derivations are made accessible to a large number of students with little or no previous background in solid or fluid mechanics. With the inclusion of more than 250 fully worked-out examples and 500 worked exercises, this book is certain to become a standard introductory text for students as well as an indispensable reference for professionals. - Provides a clear and self-contained treatment of vectors, matrices, and tensors specifically tailored to the needs of continuum mechanics - Develops the concepts and principles common to all areas in solid and fluid mechanics with a common notation and terminology - Covers the fundamentals of elasticity theory and fluid mechanics
Download or read book The Laboratory of the Mind written by James Robert Brown and published by Routledge. This book was released on 2005-09-26 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thought experiments are performed in the laboratory of the mind. Beyond this metaphor it is difficult to say just what these remarkable devices for investigating nature are or how they work. Though most scientists and philosophers would admit their great importance, there has been very little serious study of them. This volume is the first book-length investigation of thought experiments. Starting with Galileo's argument on falling bodies, Brown describes numerous examples of the most influential thought experiments from the history of science. Following this introduction to the subject, some substantial and provocative claims are made, the principle being that some thought experiments should be understood in the same way that platonists understand mathematical activity: as an intellectual grasp of an independently existing abstract realm. With its clarity of style and structure, The Laboratory of the Mind will find readers among all philosophers of science as well as scientists who have puzzled over how thought experiments work.
Download or read book The Axiom of Determinacy Forcing Axioms and the Nonstationary Ideal written by W. Hugh Woodin and published by Walter de Gruyter. This book was released on 2013-02-01 with total page 944 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of high-level monographs on all areas of mathematical logic and its applications. It is addressed to advanced students and research mathematicians, and may also serve as a guide for lectures and for seminars at the graduate level.
Download or read book Forcing For Mathematicians written by Nik Weaver and published by World Scientific. This book was released on 2014-01-24 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ever since Paul Cohen's spectacular use of the forcing concept to prove the independence of the continuum hypothesis from the standard axioms of set theory, forcing has been seen by the general mathematical community as a subject of great intrinsic interest but one that is technically so forbidding that it is only accessible to specialists. In the past decade, a series of remarkable solutions to long-standing problems in C*-algebra using set-theoretic methods, many achieved by the author and his collaborators, have generated new interest in this subject. This is the first book aimed at explaining forcing to general mathematicians. It simultaneously makes the subject broadly accessible by explaining it in a clear, simple manner, and surveys advanced applications of set theory to mainstream topics.
Download or read book Combinatorial Set Theory Partition Relations for Cardinals written by P. Erdös and published by Elsevier. This book was released on 2011-08-18 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents the most important combinatorial ideas in partition calculus and discusses ordinary partition relations for cardinals without the assumption of the generalized continuum hypothesis. A separate section of the book describes the main partition symbols scattered in the literature. A chapter on the applications of the combinatorial methods in partition calculus includes a section on topology with Arhangel'skii's famous result that a first countable compact Hausdorff space has cardinality, at most continuum. Several sections on set mappings are included as well as an account of recent inequalities for cardinal powers that were obtained in the wake of Silver's breakthrough result saying that the continuum hypothesis can not first fail at a singular cardinal of uncountable cofinality.
Download or read book The Foundations of Analysis A Straightforward Introduction written by K. G. Binmore and published by Cambridge University Press. This book was released on 1981-03-26 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: In elementary introductions to mathematical analysis, the treatment of the logical and algebraic foundations of the subject is necessarily rather skeletal. This book attempts to flesh out the bones of such treatment by providing an informal but systematic account of the foundations of mathematical analysis written at an elementary level. This book is entirely self-contained but, as indicated above, it will be of most use to university or college students who are taking, or who have taken, an introductory course in analysis. Such a course will not automatically cover all the material dealt with in this book and so particular care has been taken to present the material in a manner which makes it suitable for self-study. In a particular, there are a large number of examples and exercises and, where necessary, hints to the solutions are provided. This style of presentation, of course, will also make the book useful for those studying the subject independently of taught course.
Download or read book Zermelo s Axiom of Choice written by G.H. Moore and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of my interest in what is common to three disciplines: mathematics, philosophy, and history. The origins of Zermelo's Axiom of Choice, as well as the controversy that it engendered, certainly lie in that intersection. Since the time of Aristotle, mathematics has been concerned alternately with its assumptions and with the objects, such as number and space, about which those assumptions were made. In the historical context of Zermelo's Axiom, I have explored both the vagaries and the fertility of this alternating concern. Though Zermelo's research has provided the focus for this book, much of it is devoted to the problems from which his work originated and to the later developments which, directly or indirectly, he inspired. A few remarks about format are in order. In this book a publication is indicated by a date after a name; so Hilbert 1926, 178 refers to page 178 of an article written by Hilbert, published in 1926, and listed in the bibliography.
Download or read book The Axiom of Choice written by Thomas J. Jech and published by Courier Corporation. This book was released on 2008-01-01 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive and self-contained text examines the axiom's relative strengths and consequences, including its consistency and independence, relation to permutation models, and examples and counterexamples of its use. 1973 edition.
Download or read book Set Theory Arithmetic and Foundations of Mathematics written by Juliette Kennedy and published by Cambridge University Press. This book was released on 2011-09-01 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of papers from various areas of mathematical logic showcases the remarkable breadth and richness of the field. Leading authors reveal how contemporary technical results touch upon foundational questions about the nature of mathematics. Highlights of the volume include: a history of Tennenbaum's theorem in arithmetic; a number of papers on Tennenbaum phenomena in weak arithmetics as well as on other aspects of arithmetics, such as interpretability; the transcript of Gödel's previously unpublished 1972-1975 conversations with Sue Toledo, along with an appreciation of the same by Curtis Franks; Hugh Woodin's paper arguing against the generic multiverse view; Anne Troelstra's history of intuitionism through 1991; and Aki Kanamori's history of the Suslin problem in set theory. The book provides a historical and philosophical treatment of particular theorems in arithmetic and set theory, and is ideal for researchers and graduate students in mathematical logic and philosophy of mathematics.
Download or read book Algorithms and Complexity in Mathematics Epistemology and Science written by Nicolas Fillion and published by Springer. This book was released on 2019-02-07 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: ACMES (Algorithms and Complexity in Mathematics, Epistemology, and Science) is a multidisciplinary conference series that focuses on epistemological and mathematical issues relating to computation in modern science. This volume includes a selection of papers presented at the 2015 and 2016 conferences held at Western University that provide an interdisciplinary outlook on modern applied mathematics that draws from theory and practice, and situates it in proper context. These papers come from leading mathematicians, computational scientists, and philosophers of science, and cover a broad collection of mathematical and philosophical topics, including numerical analysis and its underlying philosophy, computer algebra, reliability and uncertainty quantification, computation and complexity theory, combinatorics, error analysis, perturbation theory, experimental mathematics, scientific epistemology, and foundations of mathematics. By bringing together contributions from researchers who approach the mathematical sciences from different perspectives, the volume will further readers' understanding of the multifaceted role of mathematics in modern science, informed by the state of the art in mathematics, scientific computing, and current modeling techniques.
Download or read book Contributions to the Founding of the Theory of Transfinite Numbers written by Georg Cantor and published by . This book was released on 1915 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Appalachian Set Theory written by James Cummings and published by Cambridge University Press. This book was released on 2012-11-15 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume takes its name from a popular series of intensive mathematics workshops hosted at institutions in Appalachia and surrounding areas. At these meetings, internationally prominent set theorists give one-day lectures that focus on important new directions, methods, tools and results so that non-experts can begin to master these and incorporate them into their own research. Each chapter in this volume was written by the workshop leaders in collaboration with select student participants, and together they represent most of the meetings from the period 2006–2012. Topics covered include forcing and large cardinals, descriptive set theory, and applications of set theoretic ideas in group theory and analysis, making this volume essential reading for a wide range of researchers and graduate students.
Download or read book The Continuum written by Hermann Weyl and published by Courier Corporation. This book was released on 1994-01-01 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise classic by great mathematician and physicist deals with logic and mathematics of set and function, concept of number and the continuum. Bibliography. Originally published 1918.
Download or read book Understanding the Infinite written by Shaughan Lavine and published by Harvard University Press. This book was released on 2009-06-30 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible history and philosophical commentary on our notion of infinity. How can the infinite, a subject so remote from our finite experience, be an everyday tool for the working mathematician? Blending history, philosophy, mathematics, and logic, Shaughan Lavine answers this question with exceptional clarity. Making use of the mathematical work of Jan Mycielski, he demonstrates that knowledge of the infinite is possible, even according to strict standards that require some intuitive basis for knowledge. Praise for Understanding the Infinite “Understanding the Infinite is a remarkable blend of mathematics, modern history, philosophy, and logic, laced with refreshing doses of common sense. It is a potted history of, and a philosophical commentary on, the modern notion of infinity as formalized in axiomatic set theory . . . An amazingly readable [book] given the difficult subject matter. Most of all, it is an eminently sensible book. Anyone who wants to explore the deep issues surrounding the concept of infinity . . . will get a great deal of pleasure from it.” —Ian Stewart, New Scientist “How, in a finite world, does one obtain any knowledge about the infinite? Lavine argues that intuitions about the infinite derive from facts about the finite mathematics of indefinitely large size . . . The issues are delicate, but the writing is crisp and exciting, the arguments original. This book should interest readers whether philosophically, historically, or mathematically inclined, and large parts are within the grasp of the general reader. Highly recommended.” —D. V. Feldman, Choice
