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Set Theoretic Approach To Algebraic Structures In Mathematics A Revelation
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Author :W. B. Vasantha Kandasamy, Florentin Smarandache Publisher :Infinite Study ISBN 13 :1599732122 Total Pages :168 pages Book Rating :4.5/5 (997 download)
Book Synopsis Set Theoretic Approach to Algebraic Structures in Mathematics - A Revelation by : W. B. Vasantha Kandasamy, Florentin Smarandache
Download or read book Set Theoretic Approach to Algebraic Structures in Mathematics - A Revelation written by W. B. Vasantha Kandasamy, Florentin Smarandache and published by Infinite Study. This book was released on 2013 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Book of Abstract Algebra by : Charles C Pinter
Download or read book A Book of Abstract Algebra written by Charles C Pinter and published by Courier Corporation. This book was released on 2010-01-14 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
Book Synopsis Revolutions and Revelations in Computability by : Ulrich Berger
Download or read book Revolutions and Revelations in Computability written by Ulrich Berger and published by Springer Nature. This book was released on 2022-06-25 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 18th Conference on Computability in Europe, CiE 2022, in Swansea, UK, in July 2022. The 19 full papers together with 7 invited papers presented in this volume were carefully reviewed and selected from 41 submissions. The motto of CiE 2022 was “Revolutions and revelations in computability”. This alludes to the revolutionary developments we have seen in computability theory, starting with Turing's and Gödel's discoveries of the uncomputable and the unprovable and continuing to the present day with the advent of new computational paradigms such as quantum computing and bio-computing, which have dramatically changed our view of computability and revealed new insights into the multifarious nature of computation.
Book Synopsis On the Formal Elements of the Absolute Algebra by : Ernst Schroeder
Download or read book On the Formal Elements of the Absolute Algebra written by Ernst Schroeder and published by LED Edizioni Universitarie. This book was released on 2012-05-23T00:00:00+02:00 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: TABLE OF CONTENTS: ALGEBRA, WHAT ELSE?: 1. The Birth of a Masterwork - 2. Commutativity and Left- and Right-Division - 3. Algorithms, Algorithms, Algorithms - 4. Formalism - 5. A Fateful Choice - 6. Overview - 7. A Strange Document - 8. Acknowledgements - 9. Tools - Notes — ON THE FORMAL ELEMENTS OF THE ABSOLUTE ALGEBRA: §. 1. Character des zu behandelnden Problems. Character of the Problem in Issue - §. 2. Einschränkungen der Aufgabe. Restrictions of our Scope - §. 3. Die Fundamentalgleichungen für nur zwei Zahlen. Algorithmen. The Fundamental Equations for only Two Numbers. Algorithms - §. 4. Vertauschungsprincipien. Principles of Permutation - §. 5. Die Fundamentalgleichungen für drei Zahlen. Elementarcyklen und Gruppen. The Fundamental Equations for Three Numbers. Elementary Cycles and Groups - §. 6. Consequenzen der Algorithmen C1; C2; C3 für drei Zahlen. Consequences of the Algorithms C1; C2; C3 for Three Numbers - §. 7. Consequenzen von C0. Consequences of C0 - §. 8. Combination der Ci. Combination of the Ci - §. 9. Das Formelsystem O1 der ordinäre Algebra. The Formal System O1 of the Usual Algebra - §. 10. Untergeordnete Algorithmen von O1: Weitere ermittelte Tragweitezahlen. Subordinate Algorithms of O1: Further Sizes — FIGURES - Notes — APPENDIX - Notes — ILLUSTRATIONS - Bibliography - Index of the Main Concepts - Index of the Illustrations.
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 Encyclopaedia of Mathematics by : Michiel Hazewinkel
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Book Synopsis The Cognitive-Theoretic Model of the Universe: A New Kind of Reality Theory by : Christopher Michael Langan
Download or read book The Cognitive-Theoretic Model of the Universe: A New Kind of Reality Theory written by Christopher Michael Langan and published by Mega Foundation Press. This book was released on 2002-06-01 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: Paperback version of the 2002 paper published in the journal Progress in Information, Complexity, and Design (PCID). ABSTRACT Inasmuch as science is observational or perceptual in nature, the goal of providing a scientific model and mechanism for the evolution of complex systems ultimately requires a supporting theory of reality of which perception itself is the model (or theory-to-universe mapping). Where information is the abstract currency of perception, such a theory must incorporate the theory of information while extending the information concept to incorporate reflexive self-processing in order to achieve an intrinsic (self-contained) description of reality. This extension is associated with a limiting formulation of model theory identifying mental and physical reality, resulting in a reflexively self-generating, self-modeling theory of reality identical to its universe on the syntactic level. By the nature of its derivation, this theory, the Cognitive Theoretic Model of the Universe or CTMU, can be regarded as a supertautological reality-theoretic extension of logic. Uniting the theory of reality with an advanced form of computational language theory, the CTMU describes reality as a Self Configuring Self-Processing Language or SCSPL, a reflexive intrinsic language characterized not only by self-reference and recursive self-definition, but full self-configuration and self-execution (reflexive read-write functionality). SCSPL reality embodies a dual-aspect monism consisting of infocognition, self-transducing information residing in self-recognizing SCSPL elements called syntactic operators. The CTMU identifies itself with the structure of these operators and thus with the distributive syntax of its self-modeling SCSPL universe, including the reflexive grammar by which the universe refines itself from unbound telesis or UBT, a primordial realm of infocognitive potential free of informational constraint. Under the guidance of a limiting (intrinsic) form of anthropic principle called the Telic Principle, SCSPL evolves by telic recursion, jointly configuring syntax and state while maximizing a generalized self-selection parameter and adjusting on the fly to freely-changing internal conditions. SCSPL relates space, time and object by means of conspansive duality and conspansion, an SCSPL-grammatical process featuring an alternation between dual phases of existence associated with design and actualization and related to the familiar wave-particle duality of quantum mechanics. By distributing the design phase of reality over the actualization phase, conspansive spacetime also provides a distributed mechanism for Intelligent Design, adjoining to the restrictive principle of natural selection a basic means of generating information and complexity. Addressing physical evolution on not only the biological but cosmic level, the CTMU addresses the most evident deficiencies and paradoxes associated with conventional discrete and continuum models of reality, including temporal directionality and accelerating cosmic expansion, while preserving virtually all of the major benefits of current scientific and mathematical paradigms.
Book Synopsis The Topos of Music III: Gestures by : Guerino Mazzola
Download or read book The Topos of Music III: Gestures written by Guerino Mazzola and published by Springer. This book was released on 2018-03-28 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third volume of the second edition of the now classic book “The Topos of Music”. The authors present gesture theory, including a gesture philosophy for music, the mathematics of gestures, concept architectures and software for musical gesture theory, the multiverse perspective which reveals the relationship between gesture theory and the string theory in theoretical physics, and applications of gesture theory to a number of musical themes, including counterpoint, modulation theory, free jazz, Hindustani music, and vocal gestures.
Download or read book The New Era in Home and School written by and published by . This book was released on 1964 with total page 860 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Logical Foundation for Potentialist Set Theory by : Sharon Berry
Download or read book A Logical Foundation for Potentialist Set Theory written by Sharon Berry and published by Cambridge University Press. This book was released on 2022-02-17 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new approach to the standard axioms of set theory, relating the theory to the philosophy of science and metametaphysics.
Download or read book The New Era written by and published by . This book was released on 1964 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Convenient Setting of Global Analysis by : Andreas Kriegl
Download or read book The Convenient Setting of Global Analysis written by Andreas Kriegl and published by American Mathematical Society. This book was released on 2024-08-15 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book lays the foundations of differential calculus in infinite dimensions and discusses those applications in infinite dimensional differential geometry and global analysis not involving Sobolev completions and fixed point theory. The approach is simple: a mapping is called smooth if it maps smooth curves to smooth curves. Up to Fr‚chet spaces, this notion of smoothness coincides with all known reasonable concepts. In the same spirit, calculus of holomorphic mappings (including Hartogs' theorem and holomorphic uniform boundedness theorems) and calculus of real analytic mappings are developed. Existence of smooth partitions of unity, the foundations of manifold theory in infinite dimensions, the relation between tangent vectors and derivations, and differential forms are discussed thoroughly. Special emphasis is given to the notion of regular infinite dimensional Lie groups. Many applications of this theory are included: manifolds of smooth mappings, groups of diffeomorphisms, geodesics on spaces of Riemannian metrics, direct limit manifolds, perturbation theory of operators, and differentiability questions of infinite dimensional representations.
Book Synopsis New Essays on Tarski and Philosophy by : Douglas Patterson
Download or read book New Essays on Tarski and Philosophy written by Douglas Patterson and published by OUP Oxford. This book was released on 2008-09-18 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: New Essays on Tarski and Philosophy aims to show the way to a proper understanding of the philosophical legacy of the great logician, mathematician, and philosopher Alfred Tarski (1902-1983). The contributors are an international group of scholars, some expert in the historical background and context of Tarski's work, others specializing in aspects of his philosophical development, others more interested in understanding Tarski in the light of contemporary thought. The essays can be seen as addressing Tarski's seminal treatment of four basic questions about logical consequence. (1) How are we to understand truth, one of the notions in terms of which logical consequence is explained? What is it that is preserved in valid inference, or that such inference allows us to discover new claims to have on the basis of old? (2) Among what kinds of things does the relation of logical consequence hold? (3) Given answers to the first two questions, what is involved in the consequence relationship itself? What is the preservation at work in 'truth preservation'? (4) Finally, what do truth and consequence so construed have to do with meaning?
Book Synopsis Belief and Probability by : J.M. Vickers
Download or read book Belief and Probability written by J.M. Vickers and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. A WORD ABOUT PRESUPPOSITIONS This book is addressed to philosophers, and not necessarily to those philosophers whose interests and competence are largely mathematical or logical in the formal sense. It deals for the most part with problems in the theory of partial judgment. These problems are naturally formulated in numerical and logical terms, and it is often not easy to formulate them precisely otherwise. Indeed, the involvement of arithmetical and logical concepts seems essential to the philosophies of mind and action at just the point where they become concerned with partial judgment and" belief. I have tried throughout to use no mathematics that is not quite elementary, for the most part no more than ordinary arithmetic and algebra. There is some rudimentary and philosophically important employment of limits, but no use is made of integrals or differentials. Mathematical induction is rarely and inessentially employed in the text, but is more frequent and important in the apP'endix on set theory and Boolean algebra. • As far as logic is concerned, the book assumes a fair acquaintance with predicate logic and its techniques. The concepts of compactness and maximal consistency turn out to have important employment, which I have tried to keep self-contained, so that extensive knowledge of meta logical topics is not assumed. In a word, the book presupposes no more logical facility than is customary among working philosophers and graduate students, though it may call for unaccustomed vigor in its application.
Book Synopsis A Course in Mathematical Logic for Mathematicians by : Yu. I. Manin
Download or read book A Course in Mathematical Logic for Mathematicians written by Yu. I. Manin and published by Springer Science & Business Media. This book was released on 2009-10-13 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. The ?rst edition of this book was published in 1977. The text has been well received and is still used, although it has been out of print for some time. In the intervening three decades, a lot of interesting things have happened to mathematical logic: (i) Model theory has shown that insights acquired in the study of formal languages could be used fruitfully in solving old problems of conventional mathematics. (ii) Mathematics has been and is moving with growing acceleration from the set-theoretic language of structures to the language and intuition of (higher) categories, leaving behind old concerns about in?nities: a new view of foundations is now emerging. (iii) Computer science, a no-nonsense child of the abstract computability theory, has been creatively dealing with old challenges and providing new ones, such as the P/NP problem. Planning additional chapters for this second edition, I have decided to focus onmodeltheory,the conspicuousabsenceofwhichinthe ?rsteditionwasnoted in several reviews, and the theory of computation, including its categorical and quantum aspects. The whole Part IV: Model Theory, is new. I am very grateful to Boris I. Zilber, who kindly agreed to write it. It may be read directly after Chapter II. The contents of the ?rst edition are basically reproduced here as Chapters I–VIII. Section IV.7, on the cardinality of the continuum, is completed by Section IV.7.3, discussing H. Woodin’s discovery.
Book Synopsis Mathematics without Numbers by : Geoffrey Hellman
Download or read book Mathematics without Numbers written by Geoffrey Hellman and published by Clarendon Press. This book was released on 1989-10-12 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geoffrey Hellman presents a detailed interpretation of mathematics as the investigation of structural possibilities, as opposed to absolute, Platonic objects. After dealing with the natural numbers and analysis, he extends his approach to set theory, and shows how to dispense with a fixed universe of sets. Finally, he addresses problems of application to the physical world.
Book Synopsis Redeeming Mathematics by : Vern S. Poythress
Download or read book Redeeming Mathematics written by Vern S. Poythress and published by Crossway. This book was released on 2015-01-31 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: What does Christianity have to do with the study of mathematics? Prolific writer and scholar Vern Poythress offers a startling answer to this perplexing question: everything. This groundbreaking book argues that the harmony of abstract mathematical truths, the physical world of things, and the personal world of our thinking depends on the existence of the Christian God. With advanced degrees in mathematics and New Testament studies, Poythress shows that these distinct “perspectives” on mathematics cohere because all three find their origin in God’s consistent character and nature. Whether it’s simple addition and subtraction or more complex mathematical concepts such as set theory and the nature of infinity, this comprehensive book lays a theistic foundation for all mathematical inquiry.
