Theory of Named Sets

Author: Mark Burgin

Publisher: Nova Science Pub Incorporated

ISBN: 9781611227888

Category: Mathematics

Page: 681

View: 8931

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Set theory has become one of the most respected fields in mathematics due to the situation in which sets are used to build all mathematical structures, pervading the whole of modern mathematics, and objects, while set theory guarantees soundness of this approach. The language of set theory, in its relative simplicity, is sufficiently powerful to formalise virtually all mathematical concepts popular in the mathematical community. As a result, the majority of mathematicians assume that a set is the most fundamental object for the whole mathematics and consequently, set theory along with logical calculi, forms the most natural and adequate ultimate foundation for mathematics. This book presents and discusses research in the study of set theory, as well as their role and place in mathematics.
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Mathematics Almost Everywhere: In Memory Of Solomon Marcus

Author: Bellow Alexandra,Calude Cristian S,Zamfirescu Tudor

Publisher: World Scientific

ISBN: 9813237325

Category: Computers

Page: 252

View: 3920

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The book is a collection of original papers, research and surveys, dedicated to the memory of the Romanian mathematician Solomon Marcus (1925-2016). Marcus published many papers and books in mathematical analysis, theoretical computer science, mathematical linguistics, poetics, theory of literature, semiotics, and several other fields less strongly connected to mathematics, like cultural anthropology, biology, history and philosophy of science, education. He exemplified an unimaginable richness of ideas. This volume intends to emphasize the mathematical fields in which Solomon Marcus worked, and demonstrate -- as he also did -- the interconnection between them. The authors who contribute to this volume are well-known experts in their fields. Most of them knew Solomon Marcus well, some even owed him for his decisive impulses for their careers and general development. With articles in so diverse areas, the volume will attract readers who would like to diversify their own knowledge or find unexpected connections with other topics. Contents: Logic, Complexity and Algebra: On Bases of Many-Valued Truth Functions (A Salomaa) Quasiperiods of Infinite Words (L Staiger) Early Romanian Contributions to Algebra and Polynomials (D Ştefănescu) Distributed Compression through the Lens of Algorithmic Information Theory: A Primer (M Zimand) Integrals, Operators, AF Algebras, Proof Mining and Monotone Nonexpansive Mappings: Monotonically Controlled Integrals (T Ball, D Preiss) Fine Properties of Duality Mappings (G Dincă) Primitive Ideal Spaces of Postliminal AF Algebras (A Lazar) An Application of Proof Miningto the Proximal Point Algorithm in CAT(0) Spaces (L Leuştean, A Sipoş) Generic Well-posedness of the Fixed Point Problem for Monotone Nonexpansive Mappings (S Reich, A J Zaslavski) Linguistics, Computer Science and Physics: Analytical Linguistics and Formal Grammars: Contributions of Solomon Marcus and Their Further Developments (M Burgin) A Contagious Creativity (Gh Păun) Entanglement through Path Identification (K Svozil) Solomon Marcus in Context: Memories about Solomon Marcus (A Bruckner) Memories With and About My Uncle (M Marcus) Index Readership: Graduate students and researchers. Keywords: Discrete Mathematics;Mathematical Analysis;Complexity Theory;Proof Mining;Mathematical Biology;Formal Languages;Theoretical Mechanics;Mathematical Linguistics;Theoretical PhysicsReview: Key Features: New results in a variety of mathematical areas including operator theory, measure theory, real and functional analysis, computable algebra, formal languages, proof mining in nonlinear analysis, theoretical mechanics, mathematical logic, and topical surveys in mathematical linguistics, complexity theory and computational biology The authors, coming from various parts of the world, are well-known experts in the areas of their contributions Interconnections between results and domains will make the volume not only informative, but also attractive and unique
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Information And Complexity

Author: Burgin Mark,Calude Cristian S

Publisher: World Scientific

ISBN: 9813109041

Category: Language Arts & Disciplines

Page: 412

View: 1513

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The book is a collection of papers of experts in the fields of information and complexity. Information is a basic structure of the world, while complexity is a fundamental property of systems and processes. There are intrinsic relations between information and complexity. The research in information theory, the theory of complexity and their interrelations is very active. The book will expand knowledge on information, complexity and their relations representing the most recent and advanced studies and achievements in this area. The goal of the book is to present the topic from different perspectives — mathematical, informational, philosophical, methodological, etc.
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History and Philosophy of Computing

Third International Conference, HaPoC 2015, Pisa, Italy, October 8-11, 2015, Revised Selected Papers

Author: Fabio Gadducci,Mirko Tavosanis

Publisher: Springer

ISBN: 3319472860

Category: Computers

Page: 321

View: 6010

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This volume constitutes the refereed post-conference proceedings of the Third International Conference on the History and Philosophy of Computing, held in Pisa, Italy in October 2015. The 18 full papers included in this volume were carefully reviewed and selected from the 30 papers presented at the conference. They cover topics ranging from the world history of computing to the role of computing in the humanities and the arts.
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General Theory of Statistics

Author: Victor Aladjev,Valery Haritonov

Publisher: Fultus Corporation

ISBN: 9781596820128

Category: Mathematics

Page: 251

View: 8195

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Book Description fields of social and economic sciences. The book presents a manual on the course General Theory of Statistics, including a series of not quite traditional topics. First of all, it concerns the mathematical bases of statistics and use of computer technologies in statistical probing. Thematic choice of the chapters and sections of the book is caused not only by interests and tastes of the authors, but also by modern tendencies in applied statistics and orientation of the given work. The book is based on a course of lectures given by the first author for undergraduates in social and economic sciences along with three books published in Russian and English in Estonia, Lithuania and Byelorussia. This book has been written for a large enough audience of teachers, researchers, statisticians, students, collegians and users of statistics in behavioral and social sciences. Above all, the book is directed to a wide circle of the readers studying statistical disciplines in high schools and colleges; however, it can be useful also to persons independently studying statistics.
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Information and Communication Technologies in Education, Research, and Industrial Applications

10th International Conference, ICTERI 2014, Kherson, Ukraine, June 9-12, 2014, Revised Selected Papers

Author: Vadim Ermolayev,Heinrich C. Mayr,Mykola Nikitchenko,Aleksander Spivakovsky,Grygoriy Zholtkevych

Publisher: Springer

ISBN: 3319132067

Category: Education

Page: 371

View: 6457

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This book constitutes the thoroughly refereed proceedings of the 10th International Conference on Information and Communication Technologies in Education, Research, and Industrial Applications, held in Kherson, Ukraine, in June 2014. The 16 revised full papers presented were carefully reviewed and selected from 66 submissions. The papers are organized in topical sections on framework and tools; information and communication technologies in teaching and learning; information and communication technologies in research and industrial applications.
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Intelligent Computer Mathematics

International Conference, CICM 2015, Washington, DC, USA, July 13-17, 2015, Proceedings.

Author: Manfred Kerber,Jacques Carette,Cezary Kaliszyk,Florian Rabe,Volker Sorge

Publisher: Springer

ISBN: 331920615X

Category: Computers

Page: 359

View: 474

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This book constitutes the refereed proceedings of the International Conference on Intelligent Computer Mathematics, CICM 2015, held in Washington, DC, USA, in July 2015. The 16 full papers and 9 short papers presented together with two invited talks plus one abstract were carefully reviewed and selected from a total of 43 submissions. The papers are organized in topical sections following the tracks of the conference: Invited Talks; Calculemus; Digital Mathematics Libraries; Mathematical Knowledge Management; Projects and Surveys; Systems and Data.
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The Beauty of Physics: Patterns, Principles, and Perspectives

Author: A. R. P. Rau

Publisher: OUP Oxford

ISBN: 0191019895

Category: Science

Page: 256

View: 4486

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The beauty of physics lies in its coherence in terms of a few fundamental concepts and principles. Even physicists have occasion to marvel at the overarching reach of basic principles and their ability to account for features stretching from the microscopic sub-atomic world to the cosmological expanses of the Universe. While mathematics is its natural language, physics is mostly about patterns, connections, and relations between objects and phenomena, and it is this aspect that is emphasized in this book. Since science tries to connect phenomena that at first sight appear widely different, while boiling them down to a small set of essential principles and laws, metaphor and analogy pervade our subject. Consider the pendulum, its swing from one extreme to the other often invoked in social or economic contexts. In molecular vibrations, such as in the CO2 molecule, the quantum motions of electrons and nuclei are metaphorically the pendulums. In electromagnetic radiation, including the visible light we observe, there are not even any concrete material particles, only electric and magnetic fields executing simple harmonic motion. But, to a physicist, they are all "just a pendulum". The selection of topics reflects the author's own four-decade career in research physics and his resultant perspective on the subject. While aimed primarily at physicists, including junior students, this book also addresses other readers who are willing to think with symbols and simple algebra in understanding the physical world around us. Each chapter, on themes such as dimensions, transformations, symmetries, or maps, begins with simple examples accessible to all while connecting them later to more sophisticated realizations in more advanced topics of physics.
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The Rise of Modern Logic: from Leibniz to Frege

Author: Dov M. Gabbay,John Woods

Publisher: Elsevier

ISBN: 9780080532875

Category: Technology & Engineering

Page: 780

View: 2032

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With the publication of the present volume, the Handbook of the History of Logic turns its attention to the rise of modern logic. The period covered is 1685-1900, with this volume carving out the territory from Leibniz to Frege. What is striking about this period is the earliness and persistence of what could be called 'the mathematical turn in logic'. Virtually every working logician is aware that, after a centuries-long run, the logic that originated in antiquity came to be displaced by a new approach with a dominantly mathematical character. It is, however, a substantial error to suppose that the mathematization of logic was, in all essentials, Frege's accomplishment or, if not his alone, a development ensuing from the second half of the nineteenth century. The mathematical turn in logic, although given considerable torque by events of the nineteenth century, can with assurance be dated from the final quarter of the seventeenth century in the impressively prescient work of Leibniz. It is true that, in the three hundred year run-up to the Begriffsschrift, one does not see a smoothly continuous evolution of the mathematical turn, but the idea that logic is mathematics, albeit perhaps only the most general part of mathematics, is one that attracted some degree of support throughout the entire period in question. Still, as Alfred North Whitehead once noted, the relationship between mathematics and symbolic logic has been an "uneasy" one, as is the present-day association of mathematics with computing. Some of this unease has a philosophical texture. For example, those who equate mathematics and logic sometimes disagree about the directionality of the purported identity. Frege and Russell made themselves famous by insisting (though for different reasons) that logic was the senior partner. Indeed logicism is the view that mathematics can be re-expressed without relevant loss in a suitably framed symbolic logic. But for a number of thinkers who took an algebraic approach to logic, the dependency relation was reversed, with mathematics in some form emerging as the senior partner. This was the precursor of the modern view that, in its four main precincts (set theory, proof theory, model theory and recursion theory), logic is indeed a branch of pure mathematics. It would be a mistake to leave the impression that the mathematization of logic (or the logicization of mathematics) was the sole concern of the history of logic between 1665 and 1900. There are, in this long interval, aspects of the modern unfolding of logic that bear no stamp of the imperial designs of mathematicians, as the chapters on Kant and Hegcl make clear. Of the two, Hcgel's influence on logic is arguably the greater, serving as a spur to the unfolding of an idealist tradition in logic - a development that will be covered in a further volume, British Logic in the Nineteenth Century.
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