Finite Theory

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Finite Model Theory and Its Applications

Author : Erich Grädel
Publisher : Springer Science & Business Media
ISBN 13 : 3540688048
Total Pages : 447 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Finite Model Theory and Its Applications by : Erich Grädel

Download or read book Finite Model Theory and Its Applications written by Erich Grädel and published by Springer Science & Business Media. This book was released on 2007-06-04 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite model theory,as understoodhere, is an areaof mathematicallogic that has developed in close connection with applications to computer science, in particular the theory of computational complexity and database theory. One of the fundamental insights of mathematical logic is that our understanding of mathematical phenomena is enriched by elevating the languages we use to describe mathematical structures to objects of explicit study. If mathematics is the science of patterns, then the media through which we discern patterns, as well as the structures in which we discern them, command our attention. It isthis aspect oflogicwhichis mostprominentin model theory,“thebranchof mathematical logic which deals with the relation between a formal language and its interpretations”. No wonder, then, that mathematical logic, and ?nite model theory in particular, should ?nd manifold applications in computer science: from specifying programs to querying databases, computer science is rife with phenomena whose understanding requires close attention to the interaction between language and structure. This volume gives a broadoverviewof some central themes of ?nite model theory: expressive power, descriptive complexity, and zero–one laws, together with selected applications to database theory and arti?cial intelligence, es- cially constraint databases and constraint satisfaction problems. The ?nal chapter provides a concise modern introduction to modal logic,which emp- sizes the continuity in spirit and technique with ?nite model theory.

Elements of Finite Model Theory

Author : Leonid Libkin
Publisher : Springer Science & Business Media
ISBN 13 : 3662070030
Total Pages : 320 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Elements of Finite Model Theory by : Leonid Libkin

Download or read book Elements of Finite Model Theory written by Leonid Libkin and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Emphasizes the computer science aspects of the subject. Details applications in databases, complexity theory, and formal languages, as well as other branches of computer science.

Finite Model Theory

Author : Heinz-Dieter Ebbinghaus
Publisher : Springer Science & Business Media
ISBN 13 : 3540287884
Total Pages : 363 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Finite Model Theory by : Heinz-Dieter Ebbinghaus

Download or read book Finite Model Theory written by Heinz-Dieter Ebbinghaus and published by Springer Science & Business Media. This book was released on 2005-12-29 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a thoroughly revised and enlarged second edition that presents the main results of descriptive complexity theory, that is, the connections between axiomatizability of classes of finite structures and their complexity with respect to time and space bounds. The logics that are important in this context include fixed-point logics, transitive closure logics, and also certain infinitary languages; their model theory is studied in full detail. The book is written in such a way that the respective parts on model theory and descriptive complexity theory may be read independently.

Finite Group Theory

Author : I. Martin Isaacs
Publisher : American Mathematical Society
ISBN 13 : 1470471604
Total Pages : 368 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Finite Group Theory by : I. Martin Isaacs

Download or read book Finite Group Theory written by I. Martin Isaacs and published by American Mathematical Society. This book was released on 2023-01-24 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text begins with a review of group actions and Sylow theory. It includes semidirect products, the Schur–Zassenhaus theorem, the theory of commutators, coprime actions on groups, transfer theory, Frobenius groups, primitive and multiply transitive permutation groups, the simplicity of the PSL groups, the generalized Fitting subgroup and also Thompson's J-subgroup and his normal $p$-complement theorem. Topics that seldom (or never) appear in books are also covered. These include subnormality theory, a group-theoretic proof of Burnside's theorem about groups with order divisible by just two primes, the Wielandt automorphism tower theorem, Yoshida's transfer theorem, the “principal ideal theorem” of transfer theory and many smaller results that are not very well known. Proofs often contain original ideas, and they are given in complete detail. In many cases they are simpler than can be found elsewhere. The book is largely based on the author's lectures, and consequently, the style is friendly and somewhat informal. Finally, the book includes a large collection of problems at disparate levels of difficulty. These should enable students to practice group theory and not just read about it. Martin Isaacs is professor of mathematics at the University of Wisconsin, Madison. Over the years, he has received many teaching awards and is well known for his inspiring teaching and lecturing. He received the University of Wisconsin Distinguished Teaching Award in 1985, the Benjamin Smith Reynolds Teaching Award in 1989, and the Wisconsin Section MAA Teaching Award in 1993, to name only a few. He was also honored by being the selected MAA Pólya Lecturer in 2003–2005.

The Mathematical Theory of Finite Element Methods

Author : Susanne Brenner
Publisher : Springer Science & Business Media
ISBN 13 : 1475736584
Total Pages : 369 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis The Mathematical Theory of Finite Element Methods by : Susanne Brenner

Download or read book The Mathematical Theory of Finite Element Methods written by Susanne Brenner and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous and thorough mathematical introduction to the subject; A clear and concise treatment of modern fast solution techniques such as multigrid and domain decomposition algorithms; Second edition contains two new chapters, as well as many new exercises; Previous edition sold over 3000 copies worldwide

An Introduction to the Mathematical Theory of Finite Elements

Author : J. T. Oden
Publisher : Courier Corporation
ISBN 13 : 0486142213
Total Pages : 450 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis An Introduction to the Mathematical Theory of Finite Elements by : J. T. Oden

Download or read book An Introduction to the Mathematical Theory of Finite Elements written by J. T. Oden and published by Courier Corporation. This book was released on 2012-05-23 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to the theory of Sobolev spaces and Hilbert space methods in partial differential equations is geared toward readers of modest mathematical backgrounds. It offers coherent, accessible demonstrations of the use of these techniques in developing the foundations of the theory of finite element approximations. J. T. Oden is Director of the Institute for Computational Engineering & Sciences (ICES) at the University of Texas at Austin, and J. N. Reddy is a Professor of Engineering at Texas A&M University. They developed this essentially self-contained text from their seminars and courses for students with diverse educational backgrounds. Their effective presentation begins with introductory accounts of the theory of distributions, Sobolev spaces, intermediate spaces and duality, the theory of elliptic equations, and variational boundary value problems. The second half of the text explores the theory of finite element interpolation, finite element methods for elliptic equations, and finite element methods for initial boundary value problems. Detailed proofs of the major theorems appear throughout the text, in addition to numerous examples.

Character Theory of Finite Groups

Author : I. Martin Isaacs
Publisher : American Mathematical Soc.
ISBN 13 : 0821842293
Total Pages : 322 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Character Theory of Finite Groups by : I. Martin Isaacs

Download or read book Character Theory of Finite Groups written by I. Martin Isaacs and published by American Mathematical Soc.. This book was released on 2006-11-21 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Character theory is a powerful tool for understanding finite groups. In particular, the theory has been a key ingredient in the classification of finite simple groups. Characters are also of interest in their own right, and their properties are closely related to properties of the structure of the underlying group. The book begins by developing the module theory of complex group algebras. After the module-theoretic foundations are laid in the first chapter, the focus is primarily on characters. This enhances the accessibility of the material for students, which was a major consideration in the writing. Also with students in mind, a large number of problems are included, many of them quite challenging. In addition to the development of the basic theory (using a cleaner notation than previously), a number of more specialized topics are covered with accessible presentations. These include projective representations, the basics of the Schur index, irreducible character degrees and group structure, complex linear groups, exceptional characters, and a fairly extensive introduction to blocks and Brauer characters. This is a corrected reprint of the original 1976 version, later reprinted by Dover. Since 1976 it has become the standard reference for character theory, appearing in the bibliography of almost every research paper in the subject. It is largely self-contained, requiring of the reader only the most basic facts of linear algebra, group theory, Galois theory and ring and module theory.

The Character Theory of Finite Groups of Lie Type

Author : Meinolf Geck
Publisher : Cambridge University Press
ISBN 13 : 1108808905
Total Pages : 406 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis The Character Theory of Finite Groups of Lie Type by : Meinolf Geck

Download or read book The Character Theory of Finite Groups of Lie Type written by Meinolf Geck and published by Cambridge University Press. This book was released on 2020-02-27 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through the fundamental work of Deligne and Lusztig in the 1970s, further developed mainly by Lusztig, the character theory of reductive groups over finite fields has grown into a rich and vast area of mathematics. It incorporates tools and methods from algebraic geometry, topology, combinatorics and computer algebra, and has since evolved substantially. With this book, the authors meet the need for a contemporary treatment, complementing in core areas the well-established books of Carter and Digne–Michel. Focusing on applications in finite group theory, the authors gather previously scattered results and allow the reader to get to grips with the large body of literature available on the subject, covering topics such as regular embeddings, the Jordan decomposition of characters, d-Harish–Chandra theory and Lusztig induction for unipotent characters. Requiring only a modest background in algebraic geometry, this useful reference is suitable for beginning graduate students as well as researchers.

Finite Frames

Author : Peter G. Casazza
Publisher : Springer Science & Business Media
ISBN 13 : 0817683739
Total Pages : 492 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Finite Frames by : Peter G. Casazza

Download or read book Finite Frames written by Peter G. Casazza and published by Springer Science & Business Media. This book was released on 2012-09-14 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert space frames have long served as a valuable tool for signal and image processing due to their resilience to additive noise, quantization, and erasures, as well as their ability to capture valuable signal characteristics. More recently, finite frame theory has grown into an important research topic in its own right, with a myriad of applications to pure and applied mathematics, engineering, computer science, and other areas. The number of research publications, conferences, and workshops on this topic has increased dramatically over the past few years, but no survey paper or monograph has yet appeared on the subject. Edited by two of the leading experts in the field, Finite Frames aims to fill this void in the literature by providing a comprehensive, systematic study of finite frame theory and applications. With carefully selected contributions written by highly experienced researchers, it covers topics including: * Finite Frame Constructions; * Optimal Erasure Resilient Frames; * Quantization of Finite Frames; * Finite Frames and Compressed Sensing; * Group and Gabor Frames; * Fusion Frames. Despite the variety of its chapters' source and content, the book's notation and terminology are unified throughout and provide a definitive picture of the current state of frame theory. With a broad range of applications and a clear, full presentation, this book is a highly valuable resource for graduate students and researchers across disciplines such as applied harmonic analysis, electrical engineering, quantum computing, medicine, and more. It is designed to be used as a supplemental textbook, self-study guide, or reference book.

The Theory of Finite Groups

Author : Hans Kurzweil
Publisher : Springer Science & Business Media
ISBN 13 : 0387405100
Total Pages : 389 pages
Book Rating : 4.3/5 (874 download)

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Book Synopsis The Theory of Finite Groups by : Hans Kurzweil

Download or read book The Theory of Finite Groups written by Hans Kurzweil and published by Springer Science & Business Media. This book was released on 2003-11-06 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: From reviews of the German edition: "This is an exciting text and a refreshing contribution to an area in which challenges continue to flourish and to captivate the viewer. Even though representation theory and constructions of simple groups have been omitted, the text serves as a springboard for deeper study in many directions." Mathematical Reviews

Theory of Groups of Finite Order

Author : William S. Burnside
Publisher : Courier Corporation
ISBN 13 : 0486159442
Total Pages : 545 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Theory of Groups of Finite Order by : William S. Burnside

Download or read book Theory of Groups of Finite Order written by William S. Burnside and published by Courier Corporation. This book was released on 2013-02-20 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic 1911 edition covers many group-related properties, including an extensive treatment of permutation groups and groups of linear substitutions, along with graphic representation of groups, congruence groups, and special topics.

K-Theory of Finite Groups and Orders

Author : Richard G. Swan
Publisher : Springer
ISBN 13 : 9783540049388
Total Pages : 238 pages
Book Rating : 4.0/5 (493 download)

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Book Synopsis K-Theory of Finite Groups and Orders by : Richard G. Swan

Download or read book K-Theory of Finite Groups and Orders written by Richard G. Swan and published by Springer. This book was released on 1986-01-01 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are from a course given at the University of Chicago. No pretense of completeness is made. A great deal of additional material may be found in Bass' book [BK] which gives a remarkably complete account of algebraic K-theory. The present notes, however, contain a number of recent results of Jacobinski [J] and Roiter [R]. An excellent survey of the theory of orders with detailed references may be found in Reiner's article [RS].

Representation Theory of Finite Groups

Author : Martin Burrow
Publisher : Academic Press
ISBN 13 : 1483258211
Total Pages : 196 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Representation Theory of Finite Groups by : Martin Burrow

Download or read book Representation Theory of Finite Groups written by Martin Burrow and published by Academic Press. This book was released on 2014-05-10 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Representation Theory of Finite Groups is a five chapter text that covers the standard material of representation theory. This book starts with an overview of the basic concepts of the subject, including group characters, representation modules, and the rectangular representation. The succeeding chapters describe the features of representation theory of rings with identity and finite groups. These topics are followed by a discussion of some of the application of the theory of characters, along with some classical theorems. The last chapter deals with the construction of irreducible representations of groups. This book will be of great value to graduate students who wish to acquire some knowledge of representation theory.

Theory and Practice of Finite Elements

Author : Alexandre Ern
Publisher : Springer Science & Business Media
ISBN 13 : 1475743556
Total Pages : 531 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Theory and Practice of Finite Elements by : Alexandre Ern

Download or read book Theory and Practice of Finite Elements written by Alexandre Ern and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presenting the mathematical theory of finite elements is organized into three main sections. The first part develops the theoretical basis for the finite element methods, emphasizing inf-sup conditions over the more conventional Lax-Milgrim paradigm. The second and third parts address various applications and practical implementations of the method, respectively. It contains numerous examples and exercises.

Extremal Finite Set Theory

Author : Daniel Gerbner
Publisher : CRC Press
ISBN 13 : 0429804113
Total Pages : 292 pages
Book Rating : 4.4/5 (298 download)

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Book Synopsis Extremal Finite Set Theory by : Daniel Gerbner

Download or read book Extremal Finite Set Theory written by Daniel Gerbner and published by CRC Press. This book was released on 2018-10-12 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extremal Finite Set Theory surveys old and new results in the area of extremal set system theory. It presents an overview of the main techniques and tools (shifting, the cycle method, profile polytopes, incidence matrices, flag algebras, etc.) used in the different subtopics. The book focuses on the cardinality of a family of sets satisfying certain combinatorial properties. It covers recent progress in the subject of set systems and extremal combinatorics. Intended for graduate students, instructors teaching extremal combinatorics and researchers, this book serves as a sound introduction to the theory of extremal set systems. In each of the topics covered, the text introduces the basic tools used in the literature. Every chapter provides detailed proofs of the most important results and some of the most recent ones, while the proofs of some other theorems are posted as exercises with hints. Features: Presents the most basic theorems on extremal set systems Includes many proof techniques Contains recent developments The book’s contents are well suited to form the syllabus for an introductory course About the Authors: Dániel Gerbner is a researcher at the Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences in Budapest, Hungary. He holds a Ph.D. from Eötvös Loránd University, Hungary and has contributed to numerous publications. His research interests are in extremal combinatorics and search theory. Balázs Patkós is also a researcher at the Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences. He holds a Ph.D. from Central European University, Budapest and has authored several research papers. His research interests are in extremal and probabilistic combinatorics.

Theory of Finite and Infinite Graphs

Author : Denes König
Publisher : Springer Science & Business Media
ISBN 13 : 1468489712
Total Pages : 430 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Theory of Finite and Infinite Graphs by : Denes König

Download or read book Theory of Finite and Infinite Graphs written by Denes König and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: To most graph theorists there are two outstanding landmarks in the history of their subject. One is Euler's solution of the Konigsberg Bridges Problem, dated 1736, and the other is the appearance of Denes Konig's textbook in 1936. "From Konigsberg to Konig's book" sings the poetess, "So runs the graphic tale . . . " 10]. There were earlier books that took note of graph theory. Veb len's Analysis Situs, published in 1931, is about general combinato rial topology. But its first two chapters, on "Linear graphs" and "Two-Dimensional Complexes," are almost exclusively concerned with the territory still explored by graph theorists. Rouse Ball's Mathematical Recreations and Essays told, usually without proofs, of the major graph-theoretical advances ofthe nineteenth century, of the Five Colour Theorem, of Petersen's Theorem on I-factors, and of Cayley's enumerations of trees. It was Rouse Ball's book that kindled my own graph-theoretical enthusiasm. The graph-theoretical papers of Hassler Whitney, published in 1931-1933, would have made an excellent textbook in English had they been collected and published as such. But the honour of presenting Graph Theory to the mathe matical world as a subject in its own right, with its own textbook, belongs to Denes Konig. Low was the prestige of Graph Theory in the Dirty Thirties. It is still remembered, with resentment now shading into amuse ment, how one mathematician scorned it as "The slums of Topol ogy.""

Introduction to Finite Strain Theory for Continuum Elasto-Plasticity

Author : Koichi Hashiguchi
Publisher : John Wiley & Sons
ISBN 13 : 1118437721
Total Pages : 371 pages
Book Rating : 4.1/5 (184 download)

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Book Synopsis Introduction to Finite Strain Theory for Continuum Elasto-Plasticity by : Koichi Hashiguchi

Download or read book Introduction to Finite Strain Theory for Continuum Elasto-Plasticity written by Koichi Hashiguchi and published by John Wiley & Sons. This book was released on 2012-10-09 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive introduction to finite elastoplasticity, addressing various analytical and numerical analyses & including state-of-the-art theories Introduction to Finite Elastoplasticity presents introductory explanations that can be readily understood by readers with only a basic knowledge of elastoplasticity, showing physical backgrounds of concepts in detail and derivation processes of almost all equations. The authors address various analytical and numerical finite strain analyses, including new theories developed in recent years, and explain fundamentals including the push-forward and pull-back operations and the Lie derivatives of tensors. As a foundation to finite strain theory, the authors begin by addressing the advanced mathematical and physical properties of continuum mechanics. They progress to explain a finite elastoplastic constitutive model, discuss numerical issues on stress computation, implement the numerical algorithms for stress computation into large-deformation finite element analysis and illustrate several numerical examples of boundary-value problems. Programs for the stress computation of finite elastoplastic models explained in this book are included in an appendix, and the code can be downloaded from an accompanying website.