Ordered Sets

An Introduction with Connections from Combinatorics to Topology

DOWNLOAD NOW »

Author: Bernd Schröder

Publisher: Birkhäuser

ISBN: 3319297880

Category: Mathematics

Page: 420

View: 7487

An introduction to the basic tools of the theory of (partially) ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoretical constructions and classes of ordered sets. Using a thematic approach, the author presents open or recently solved problems to motivate the development of constructions and investigations for new classes of ordered sets. The text can be used as a focused follow-up or companion to a first proof (set theory and relations) or graph theory course.

Ordered Sets

An Introduction

DOWNLOAD NOW »

Author: Bernd Schroeder

Publisher: Springer Science & Business Media

ISBN: 9780817641283

Category: Mathematics

Page: 391

View: 2290

This work is an introduction to the basic tools of the theory of (partially) ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoretical constructions, and classes of ordered sets. Using a thematic approach, the author presents open or recently solved problems to motivate the development of constructions and investigations for new classes of ordered sets. A wide range of material is presented, from classical results such as Dilworth's, Szpilrajn's and Hashimoto's Theorems to more recent results such as the Li--Milner Structure Theorem. Major topics covered include: chains and antichains, lowest upper and greatest lower bounds, retractions, lattices, the dimension of ordered sets, interval orders, lexicographic sums, products, enumeration, algorithmic approaches and the role of algebraic topology. Since there are few prerequisites, the text can be used as a focused follow-up or companion to a first proof (set theory and relations) or graph theory class. After working through a comparatively lean core, the reader can choose from a diverse range of topics such as structure theory, enumeration or algorithmic aspects. Also presented are some key topics less customary to discrete mathematics/graph theory, including a concise introduction to homology for graphs, and the presentation of forward checking as a more efficient alternative to the standard backtracking algorithm. The coverage throughout provides a solid foundation upon which research can be started by a mathematically mature reader. Rich in exercises, illustrations, and open problems, Ordered Sets: An Introduction is an excellent text for undergraduate and graduate students and a good resource for the interested researcher. Readers will discover order theory's role in discrete mathematics as a supplier of ideas as well as an attractive source of applications.

Enzyklopädie Philosophie und Wissenschaftstheorie

Bd. 5: Log–N

DOWNLOAD NOW »

Author: Jürgen Mittelstraß

Publisher: Springer-Verlag

ISBN: 3476001407

Category: Philosophy

Page: 629

View: 5210

Das gesamte Wissen der Philosophie und Wissenschaftstheorie. Die Sach- und Personenartikel des Nachschlagewerks erfassen nicht nur den klassischen Bestand des philosophischen Wissens, sondern werden auch den neueren Entwicklungen in der Philosophie gerecht. Insbesondere in den Bereichen Logik, Erkenntnis- und Wissenschaftstheorie sowie Sprachphilosophie. Jetzt erscheint der fünfte Band der Neuauflage mit über 70 neuen Artikeln u. a. zu diesen Begriffen: antike Logik, Lüge, Macht, Medizin, Nano und Neurowissenschaften. Mit neuen Personenartikeln, darunter Luhmann, Lyotard, Maturana.

An Introduction to Fuzzy Sets

Analysis and Design

DOWNLOAD NOW »

Author: Witold Pedrycz,Fernando Gomide

Publisher: MIT Press

ISBN: 9780262161718

Category: Computers

Page: 465

View: 5956

"The Pedrycz and Gomide text is superb in all respects. Its exposition of fuzzy-neural networks and fuzzy-genetic systems adds much to its value as a textbook" -- Lotfi A. Zadeh, University of California, Berkeley. The concept of fuzzy sets is one of the most fundamental and influential tools in computational intelligence. Fuzzy sets can provide solutions to a broad range of problems of control, pattern classification, reasoning, planning, and computer vision. This book bridges the gap that has developed between theory and practice. The authors explain what fuzzy sets are, why they work, when they should be used (and when they shouldn't), and how to design systems using them. The authors take an unusual top-down approach to the design of detailed algorithms. They begin with illustrative examples, explain the fundamental theory and design methodologies, and then present more advanced case studies dealing with practical tasks. While they use mathematics to introduce concepts, they ground them in examples of real-world problems that can be solved through fuzzy set technology. The only mathematics prerequisites are a basic knowledge of introductory calculus and linear algebra.

An Introduction to Random Sets

DOWNLOAD NOW »

Author: Hung T. Nguyen

Publisher: CRC Press

ISBN: 9781420010619

Category: Mathematics

Page: 272

View: 9796

The study of random sets is a large and rapidly growing area with connections to many areas of mathematics and applications in widely varying disciplines, from economics and decision theory to biostatistics and image analysis. The drawback to such diversity is that the research reports are scattered throughout the literature, with the result that in science and engineering, and even in the statistics community, the topic is not well known and much of the enormous potential of random sets remains untapped. An Introduction to Random Sets provides a friendly but solid initiation into the theory of random sets. It builds the foundation for studying random set data, which, viewed as imprecise or incomplete observations, are ubiquitous in today's technological society. The author, widely known for his best-selling A First Course in Fuzzy Logic text as well as his pioneering work in random sets, explores motivations, such as coarse data analysis and uncertainty analysis in intelligent systems, for studying random sets as stochastic models. Other topics include random closed sets, related uncertainty measures, the Choquet integral, the convergence of capacity functionals, and the statistical framework for set-valued observations. An abundance of examples and exercises reinforce the concepts discussed. Designed as a textbook for a course at the advanced undergraduate or beginning graduate level, this book will serve equally well for self-study and as a reference for researchers in fields such as statistics, mathematics, engineering, and computer science.

Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems

DOWNLOAD NOW »

Author: Guanrong Chen,Trung Tat Pham

Publisher: CRC Press

ISBN: 9781420039818

Category: Mathematics

Page: 328

View: 5054

In the early 1970s, fuzzy systems and fuzzy control theories added a new dimension to control systems engineering. From its beginnings as mostly heuristic and somewhat ad hoc, more recent and rigorous approaches to fuzzy control theory have helped make it an integral part of modern control theory and produced many exciting results. Yesterday's "art" of building a working fuzzy controller has turned into today's "science" of systematic design. To keep pace with and further advance the rapidly developing field of applied control technologies, engineers, both present and future, need some systematic training in the analytic theory and rigorous design of fuzzy control systems. Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems provides that training by introducing a rigorous and complete fundamental theory of fuzzy sets and fuzzy logic, and then building a practical theory for automatic control of uncertain and ill-modeled systems encountered in many engineering applications. The authors proceed through basic fuzzy mathematics and fuzzy systems theory and conclude with an exploration of some industrial application examples. Almost entirely self-contained, Introduction to Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems establishes a strong foundation for designing and analyzing fuzzy control systems under uncertain and irregular conditions. Mastering its contents gives students a clear understanding of fuzzy control systems theory that prepares them for deeper and broader studies and for many practical challenges faced in modern industry.

An Introduction to Fuzzy Logic and Fuzzy Sets

DOWNLOAD NOW »

Author: James J. Buckley,Esfandiar Eslami

Publisher: Springer Science & Business Media

ISBN: 3790817996

Category: Computers

Page: 285

View: 3046

This book is an excellent starting point for any curriculum in fuzzy systems fields such as computer science, mathematics, business/economics and engineering. It covers the basics leading to: fuzzy clustering, fuzzy pattern recognition, fuzzy database, fuzzy image processing, soft computing, fuzzy applications in operations research, fuzzy decision making, fuzzy rule based systems, fuzzy systems modeling, fuzzy mathematics. It is not a book designed for researchers - it is where you really learn the "basics" needed for any of the above-mentioned applications. It includes many figures and problem sets at the end of sections.

INTRODUCTION TO FUZZY SETS AND FUZZY LOGIC

DOWNLOAD NOW »

Author: M. GANESH

Publisher: PHI Learning Pvt. Ltd.

ISBN: 8120328612

Category: Mathematics

Page: 256

View: 7962

Reflecting the tremendous advances that have taken place in the study of fuzzy set theory and fuzzy logic, this book not only details the theoretical advances in these areas, but also considers a broad variety of applications of fuzzy sets and fuzzy logic. This comprehensive and up-to-date text is organized in three parts. The concepts pertaining to the “crisp” situation such as Set Theory, Logic, Switching Function Theory and Boolean Algebra are covered in Part I of the text. Part II is devoted to fuzzy Set Theory, Fuzzy Relations and Fuzzy Logic. The applications of fuzzy set theory and fuzzy logic to Control Theory and Decision Making are designated Part III of the text. Designed as a textbook for the undergraduate and postgraduate students of Science and Engineering, the book will also be immensely useful to practicing engineers and computer scientists.

Introduction to Set Theory, Third Edition, Revised and Expanded

DOWNLOAD NOW »

Author: Karel Hrbacek,Thomas Jech

Publisher: CRC Press

ISBN: 9780824779153

Category: Mathematics

Page: 310

View: 2622

Thoroughly revised, updated, expanded, and reorganized to serve as a primary text for mathematics courses, Introduction to Set Theory, Third Edition covers the basics: relations, functions, orderings, finite, countable, and uncountable sets, and cardinal and ordinal numbers. It also provides five additional self-contained chapters, consolidates the material on real numbers into a single updated chapter affording flexibility in course design, supplies end-of-section problems, with hints, of varying degrees of difficulty, includes new material on normal forms and Goodstein sequences, and adds important recent ideas including filters, ultrafilters, closed unbounded and stationary sets, and partitions.

Introduction to the Theory of Sets

DOWNLOAD NOW »

Author: Joseph Breuer

Publisher: Courier Corporation

ISBN: 0486154874

Category: Mathematics

Page: 128

View: 7874

This undergraduate text develops its subject through observations of the physical world, covering finite sets, cardinal numbers, infinite cardinals, and ordinals. Includes exercises with answers. 1958 edition.

Introduction To Set Theory

DOWNLOAD NOW »

Author: A. K. Sharma

Publisher: Discovery Publishing House

ISBN: 9788171418770

Category: Set theory

Page: 118

View: 2230

This book Introduction to Set Theory is very important in the field of modern algebra. It is very important to study this book to study modern mathematics. This book contain preliminary Notation, Sets, Subsets, Mapping Function and Relation. This book is useful to the students of under graduate, post graduate students and the candidate appearing in various competitions like pre Engineering/I.A.S/ P.C.S. etc. Contents: Preliminary Notation, Relations, Product or Composite of Mapping, Mapping or Functions

Introduction to Modern Set Theory

DOWNLOAD NOW »

Author: Judith Roitman

Publisher: John Wiley & Sons

ISBN: 9780471635192

Category: Mathematics

Page: 156

View: 8018

This is modern set theory from the ground up--from partial orderings and well-ordered sets to models, infinite cobinatorics and large cardinals. The approach is unique, providing rigorous treatment of basic set-theoretic methods, while integrating advanced material such as independence results, throughout. The presentation incorporates much interesting historical material and no background in mathematical logic is assumed. Treatment is self-contained, featuring theorem proofs supported by diagrams, examples and exercises. Includes applications of set theory to other branches of mathematics.

Introduction to Set Theory and Topology

DOWNLOAD NOW »

Author: Kazimierz Kuratowski

Publisher: Elsevier

ISBN: 1483151638

Category: Mathematics

Page: 352

View: 8096

Introduction to Set Theory and Topology describes the fundamental concepts of set theory and topology as well as its applicability to analysis, geometry, and other branches of mathematics, including algebra and probability theory. Concepts such as inverse limit, lattice, ideal, filter, commutative diagram, quotient-spaces, completely regular spaces, quasicomponents, and cartesian products of topological spaces are considered. This volume consists of 21 chapters organized into two sections and begins with an introduction to set theory, with emphasis on the propositional calculus and its application to propositions each having one of two logical values, 0 and 1. Operations on sets which are analogous to arithmetic operations are also discussed. The chapters that follow focus on the mapping concept, the power of a set, operations on cardinal numbers, order relations, and well ordering. The section on topology explores metric and topological spaces, continuous mappings, cartesian products, and other spaces such as spaces with a countable base, complete spaces, compact spaces, and connected spaces. The concept of dimension, simplexes and their properties, and cuttings of the plane are also analyzed. This book is intended for students and teachers of mathematics.

Fundamentals of Mathematics, An Introduction to Proofs, Logic, Sets, and Numbers

Mathematics, Mathematics

DOWNLOAD NOW »

Author: CTI Reviews

Publisher: Cram101 Textbook Reviews

ISBN: 1467211346

Category: Education

Page: 62

View: 6207

Facts101 is your complete guide to Fundamentals of Mathematics, An Introduction to Proofs, Logic, Sets, and Numbers. In this book, you will learn topics such as as those in your book plus much more. With key features such as key terms, people and places, Facts101 gives you all the information you need to prepare for your next exam. Our practice tests are specific to the textbook and we have designed tools to make the most of your limited study time.

Set Theory: An Introduction

DOWNLOAD NOW »

Author: Robert L. Vaught

Publisher: Springer Science & Business Media

ISBN: 9780817642563

Category: Mathematics

Page: 167

View: 9903

By its nature, set theory does not depend on any previous mathematical knowl edge. Hence, an individual wanting to read this book can best find out if he is ready to do so by trying to read the first ten or twenty pages of Chapter 1. As a textbook, the book can serve for a course at the junior or senior level. If a course covers only some of the chapters, the author hopes that the student will read the rest himself in the next year or two. Set theory has always been a sub ject which people find pleasant to study at least partly by themselves. Chapters 1-7, or perhaps 1-8, present the core of the subject. (Chapter 8 is a short, easy discussion of the axiom of regularity). Even a hurried course should try to cover most of this core (of which more is said below). Chapter 9 presents the logic needed for a fully axiomatic set th~ory and especially for independence or consistency results. Chapter 10 gives von Neumann's proof of the relative consistency of the regularity axiom and three similar related results. Von Neumann's 'inner model' proof is easy to grasp and yet it prepares one for the famous and more difficult work of GOdel and Cohen, which are the main topics of any book or course in set theory at the next level.

Set Theory An Introduction To Independence Proofs

DOWNLOAD NOW »

Author: K. Kunen

Publisher: Elsevier

ISBN: 0080570585

Category: Mathematics

Page: 330

View: 6988

Studies in Logic and the Foundations of Mathematics, Volume 102: Set Theory: An Introduction to Independence Proofs offers an introduction to relative consistency proofs in axiomatic set theory, including combinatorics, sets, trees, and forcing. The book first tackles the foundations of set theory and infinitary combinatorics. Discussions focus on the Suslin problem, Martin's axiom, almost disjoint and quasi-disjoint sets, trees, extensionality and comprehension, relations, functions, and well-ordering, ordinals, cardinals, and real numbers. The manuscript then ponders on well-founded sets and easy consistency proofs, including relativization, absoluteness, reflection theorems, properties of well-founded sets, and induction and recursion on well-founded relations. The publication examines constructible sets, forcing, and iterated forcing. Topics include Easton forcing, general iterated forcing, Cohen model, forcing with partial functions of larger cardinality, forcing with finite partial functions, and general extensions. The manuscript is a dependable source of information for mathematicians and researchers interested in set theory.

An Introduction to Inverse Limits with Set-valued Functions

DOWNLOAD NOW »

Author: W.T. Ingram

Publisher: Springer Science & Business Media

ISBN: 146144487X

Category: Mathematics

Page: 86

View: 1814

Inverse limits with set-valued functions are quickly becoming a popular topic of research due to their potential applications in dynamical systems and economics. This brief provides a concise introduction dedicated specifically to such inverse limits. The theory is presented along with detailed examples which form the distinguishing feature of this work. The major differences between the theory of inverse limits with mappings and the theory with set-valued functions are featured prominently in this book in a positive light. The reader is assumed to have taken a senior level course in analysis and a basic course in topology. Advanced undergraduate and graduate students, and researchers working in this area will find this brief useful. ​

An Introduction to Abstract Mathematics

DOWNLOAD NOW »

Author: Robert J. Bond,William J. Keane

Publisher: Waveland Press

ISBN: 1478608056

Category: Mathematics

Page: 323

View: 6446

Bond and Keane explicate the elements of logical, mathematical argument to elucidate the meaning and importance of mathematical rigor. With definitions of concepts at their disposal, students learn the rules of logical inference, read and understand proofs of theorems, and write their own proofs all while becoming familiar with the grammar of mathematics and its style. In addition, they will develop an appreciation of the different methods of proof (contradiction, induction), the value of a proof, and the beauty of an elegant argument. The authors emphasize that mathematics is an ongoing, vibrant disciplineits long, fascinating history continually intersects with territory still uncharted and questions still in need of answers. The authors extensive background in teaching mathematics shines through in this balanced, explicit, and engaging text, designed as a primer for higher- level mathematics courses. They elegantly demonstrate process and application and recognize the byproducts of both the achievements and the missteps of past thinkers. Chapters 1-5 introduce the fundamentals of abstract mathematics and chapters 6-8 apply the ideas and techniques, placing the earlier material in a real context. Readers interest is continually piqued by the use of clear explanations, practical examples, discussion and discovery exercises, and historical comments.

Intelligent Control Systems with an Introduction to System of Systems Engineering

DOWNLOAD NOW »

Author: Thrishantha Nanayakkara,Ferat Sahin,Mo Jamshidi

Publisher: CRC Press

ISBN: 9781420079258

Category: Technology & Engineering

Page: 441

View: 6670

From aeronautics and manufacturing to healthcare and disaster management, systems engineering (SE) now focuses on designing applications that ensure performance optimization, robustness, and reliability while combining an emerging group of heterogeneous systems to realize a common goal. Use SoS to Revolutionize Management of Large Organizations, Factories, and Systems Intelligent Control Systems with an Introduction to System of Systems Engineering integrates the fundamentals of artificial intelligence and systems control in a framework applicable to both simple dynamic systems and large-scale system of systems (SoS). For decades, NASA has used SoS methods, and major manufacturers—including Boeing, Lockheed-Martin, Northrop-Grumman, Raytheon, BAE Systems—now make large-scale systems integration and SoS a key part of their business strategies, dedicating entire business units to this remarkably efficient approach. Simulate Novel Robotic Systems and Applications Transcending theory, this book offers a complete and practical review of SoS and some of its fascinating applications, including: Manipulation of robots through neural-based network control Use of robotic swarms, based on ant colonies, to detect mines Other novel systems in which intelligent robots, trained animals, and humans cooperate to achieve humanitarian objectives Training engineers to integrate traditional systems control theory with soft computing techniques further nourishes emerging SoS technology. With this in mind, the authors address the fundamental precepts at the core of SoS, which uses human heuristics to model complex systems, providing a scientific rationale for integrating independent, complex systems into a single coordinated, stabilized, and optimized one. They provide readers with MATLAB® code, which can be downloaded from the publisher's website to simulate presented results and projects that offer practical, hands-on experience using concepts discussed throughout the book.

Rough Sets and Knowledge Technology

First International Conference, RSKT 2006, Chongquing, China, July 24-26, 2006, Proceedings

DOWNLOAD NOW »

Author: Guoyin Wang,James F. Peters,Yiju Yao,Andrzej Skowron

Publisher: Springer Science & Business Media

ISBN: 3540362975

Category: Computers

Page: 810

View: 7596

This volume contains the papers selected for presentation at the First Int- national Conference on Rough Sets and Knowledge Technology (RSKT 2006) organized in Chongqing, P. R. China, July 24-26, 2003. There were 503 s- missions for RSKT 2006 except for 1 commemorative paper, 4 keynote papers and 10 plenary papers. Except for the 15 commemorative and invited papers, 101 papers were accepted by RSKT 2006 and are included in this volume. The acceptance rate was only 20%. These papers were divided into 43 regular oral presentation papers (each allotted 8 pages), and 58 short oral presentation - pers (each allotted 6 pages) on the basis of reviewer evaluation. Each paper was reviewed by two to four referees. Since the introduction of rough sets in 1981 by Zdzis law Pawlak, many great advances in both the theory and applications have been introduced. Rough set theory is closely related to knowledge technology in a variety of forms such as knowledge discovery, approximate reasoning, intelligent and multiagent systems design, and knowledge intensive computations that signal the emergence of a knowledge technology age. The essence of growth in cutting-edge, state-of-t- art and promising knowledge technologies is closely related to learning, pattern recognition,machine intelligence and automation of acquisition, transformation, communication, exploration and exploitation of knowledge. A principal thrust of such technologies is the utilization of methodologies that facilitate knowledge processing.