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Books > Academic & Education > Professional & Technical > Mathematics
The aim of this book is to present the fundamental theoretical results concerning inference rules in deductive formal systems. Primary attention is focused on: - admissible or permissible inference rules - the derivability of the admissible inference rules - the structural completeness of logics - the bases for admissible and valid inference rules. There is particular emphasis on propositional non-standard logics (primary, superintuitionistic and modal logics) but general logical consequence relations and classical first-order theories are also considered. The book is basically self-contained and special attention has been made to present the material in a convenient manner for the reader. Proofs of results, many of which are not readily available elsewhere, are also included. The book is written at a level appropriate for first-year graduate students in mathematics or computer science. Although some knowledge of elementary logic and universal algebra are necessary, the first chapter includes all the results from universal algebra and logic that the reader needs. For graduate students in mathematics and computer science the book is an excellent textbook.
This English translation of the author's original work has been thoroughly revised, expanded and updated. The book covers logical systems known as "type-free" or "self-referential." These traditionally arise from any discussion on logical and semantical paradoxes. This particular volume, however, is not concerned with paradoxes but with the investigation of type-free sytems to show that: (i) there are rich theories of self-application, involving both operations and truth which can serve as foundations for property theory and formal semantics; (ii) these theories provide a new outlook on classical topics, such as inductive definitions and predicative mathematics; (iii) they are particularly promising with regard to applications. Research arising from paradoxes has moved progressively closer to the mainstream of mathematical logic and has become much more prominent in the last twenty years. A number of significant developments, techniques and results have been discovered. Academics, students and researchers will find that the book contains a thorough overview of all relevant research in this field.
Fractal Functions, Fractal Surfaces, and Wavelets is the first systematic exposition of the theory of fractal surfaces, a natural outgrowth of fractal sets and fractal functions. It is also the first treatment to bring these general considerations to bear on the burgeoning field of wavelets. The text is based on Massopusts work on and contributions to the theory of fractal functions, and the author uses a number of tools--including analysis, topology, algebra, and probability theory--to introduce readers to this new subject. Though much of the material presented in this book is relatively current (developed in the past decade by the author and his colleagues) and fairly specialized, an informative background is provided for those * First systematic treatment of fractal surfaces
The main purpose of this volume is to provide a new perception of multivariate environmental statistics using some examples that are of concern and interest today. The papers are presented by outstanding research workers. They discuss the current state of the art in different areas of multivariate environmental statistics and provide new problems for future research and instruction. A perspective is to cover a broad spectrum of methods and issues involving multivariate observations and processes, and not just classical multivariate analysis. The book will be valuable to current statistical theory and practice in this area, and will be used by researchers, teachers, and students alike.
Handbook of Convex Geometry, Volume A offers a survey of convex geometry and its many ramifications and relations with other areas of mathematics, including convexity, geometric inequalities, and convex sets. The selection first offers information on the history of convexity, characterizations of convex sets, and mixed volumes. Topics include elementary convexity, equality in the Aleksandrov-Fenchel inequality, mixed surface area measures, characteristic properties of convex sets in analysis and differential geometry, and extensions of the notion of a convex set. The text then reviews the standard isoperimetric theorem and stability of geometric inequalities. The manuscript takes a look at selected affine isoperimetric inequalities, extremum problems for convex discs and polyhedra, and rigidity. Discussions focus on include infinitesimal and static rigidity related to surfaces, isoperimetric problem for convex polyhedral, bounds for the volume of a convex polyhedron, curvature image inequality, Busemann intersection inequality and its relatives, and Petty projection inequality. The book then tackles geometric algorithms, convexity and discrete optimization, mathematical programming and convex geometry, and the combinatorial aspects of convex polytopes. The selection is a valuable source of data for mathematicians and researchers interested in convex geometry.
Handbook of Convex Geometry, Volume B offers a survey of convex geometry and its many ramifications and connections with other fields of mathematics, including convexity, lattices, crystallography, and convex functions. The selection first offers information on the geometry of numbers, lattice points, and packing and covering with convex sets. Discussions focus on packing in non-Euclidean spaces, problems in the Euclidean plane, general convex bodies, computational complexity of lattice point problem, centrally symmetric convex bodies, reduction theory, and lattices and the space of lattices. The text then examines finite packing and covering and tilings, including plane tilings, monohedral tilings, bin packing, and sausage problems. The manuscript takes a look at valuations and dissections, geometric crystallography, convexity and differential geometry, and convex functions. Topics include differentiability, inequalities, uniqueness theorems for convex hypersurfaces, mixed discriminants and mixed volumes, differential geometric characterization of convexity, reduction of quadratic forms, and finite groups of symmetry operations. The selection is a dependable source of data for mathematicians and researchers interested in convex geometry.
The aim of this book is to introduce a range of combinatorial methods for those who want to apply these methods in the solution of practical and theoretical problems. Various tricks and techniques are taught by means of exercises. Hints are given in a separate section and a third section contains all solutions in detail. A dictionary section gives definitions of the combinatorial notions occurring in the book. "Combinatorial Problems and Exercises" was first published in 1979. This revised edition has the same basic structure but has been brought up to date with a series of exercises on random walks on graphs and their relations to eigenvalues, expansion properties and electrical resistance. In various chapters the author found lines of thought that have been extended in a natural and significant way in recent years. About 60 new exercises (more counting sub-problems) have been added and several solutions have been simplified.
Presented in this monograph is the current state-of-the-art in the theory of convex structures. The notion of convexity covered here is considerably broader than the classic one; specifically, it is not restricted to the context of vector spaces. Classical concepts of order-convex sets (Birkhoff) and of geodesically convex sets (Menger) are directly inspired by intuition; they go back to the first half of this century. An axiomatic approach started to develop in the early Fifties. The author became attracted to it in the mid-Seventies, resulting in the present volume, in which graphs appear side-by-side with Banach spaces, classical geometry with matroids, and ordered sets with metric spaces. A wide variety of results has been included (ranging for instance from the area of partition calculus to that of continuous selection). The tools involved are borrowed from areas ranging from discrete mathematics to infinite-dimensional topology. Although addressed primarily to the researcher, parts of this monograph can be used as a basis for a well-balanced, one-semester graduate course.
This text brings the reader to the frontiers of current research in topological rings. The exercises illustrate many results and theorems while a comprehensive bibliography is also included. The book is aimed at those readers acquainted with some very basic point-set topology and algebra, as normally presented in semester courses at the beginning graduate level or even at the advanced undergraduate level. Familiarity with Hausdorff, metric, compact and locally compact spaces and basic properties of continuous functions, also with groups, rings, fields, vector spaces and modules, and with Zorn's Lemma, is also expected.
In this book, the general theory of submanifolds in a multidimensional projective space is constructed. The topics dealt with include osculating spaces and fundamental forms of different orders, asymptotic and conjugate lines, submanifolds on the Grassmannians, different aspects of the normalization problems for submanifolds (with special emphasis given to a connection in the normal bundle) and the problem of algebraizability for different kinds of submanifolds, the geometry of hypersurfaces and hyperbands, etc. A series of special types of submanifolds with special projective structures are studied: submanifolds carrying a net of conjugate lines (in particular, conjugate systems), tangentially degenerate submanifolds, submanifolds with asymptotic and conjugate distributions etc. The method of moving frames and the apparatus of exterior differential forms are systematically used in the book and the results presented can be applied to the problems dealing with the linear subspaces or their generalizations. Graduate students majoring in differential geometry will find this monograph of great interest, as will researchers in differential and algebraic geometry, complex analysis and theory of several complex variables.
The three chapters of this book are entitled Basic Concepts, Tensor Norms, and Special Topics. The first may serve as part of an introductory course in Functional Analysis since it shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. The second chapter is the main part of the book: it presents the theory of tensor norms as designed by Grothendieck in the Resume and deals with the relation between tensor norms and operator ideals. The last chapter deals with special questions. Each section is accompanied by a series of exercises.
These papers survey the developments in General Topology and the applications of it which have taken place since the mid 1980s. The book may be regarded as an update of some of the papers in the Handbook of Set-Theoretic Topology (eds. Kunen/Vaughan, North-Holland, 1984), which gives an almost complete picture of the state of the art of Set Theoretic Topology before 1984. In the present volume several important developments are surveyed that surfaced in the period 1984-1991. This volume may also be regarded as a partial update of Open Problems in Topology (eds. van Mill/Reed, North-Holland, 1990). Solutions to some of the original 1100 open problems are discussed and new problems are posed.
The theory of tree languages, founded in the late Sixties and still active in the Seventies, was much less active during the Eighties. Now there is a simultaneous revival in several countries, with a number of significant results proved in the past five years. A large proportion of them appear in the present volume. The editors of this volume suggested that the authors should write comprehensive half-survey papers. This collection is therefore useful for everyone interested in the theory of tree languages as it covers most of the recent questions which are not treated in the very few rather old standard books on the subject. Trees appear naturally in many chapters of computer science and each new property is likely to result in improvement of some computational solution of a real problem in handling logical formulae, data structures, programming languages on systems, algorithms etc. The point of view adopted here is to put emphasis on the properties themselves and their rigorous mathematical exposition rather than on the many possible applications. This volume is a useful source of concepts and methods which may be applied successfully in many situations: its philosophy is very close to the whole philosophy of the ESPRIT Basic Research Actions and to that of the European Association for Theoretical Computer Science.
In this revolutionary work, the author sets the stage for the
science of In the field of
1988 marked the first centenary of Recursion Theory, since Dedekind's 1888 paper on the nature of number. Now available in paperback, this book is both a comprehensive reference for the subject and a textbook starting from first principles. Among the subjects covered are: various equivalent approaches to
effective computability and their relations with computers and
programming languages; a discussion of Church's thesis; a modern
solution to Post's problem; global properties of Turing degrees;
and a complete algebraic characterization of many-one degrees.
Included are a number of applications to logic (in particular
Godel's theorems) and to computer science, for which Recursion
Theory provides the theoretical foundation.
When soliton theory, based on water waves, plasmas, fiber optics etc., was developing in the 1960-1970 era it seemed that perhaps KdV (and a few other equations) were really rather special in the set of all interesting partial differential equations. As it turns out, although integrable systems are still special, the mathematical interaction of integrable systems theory with virtually all branches of mathematics (and with many currently developing areas of theoretical physics) illustrates the importance of this area. This book concentrates on developing the theme of the tau function. KdV and KP equations are treated extensively, with material on NLS and AKNS systems, and in following the tau function theme one is led to conformal field theory, strings, and other topics in physics. The extensive list of references contains about 1000 entries.
Anyone involved in the philosophy of science is naturally drawn
into the study of the foundations of probability. Different
interpretations of probability, based on competing philosophical
ideas, lead to different statistical techniques, and frequently to
mutually contradictory consequences. This unique book presents a new interpretation of probability, rooted in the traditional interpretation that was current in the 17th and 18th centuries. Mathematical models are constructed based on this interpretation, and statistical inference and decision theory are applied, including some examples in artificial intelligence, solving the main foundational problems. Nonstandard analysis is extensively developed for the construction of the models and in some of the proofs. Many nonstandard theorems are proved, some of them new, in particular, a representation theorem that asserts that any stochastic process can be approximated by a process defined over a space with equiprobable outcomes.
This monograph began life as a series of papers documenting five years of research into the logical foundations of Categorial Grammar, a grammatical paradigm which has close analogies with Lambda Calculus and Type Theory. The technical theory presented here stems from the interface between Logic and Linguistics and, in particular, the theory of generalized quantification. A categorical framework with lambda calculus-oriented semantics is a convenient vehicle for generalizing semantic insights (obtained in various corners of natural language) into one coherent theory.
In 1974 the editors of the present volume published a well-received
book entitled Latin Squares and their Applications''. It included a
list of 73 unsolved problems of which about 20 have been completely
solved in the intervening period and about 10 more have been
partially solved.
The first part of this book is a text for graduate courses in
topology. In chapters 1 - 5, part of the basic material of plane
topology, combinatorial topology, dimension theory and ANR theory
is presented. For a student who will go on in geometric or
algebraic topology this material is a prerequisite for later work.
Chapter 6 is an introduction to infinite-dimensional topology; it
uses for the most part geometric methods, and gets to spectacular
results fairly quickly. The second part of this book, chapters 7
& 8, is part of geometric topology and is meant for the more
advanced mathematician interested in manifolds.
This classic work has been fundamentally revised to take account of
recent developments in general topology. The first three chapters
remain unchanged except for numerous minor corrections and
additional exercises, but chapters IV-VII and the new chapter VIII
cover the rapid changes that have occurred since 1968 when the
first edition appeared.
Get "Up and Running" with AutoCAD using Gindis combination of
step-by-step instruction, examples, and insightful explanations.
The emphasis from the beginning is on core concepts and practical
application of AutoCAD in architecture, engineering and design.
Equally useful in instructor-led classroom training or self-study,
the book is written with the student in mind by a long-time AutoCAD
user and instructor, based on what works in the industry and the
classroom. Explains "why" something is done, not just "how": the theory behind each concept or command is discussed prior to engaging AutoCAD, so the student has a clear idea of what they are attempting to do. All basic commands are documented step-by-step: what the student types in and how AutoCAD responds is spelled out in discrete and clear steps with numerous screen shots. Extensive supporting graphics (screen shots) and a summary with a self-test section and topic specific drawing exercises are included at the end of each chapter. Additional practice is gained through projects that the students work on as they progress through the chapters. Also available in a comprehensive volume that includes coverage of 3D drawing and modeling in AutoCad. ISBN for comprehensive volume is 978-0-12-375717-3 "
Gindis introduces AutoCAD with step-by-step instructions, stripping away complexities to begin working in AutoCAD immediately. All concepts are explained first in theory, and then shown in practice, helping the reader understand "what "it is they are doing and why before they do it. The book contains supporting graphics (screen shots) and a
summary with a self-test section at the end of each chapter. Also
included are drawing examples and exercises, and two running
projects that the reader works on as they progresses through the
chaptersExplains the why and how of AutoCAD commands: all concepts
are explained first in theory andthencovered in step-by-step
detailExtensive use of screen shots, chapter summaries, and
aself-test section at the end of each chapter Includesdrawing
examples and exercises, and two running projects that the reader
works on as he/she progresses through the chaptersEach chapter
features a "Spotlight On..." section, highlighting theuse of
AutoCAD in various industries Fully updated for AutoCAD 2010
release, including introduction of the ribbon menu structurein
chapter 1Strips away complexities, both real and perceived, and
reduces AutoCAD to easy-to-understand basic concepts; using the
author's extensive multi-industry knowledge of what is widely used
in practice, the material is presented by immediately immersing the
reader in practical, critically essential knowledge
"Partial Differential Equations and Boundary Value Problems with Maple" presents all of the material normally covered in a standard course on partial differential equations, while focusing on the natural union between this material and the powerful computational software, Maple. The Maple commands are so intuitive and easy to learn, students can learn what they need to know about the software in a matter of hours- an investment that provides substantial returns. Maple's animation capabilities allow students and practitioners to see real-time displays of the solutions of partial differential equations. Maplefiles can be found on the books website. Ancillary list: Maple files- http:
//www.elsevierdirect.com/companion.jsp?ISBN=9780123747327 |
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