This monograph gives an introductory treatment of the most important iterative methods for constructing fixed points of nonlinear contractive type mappings. For each iterative method considered, it summarizes the most significant contributions in the area by presenting some of the most relevant convergence theorems. It also presents applications to the solution of nonlinear operator equations as well as the appropriate error analysis of the main iterative methods.

Charles Chihara's new book develops and defends a structural view of the nature of mathematics, and uses it to explain a number of striking features of mathematics that have puzzled philosophers for centuries. The view is used to show that, in order to understand how mathematical systems are applied in science and everyday life, it is not necessary to assume that its theorems either presuppose mathematical objects or are even true.
Chihara builds upon his previous work, in which he presented a new system of mathematics, the constructibility theory, which did not make reference to, or resuppose, mathematical objects. Now he develops the project further by analyzing mathematical systems currently used by scientists to show how such systems are compatible with this nominalistic outlook. He advances several new ways of undermining the heavily discussed indispensability argument for the existence of mathematical objects made famous by Willard Quine and Hilary Putnam. And Chihara presents a rationale for the nominalistic outlook that is quite different from those generally put forward, which he maintains have led to serious misunderstandings.
A Structural Account of Mathematics will be required reading for anyone working in this field.

"This engagingly written text provides a useful pedagogical introduction to an extensive class of geometrical phenomena in the optics of polarization and phase, including simple explanations of much of the underlying mathematics." -Michael Berry, University of Bristol, UK "The author covers a vast number of topics in great detail, with a unifying mathematical treatment. It will be a useful reference for both beginners and experts...." -Enrique Galvez, Charles A. Dana Professor of Physics and Astronomy, Colgate University "a firm and comprehensive grounding both for those looking to acquaint themselves with the field and those of us that need reminding of the things we thought we knew, but hitherto did not understand: an essential point of reference." -Miles Padgett, Kelvin Chair of Natural Philosophy and Vice Principal (Research), University of Glasgow This book focuses on the various forms of wavefield singularities, including optical vortices and polarization singularities, as well as orbital angular momentum and associated applications. It highlights how an understanding of singular optics provides a completely different way to look at light. Whereas traditional optics focuses on the shape and structure of the non-zero portions of the wavefield, singular optics describes a wave's properties from its null regions. The contents cover the three main areas of the field: the study of generic features of wavefields, determination of unusual properties of vortices and wavefields that contain singularities, and practical applications of vortices and other singularities.

Model theory is a branch of mathematical logic that has found applications in several areas of algebra and geometry. It provides a unifying framework for the understanding of old results and more recently has led to significant new results, such as a proof of the Mordell-Lang conjecture for function fields in positive characteristic. Perhaps surprisingly, it is sometimes the most abstract aspects of model theory that are relevant to those applications. This book gives the necessary background for understanding both the model theory and the mathematics behind the applications. Aimed at graduate students and researchers, it contains introductory surveys by leading experts covering the whole spectrum of contemporary model theory (stability, simplicity, o-minimality and variations), and introducing and discussing the diverse areas of geometry (algebraic, diophantine, real analytic, p-adic, and rigid) to which the model theory is applied. The book begins with an introduction to model theory by David Marker. It then broadens into three components: pure model theory (Bradd Hart, Dugald Macpherson), geometry(Barry Mazur, Ed Bierstone and Pierre Milman, Jan Denef), and the model theory of fields (Marker, Lou van den Dries, Zoe Chatzidakis).

By presenting state-of-the-art results in logical reasoning and formal methods in the context of artificial intelligence and AI applications, this book commemorates the 60th birthday of JArg H. Siekmann.

The 30 revised reviewed papers are written by former and current students and colleagues of JArg Siekmann; also included is an appraisal of the scientific career of JArg Siekmann entitled "A Portrait of a Scientist: Logics, AI, and Politics." The papers are organized in four parts on logic and deduction, applications of logic, formal methods and security, and agents and planning.

This concisely written book gives an elementary introduction to a classical area of mathematicsa "approximation theorya "in a way that naturally leads to the modern field of wavelets. The exposition, driven by ideas rather than technical details and proofs, demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications.

Key features and topics:

* Description of wavelets in words rather than mathematical symbols

* Elementary introduction to approximation using polynomials (Weierstrassa (TM) and Taylora (TM)s theorems)

* Introduction to infinite series, with emphasis on approximation-theoretic aspects

* Introduction to Fourier analysis

* Numerous classical, illustrative examples and constructions

* Discussion of the role of wavelets in digital signal processing and data compression, such as the FBIa (TM)s use of wavelets to store fingerprints

* Minimal prerequisites: elementary calculus

* Exercises that may be used in undergraduate and graduate courses on infinite series and Fourier series

Approximation Theory: From Taylor Polynomials to Wavelets will be an excellent textbook or self-study reference for students and instructors in pure and applied mathematics, mathematical physics, and engineering. Readers will find motivation and background material pointing toward advanced literature and research topics in pure and applied harmonic analysis and related areas.

This is the concluding volume of the second edition of the standard text on design theory. Since the first edition there has been extensive development of the theory and this book has been thoroughly rewritten to reflect this. In particular the growing importance of discrete mathematics to many parts of engineering and science have made designs a useful tool for applications, and this fact has been acknowledged here with the inclusion of an additional chapter on applications. It is suitable for advanced courses and as a reference work, not only for researchers in discrete mathematics or finite algebra, but also for those working in computer and communications engineering and other mathematically oriented disciplines. Exercises are included throughout, and the book concludes with an extensive and updated bibliography of well over 1800 items.

This book presents in detail a complete set of best-fit algorithms for general curves and surfaces in space. Such best-fit algorithms approximate and estimate curve and surface parameters by minimizing the shortest distances between the curve or surface and the measurement point.

After reviewing the basics for representing curves and surfaces in space and fitting in general, the author presents three algorithms for orthogonal distance fitting combining numerical methods and minimizational methods. These algorithms are applied to implicit and parametric curves and surfaces in 2D and 3D space possessing a broad variety of algorithmic features. Finally, an appendix provides practical information for applying the general orthogonal distance fitting algorithms to fit special model features.

Obvious application areas of the algorithms presented are robot navigation, including the navigation of autonomous vehicles or the grasping of work pieces, as well as factory digitization in general.

During 1996-97 MSRI held a full academic-year program on combinatorics, with special emphasis on its connections to other branches of mathematics, such as algebraic geometry, topology, commutative algebra, representation theory, and convex geometry. The rich combinatorial problems arising from the study of various algebraic structures are the subject of this book, which features work done or presented at the program's seminars. The text contains contributions on matroid bundles, combinatorial representation theory, lattice points in polyhedra, bilinear forms, combinatorial differential topology and geometry, Macdonald polynomials and geometry, enumeration of matchings, the generalized Baues problem, and Littlewood-Richardson semigroups. These expository articles, written by some of the most respected researchers in the field, present the state of the art to graduate students and researchers in combinatorics as well as in algebra, geometry, and topology.

The British Combinatorial Conference is one of the most well-known meetings for combinatorialists. This volume collects the invited talks from the 1999 conference held at the University of Kent, and together these span a broad range of combinatorial topics. The nine talks are from: S. Ball, J. Dinitz, M. Dyer, K. Metsch, J. Pach, R. Thomas, C. Thomassen, N. Wormald, plus a special contribution from W. T. Tutte. All researchers into combinatorics will find that this volume is an outstanding and up-to-date resource.

The 7th International Conference on Theory and Applications of Satis?ab- ity Testing (SAT 2004) was held 10-13 May 2004 in Vancouver, BC, Canada. The conference featured 9 technical paper sessions, 2 poster sessions, as well as the 2004 SAT Solver Competition and the 2004 QBF Solver Evaluation. It also included invited talks by Stephen A. Cook (University of Toronto) and Kenneth McMillan (Cadence Berkeley Labs). The 89 participants represented no less than 17 countries and four continents. SAT 2004 continued the series of meetings which started with the Workshops on Satis?ability held in Siena, Italy (1996), Paderborn, Germany (1998) and Renesse, The Netherlands (2000); the Workshop on Theory and Applications of Satis?ability Testing held in Boston, USA(2001);theSymposiumonTheoryandApplicationsofSatis?abilityTesting held in Cincinnati, USA (2002); and the 6th International Conference on Theory and Applications of Satis?ability Testing held in Santa Margherita Ligure, Italy (2003). The International Conference on Theory and Applications of Satis?ability Testing is the primary annual meeting for researchers studying the propo- tional satis?ability problem (SAT), a prominent problem in both theoretical and applied computer science. SAT lies at the heart of the most important open problem in complexity theory (P vsNP) and underlies many applications in, among other examples, arti?cial intelligence, operations research and electronic design engineering. The primary objective of the conferences is to bring together researchersfromvariousareasandcommunities, includingtheoreticalandexp- imental computer science as well as many relevant application areas, to promote collaboration and the communication of new theoretical and practical results in SAT-related research and its industrial applications

The theory of natural dualities, as presented in this text, is broad enough to encompass many known dualities through a rich assortment of substantive theorems, yet concrete enough to be used to generate an array of previously undiscovered dualities. This text will serve as a user manual for algebraists, for category theorists and for those who use algebra in their work, particularly mathematicians and computer scientists interested in non-classical logics. It will also give the specialist a complete account of the foundations, leading to the research frontier of this rapidly developing field. As the first text devoted to the theory of Natural Dualities, it provides an efficient path through a large body of results, examples and applications in this subject which is otherwise available only in scattered research papers. To enable the book to be used in courses, each chapter ends with an extensive exercise set. Several fundamental unsolved problems are included.

Now in paperback, this book provides a self-contained introduction to the cohomology theory of Lie groups and algebras and to some of its applications in physics. No previous knowledge of the mathematical theory is assumed beyond some notions of Cartan calculus and differential geometry (which are nevertheless reviewed in the book in detail). The examples, of current interest, are intended to clarify certain mathematical aspects and to show their usefulness in physical problems. The topics treated include the differential geometry of Lie groups, fiber bundles and connections, characteristic classes, index theorems, monopoles, instantons, extensions of Lie groups and algebras, some applications in supersymmetry, Chevalley-Eilenberg approach to Lie algebra cohomology, symplectic cohomology, jet-bundle approach to variational principles in mechanics, Wess-Zumino-Witten terms, infinite Lie algebras, the cohomological descent in mechanics and in gauge theories and anomalies. This book will be of interest to graduate students and researchers in theoretical physics and applied mathematics.

The NATO Advanced Study Institute "Axiomatic, enriched and rna tivic homotopy theory" took place at the Isaac Newton Institute of Mathematical Sciences, Cambridge, England during 9-20 September 2002. The Directors were J.P.C.Greenlees and I.Zhukov; the other or ganizers were P.G.Goerss, F.Morel, J.F.Jardine and V.P.Snaith. The title describes the content well, and both the event and the contents of the present volume reflect recent remarkable successes in model categor ies, structured ring spectra and homotopy theory of algebraic geometry. The ASI took the form of a series of 15 minicourses and a few extra lectures, and was designed to provide background, and to bring the par ticipants up to date with developments. The present volume is based on a number of the lectures given during the workshop. The ASI was the opening workshop of the four month programme "New Contexts for Stable Homotopy Theory" which explored several themes in greater depth. I am grateful to the Isaac Newton Institute for providing such an ideal venue, the NATO Science Committee for their funding, and to all the speakers at the conference, whether or not they were able to contribute to the present volume. All contributions were refereed, and I thank the authors and referees for their efforts to fit in with the tight schedule. Finally, I would like to thank my coorganizers and all the staff at the Institute for making the ASI run so smoothly. J.P.C.GREENLEES."

This text presents six mini-courses, all devoted to interactions between representation theory of algebras, homological algebra, and the new ever-expanding theory of cluster algebras. The interplay between the topics discussed in this text will continue to grow and this collection of courses stands as a partial testimony to this new development. The courses are useful for any mathematician who would like to learn more about this rapidly developing field; the primary aim is to engage graduate students and young researchers. Prerequisites include knowledge of some noncommutative algebra or homological algebra. Homological algebra has always been considered as one of the main tools in the study of finite-dimensional algebras. The strong relationship with cluster algebras is more recent and has quickly established itself as one of the important highlights of today's mathematical landscape. This connection has been fruitful to both areas-representation theory provides a categorification of cluster algebras, while the study of cluster algebras provides representation theory with new objects of study. The six mini-courses comprising this text were delivered March 7-18, 2016 at a CIMPA (Centre International de Mathematiques Pures et Appliquees) research school held at the Universidad Nacional de Mar del Plata, Argentina. This research school was dedicated to the founder of the Argentinian research group in representation theory, M.I. Platzeck. The courses held were: Advanced homological algebra Introduction to the representation theory of algebras Auslander-Reiten theory for algebras of infinite representation type Cluster algebras arising from surfaces Cluster tilted algebras Cluster characters Introduction to K-theory Brauer graph algebras and applications to cluster algebras

Here is an introduction to dynamical systems and ergodic theory with an emphasis on smooth actions of noncompact Lie groups. The main goal is to serve as an entry into the current literature on the ergodic theory of measure preserving actions of semisimple Lie groups for students who have taken the standard first year graduate courses in mathematics. The author develops in a detailed and self-contained way the main results on Lie groups, Lie algebras, and semisimple groups, including basic facts normally covered in first courses on manifolds and Lie groups plus topics such as integration of infinitesimal actions of Lie groups. He then derives the basic structure theorems for the real semisimple Lie groups, such as the Cartan and Iwasawa decompositions and gives an extensive exposition of the general facts and concepts from topological dynamics and ergodic theory, including detailed proofs of the multiplicative ergodic theorem and Moore's ergodicity theorem. This book should appeal to anyone interested in Lie theory, differential geometry and dynamical systems.

This book, written by one of philosophy's preeminent logicians, argues that many of the basic assumptions common to logic, philosophy of mathematics and metaphysics are in need of change. Jaakko Hintikka proposes a new basic first-order logic and uses it to explore the foundations of mathematics. This new logic enables logicians to express on the first-order level such concepts as equicardinality, infinity, and truth in the same language. Hintikka's new logic is highly original and will prove appealing to logicians, philosophers of mathematics, and mathematicians concerned with the foundations of the discipline.

This book eases students into the rigors of university mathematics. The emphasis is on understanding and constructing proofs and writing clear mathematics. The author achieves this by exploring set theory, combinatorics, and number theory, topics that include many fundamental ideas and may not be a part of a young mathematician's toolkit. This material illustrates how familiar ideas can be formulated rigorously, provides examples demonstrating a wide range of basic methods of proof, and includes some of the all-time-great classic proofs. The book presents mathematics as a continually developing subject. Material meeting the needs of readers from a wide range of backgrounds is included. The over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.

  This book constitutes the joint refereed proceedings of the 17th International Workshop on Computer Science Logic, CSL 2003, held as the 12th Annual Conference of the EACSL and of the 8th Kurt Gödel Colloquium, KGC 2003 in Vienna, Austria, in August 2003. The 30 revised full papers presented together with abstracts of 9 invited presentations were carefully reviewed and selected from a total of 112 submissions. All current aspects of computer science logic are addressed ranging from mathematical logic and logical foundations to the application of logics in various computing aspects.

Michael Powell is one of the world's foremost figures in numerical analysis. This volume is derived from invited talks given at a meeting celebrating his 60th birthday and, reflecting Powell's own achievements, focuses on innovative work in optimization and in approximation theory. The individual papers have been written by leading authorities in their subjects and are a mix of expository articles and surveys on new work. They have all been reviewed and edited to form a volume that represents the state of the art in an important discipline within mathematics, with highly relevant applications throughout science and engineering.

This volume consists of the papers presented by the invited lecturers at the 16th British Combinatorial Conference. This biennial meeting is one of the most important for combinatorialists, attracting leading figures in the field. This overview of up-to-date research will be a valuable resource for researchers and graduate students.

Absolutely everything you need to get ready for Algebra Scared of square roots? Suspicious of powers of ten? You're not alone. Plenty of school-age students and adult learners don't care for math. But, with the right guide, you can make math basics "click" for you too! In Basic Math & Pre-Algebra All-in-One For Dummies, you'll find everything you need to be successful in your next math class and tackle basic math tasks in the real world. Whether you're trying to get a handle on pre-algebra before moving to the next grade or looking to get more comfortable with everyday math--such as tipping calculations or balancing your checkbook--this book walks you through every step--in plain English, and with clear explanations--to help you build a firm foundation in math. You'll also get: Practice quizzes at the end of each chapter to test your comprehension and understanding A bonus online quiz for each chapter, with answer choices presented in multiple choice format A ton of explanations, examples, and practice problems that prepare you to tackle more advanced algebraic concepts From the different categories of numbers to mathematical operations, fractions, percentages, roots and powers, and a short intro to algebraic expressions and equations, Basic Math & Pre-Algebra All-in-One For Dummies is an essential companion for anyone who wants to get a handle on the foundational math concepts that are the building blocks for Algebra and beyond.

Charles Chihara's new book develops and defends a structural view of the nature of mathematics, and uses it to explain a number of striking features of mathematics that have puzzled philosophers for centuries. The view is used to show that, in order to understand how mathematical systems are applied in science and everyday life, it is not necessary to assume that its theorems either presuppose mathematical objects or are even true. Chihara builds upon his previous work, in which he presented a new system of mathematics, the constructibility theory, which did not make reference to, or presuppose, mathematical objects. Now he develops the project further by analysing mathematical systems currently used by scientists to show how such systems are compatible with this nominalistic outlook. He advances several new ways of undermining the heavily discussed indispensability argument for the existence of mathematical objects made famous by Willard Quine and Hilary Putnam. And Chihara presents a rationale for the nominalistic outlook that is quite different from those generally put forward, which he maintains have led to serious misunderstandings. A Structural Account of Mathematics will be required reading for anyone working in this field.

Series Editor's Preface. Preface. A. Kaleidoscopic Excursion into numerical Calculations of Differential Equations; E. van Groesen. An Introduction to the Finite Element Method; J. van Kan. Coupling of Sound and Structural Vibrations; C. Kauffmann. Mathematical Modeling and Dimensional Analysis; J. Molenaar. About Difference Equations, Algebras and Discrete Events; G.J. Olsder. Acoustical Detection of Obstructions in a Pipe with a Temperature Gradient; S.W. Rienstra. Interior Point Approach to linear Programming: Theory, Algorithms and Parametric Analysis; C. Roos. Some Reflections on Newton's Method; F. Twilt. Recurrence and Induction in Computer Science; A.J. van Zanten.

This third volume turns to topos theory and the idea of sheaves. The theory of locales is considered first, and Grothendieck toposes are introduced. Notions of sketchability and accessible categories are discussed, and an axiomatic generalization of the category of sheaves is given.