Introduction to Model Spaces and their Operators

Author: Stephan Ramon Garcia,Javad Mashreghi,William T. Ross

Publisher: Cambridge University Press

ISBN: 1107108748

Category: Mathematics

Page: 335

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A self-contained textbook which opens up this challenging field to newcomers and points to areas of future research.

Models and Games

Author: Jouko Väänänen

Publisher: Cambridge University Press

ISBN: 1139496336

Category: Mathematics

Page: N.A

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This gentle introduction to logic and model theory is based on a systematic use of three important games in logic: the semantic game; the Ehrenfeucht–Fraïssé game; and the model existence game. The third game has not been isolated in the literature before but it underlies the concepts of Beth tableaux and consistency properties. Jouko Väänänen shows that these games are closely related and in turn govern the three interrelated concepts of logic: truth, elementary equivalence and proof. All three methods are developed not only for first order logic but also for infinitary logic and generalized quantifiers. Along the way, the author also proves completeness theorems for many logics, including the cofinality quantifier logic of Shelah, a fully compact extension of first order logic. With over 500 exercises this book is ideal for graduate courses, covering the basic material as well as more advanced applications.

Random Graphs

Author: Béla Bollobás,Bollobás Béla

Publisher: Cambridge University Press

ISBN: 9780521797221

Category: Mathematics

Page: 498

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This is a revised and updated version of the classic first edition.

An Introduction to Random Matrices

Author: Greg W. Anderson,Alice Guionnet,Ofer Zeitouni

Publisher: Cambridge University Press

ISBN: 0521194520

Category: Mathematics

Page: 492

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A rigorous introduction to the basic theory of random matrices designed for graduate students with a background in probability theory.

A User's Guide to Spectral Sequences

Author: John McCleary

Publisher: Cambridge University Press

ISBN: 9780521567596

Category: Mathematics

Page: 561

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Spectral sequences are among the most elegant and powerful methods of computation in mathematics. This book describes some of the most important examples of spectral sequences and some of their most spectacular applications. The first part treats the algebraic foundations for this sort of homological algebra, starting from informal calculations. The heart of the text is an exposition of the classical examples from homotopy theory, with chapters on the Leray-Serre spectral sequence, the Eilenberg-Moore spectral sequence, the Adams spectral sequence, and, in this new edition, the Bockstein spectral sequence. The last part of the book treats applications throughout mathematics, including the theory of knots and links, algebraic geometry, differential geometry and algebra. This is an excellent reference for students and researchers in geometry, topology, and algebra.

Modelling Biological Populations in Space and Time

Author: Eric Renshaw

Publisher: Cambridge University Press

ISBN: 9780521448550

Category: Mathematics

Page: 403

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This volume develops a unifying approach to population studies, emphasising the interplay between modelling and experimentation. Throughout, mathematicians and biologists are provided with a framework within which population dynamics can be fully explored and understood. Aspects of population dynamics covered include birth-death and logistic processes, competition and predator-prey relationships, chaos, reaction time-delays, fluctuating environments, spatial systems, velocities of spread, epidemics, and spatial branching structures. Both deterministic and stochastic models are considered. Whilst the more theoretically orientated sections will appeal to mathematical biologists, the material is presented so that readers with little mathematical expertise can bypass these without losing the main flow of the text.

Algebraic Computability and Enumeration Models

Recursion Theory and Descriptive Complexity

Author: Cyrus F. Nourani

Publisher: CRC Press

ISBN: 1771882484

Category: Mathematics

Page: 310

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This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint. The reader is first introduced to categories and functorial models, with Kleene algebra examples for languages. Functorial models for Peano arithmetic are described toward important computational complexity areas on a Hilbert program, leading to computability with initial models. Infinite language categories are also introduced to explain descriptive complexity with recursive computability with admissible sets and urelements. Algebraic and categorical realizability is staged on several levels, addressing new computability questions with omitting types realizably. Further applications to computing with ultrafilters on sets and Turing degree computability are examined. Functorial models computability is presented with algebraic trees realizing intuitionistic types of models. New homotopy techniques are applied to Marin Lof types of computations with model categories. Functorial computability, induction, and recursion are examined in view of the above, presenting new computability techniques with monad transformations and projective sets. This informative volume will give readers a complete new feel for models, computability, recursion sets, complexity, and realizability. This book pulls together functorial thoughts, models, computability, sets, recursion, arithmetic hierarchy, filters, with real tree computing areas, presented in a very intuitive manner for university teaching, with exercises for every chapter. The book will also prove valuable for faculty in computer science and mathematics.

Models of Adaptive Behaviour

An Approach Based on State

Author: Alasdair I. Houston,John M. McNamara

Publisher: Cambridge University Press

ISBN: 9780521655392

Category: Science

Page: 378

View: 7219

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Exciting findings in field of adaptive dynamic modelling of behaviour.

Stone Spaces

Author: Peter T. Johnstone

Publisher: Cambridge University Press

ISBN: 9780521337793

Category: Mathematics

Page: 370

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A unified treatment of the corpus of mathematics that has developed out of M. H. Stone's representation theorem for Boolean algebras (1936) which has applications in almost every area of modern mathematics.

Stochastic Flows and Stochastic Differential Equations

Author: Hiroshi Kunita

Publisher: Cambridge University Press

ISBN: 9780521599252

Category: Mathematics

Page: 346

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Stochastic analysis and stochastic differential equations are rapidly developing fields in probability theory and its applications. This book provides a systematic treatment of stochastic differential equations and stochastic flow of diffeomorphisms and describes the properties of stochastic flows. Professor Kunita's approach regards the stochastic differential equation as a dynamical system driven by a random vector field, including K. Itô's classical theory. Beginning with a discussion of Markov processes, martingales and Brownian motion, Kunita reviews Itô's stochastic analysis. He places emphasis on establishing that the solution defines a flow of diffeomorphisms. This flow property is basic in the modern and comprehensive analysis of the solution and will be applied to solve the first and second order stochastic partial differential equations. This book will be valued by graduate students and researchers in probability. It can also be used as a textbook for advanced probability courses.

Epidemic Modelling

An Introduction

Author: D. J. Daley,J. Gani

Publisher: Cambridge University Press

ISBN: 9780521014670

Category: Mathematics

Page: 213

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This is a general introduction to the mathematical modelling of diseases.

Generalized Descriptive Set Theory and Classification Theory

Author: Sy-David Friedman,Tapani Hyttinen, Vadim Kulikov

Publisher: American Mathematical Soc.

ISBN: 0821894757

Category: Mathematics

Page: 80

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Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper the authors study the generalization where countable is replaced by uncountable. They explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in this generalized setting compared to the classical, countable case. They also draw the connection between the stability theoretic complexity of first-order theories and the descriptive set theoretic complexity of their isomorphism relations. The authors' results suggest that Borel reducibility on uncountable structures is a model theoretically natural way to compare the complexity of isomorphism relations.

Algebraic Number Theory

Author: A. Fröhlich,M. J. Taylor,Martin J. Taylor

Publisher: Cambridge University Press

ISBN: 9780521438346

Category: Mathematics

Page: 355

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This book provides a brisk, thorough treatment of the foundations of algebraic number theory on which it builds to introduce more advanced topics. Throughout, the authors emphasize the systematic development of techniques for the explicit calculation of the basic invariants such as rings of integers, class groups, and units, combining at each stage theory with explicit computations.

Mathematical Aspects of Quantum Field Theory

Author: Edson de Faria,Welington de Melo

Publisher: Cambridge University Press

ISBN: 1139489801

Category: Science

Page: N.A

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Over the last century quantum field theory has made a significant impact on the formulation and solution of mathematical problems and inspired powerful advances in pure mathematics. However, most accounts are written by physicists, and mathematicians struggle to find clear definitions and statements of the concepts involved. This graduate-level introduction presents the basic ideas and tools from quantum field theory to a mathematical audience. Topics include classical and quantum mechanics, classical field theory, quantization of classical fields, perturbative quantum field theory, renormalization, and the standard model. The material is also accessible to physicists seeking a better understanding of the mathematical background, providing the necessary tools from differential geometry on such topics as connections and gauge fields, vector and spinor bundles, symmetries and group representations.

Mathematical Models in the Applied Sciences

Author: A. C. Fowler

Publisher: Cambridge University Press

ISBN: 9780521467032

Category: Mathematics

Page: 402

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Presents a thorough grounding in the techniques of mathematical modelling, and proceeds to explore a range of classical and continuum models from an array of disciplines.

Random Walk: A Modern Introduction

Author: Gregory F. Lawler,Vlada Limic

Publisher: Cambridge University Press

ISBN: 1139488767

Category: Mathematics

Page: N.A

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Random walks are stochastic processes formed by successive summation of independent, identically distributed random variables and are one of the most studied topics in probability theory. This contemporary introduction evolved from courses taught at Cornell University and the University of Chicago by the first author, who is one of the most highly regarded researchers in the field of stochastic processes. This text meets the need for a modern reference to the detailed properties of an important class of random walks on the integer lattice. It is suitable for probabilists, mathematicians working in related fields, and for researchers in other disciplines who use random walks in modeling.

Introduction to Banach Spaces: Analysis and Probability

Author: Daniel Li,Hervé Queffélec

Publisher: Cambridge University Press

ISBN: 1107162629

Category: Mathematics

Page: 412

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This two-volume text provides a complete overview of the theory of Banach spaces, emphasising its interplay with classical and harmonic analysis (particularly Sidon sets) and probability. The authors give a full exposition of all results, as well as numerous exercises and comments to complement the text and aid graduate students in functional analysis. The book will also be an invaluable reference volume for researchers in analysis. Volume 1 covers the basics of Banach space theory, operatory theory in Banach spaces, harmonic analysis and probability. The authors also provide an annex devoted to compact Abelian groups. Volume 2 focuses on applications of the tools presented in the first volume, including Dvoretzky's theorem, spaces without the approximation property, Gaussian processes, and more. Four leading experts also provide surveys outlining major developments in the field since the publication of the original French edition.

Singularities of the Minimal Model Program

Author: János Kollár,Sándor Kovács

Publisher: Cambridge University Press

ISBN: 1107035341

Category: Mathematics

Page: 370

View: 7152

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An authoritative reference and the first comprehensive treatment of the singularities of the minimal model program.

Mathematical Methods and Models for Economists

Author: Angel de la Fuente

Publisher: Cambridge University Press

ISBN: 9780521585293

Category: Business & Economics

Page: 835

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A textbook for a first-year PhD course in mathematics for economists and a reference for graduate students in economics.