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Introduction To Game Theory

Author: Peter Morris
Publisher: Springer Science & Business Media
ISBN: 1461243165
Size: 72.93 MB
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This advanced textbook covers the central topics in game theory and provides a strong basis from which readers can go on to more advanced topics. The subject matter is approached in a mathematically rigorous, yet lively and interesting way. New definitions and topics are motivated as thoroughly as possible. Coverage includes the idea of iterated Prisoner's Dilemma (super games) and challenging game-playing computer programs.

Approaches To Geo Mathematical Modelling

Author: Alan G. Wilson
Publisher: John Wiley & Sons
ISBN: 1118937457
Size: 49.80 MB
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Geo-mathematical modelling: models from complexity science Sir Alan Wilson, Centre for Advanced Spatial Analysis, University College London Mathematical and computer models for a complexity science tool kit Geographical systems are characterised by locations, activities at locations, interactions between them and the infrastructures that carry these activities and flows. They can be described at a great variety of scales, from individuals and organisations to countries. Our understanding, often partial, of these entities, and in many cases this understanding is represented in theories and associated mathematical models. In this book, the main examples are models that represent elements of the global system covering such topics as trade, migration, security and development aid together with examples at finer scales. This provides an effective toolkit that can not only be applied to global systems, but more widely in the modelling of complex systems. All complex systems involve nonlinearities involving path dependence and the possibility of phase changes and this makes the mathematical aspects particularly interesting. It is through these mechanisms that new structures can be seen to ‘emerge’, and hence the current notion of ‘emergent behaviour’. The range of models demonstrated include account-based models and biproportional fitting, structural dynamics, space-time statistical analysis, real-time response models, Lotka-Volterra models representing ‘war’, agent-based models, epidemiology and reaction-diffusion approaches, game theory, network models and finally, integrated models. Geo-mathematical modelling: Presents mathematical models with spatial dimensions. Provides representations of path dependence and phase changes. Illustrates complexity science using models of trade, migration, security and development aid. Demonstrates how generic models from the complexity science tool kit can each be applied in a variety of situations This book is for practitioners and researchers in applied mathematics, geography, economics, and interdisciplinary fields such as regional science and complexity science. It can also be used as the basis of a modelling course for postgraduate students.

Introduction To Hyperbolic Geometry

Author: Arlan Ramsay
Publisher: Springer Science & Business Media
ISBN: 9780387943398
Size: 12.26 MB
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This book is an introduction to hyperbolic and differential geometry that provides material in the early chapters that can serve as a textbook for a standard upper division course on hyperbolic geometry. For that material, the students need to be familiar with calculus and linear algebra and willing to accept one advanced theorem from analysis without proof. The book goes well beyond the standard course in later chapters, and there is enough material for an honors course, or for supplementary reading. Indeed, parts of the book have been used for both kinds of courses. Even some of what is in the early chapters would surely not be nec essary for a standard course. For example, detailed proofs are given of the Jordan Curve Theorem for Polygons and of the decomposability of poly gons into triangles, These proofs are included for the sake of completeness, but the results themselves are so believable that most students should skip the proofs on a first reading. The axioms used are modern in character and more "user friendly" than the traditional ones. The familiar real number system is used as an in gredient rather than appearing as a result of the axioms. However, it should not be thought that the geometric treatment is in terms of models: this is an axiomatic approach that is just more convenient than the traditional ones.

An Invitation To Morse Theory

Author: Liviu Nicolaescu
Publisher: Springer Science & Business Media
ISBN: 038749510X
Size: 58.30 MB
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This book offers readers a taste of the "unreasonable effectiveness" of Morse theory. It covers many of the most important topics in Morse theory along with applications. The book details topics such as Morse-Smale flows, min-max theory, moment maps and equivariant cohomology, and complex Morse theory. In addition, many examples, problems, and illustrations further enhance the value of this useful introduction to Morse Theory.

Introduction To The Mori Program

Author: Kenji Matsuki
Publisher: Springer Science & Business Media
ISBN: 9780387984650
Size: 11.30 MB
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Mori's Program is a fusion of the so-called Minimal Model Program and the IItaka Program toward the biregular and/or birational classification of higher dimensional algebraic varieties. The author presents this theory in an easy and understandable way with lots of background motivation. Prerequisites are those covered in Hartshorne's book "Algebraic Geometry." This is the first book in this extremely important and active field of research and will become a key resource for graduate students wanting to get into the area.

Games Theory And Applications

Author: L. C. Thomas
Publisher: Courier Corporation
ISBN: 9780486432373
Size: 34.49 MB
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Accessible and informative, this introduction to game theory explores 2-person zero-sum games, 2-person non-zero sum games, n-person games, and a variety of applications. Numerous exercises with full solutions. Includes 30 illustrations. 1986 edition.

Advanced Analysis

Author: Rangachary Kannan
Publisher: Springer Verlag
ISBN: 9780387946429
Size: 78.12 MB
Format: PDF
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The goal of this book is to provide an extensive collection of results which generalize classical real analysis. Besides discussing density, approximate continuity, and approximate derivatives in detail, culminating with the Denjoy-Saks-Young Theorem, the authors also present an interesting example due to Ruziewicz on an infinite number of functions with the same derivative (not everywhere finite) but the difference of any two is not a constant and Sierpinski's theorem on the extension of approximate continuity to nonmeasurable functions. There is also a chapter on monotonic functions and one dealing with the Tonelli-Goldowsky result of the weakening of the hypotheses on a function f such that f'r >- < f is increasing. The latter part of the book deals with functions of bounded variation and approximately continuous functions. Finally there is an exhaustive chapter on the generalized Cantor sets and Cantor functions. The bibliography is extensive and a great variety of exercises serves to clarify and sometimes extend the results presented in the text.