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Galilean Mechanics and Thermodynamics of Continua
by Géry De SaxcéThis title proposes a unified approach to continuum mechanics which is consistent with Galilean relativity. Based on the notion of affine tensors, a simple generalization of the classical tensors, this approach allows gathering the usual mechanical entities -- mass, energy, force, moment, stresses, linear and angular momentum -- in a single tensor. Starting with the basic subjects, and continuing through to the most advanced topics, the authors' presentation is progressive, inductive and bottom-up. They begin with the concept of an affine tensor, a natural extension of the classical tensors. The simplest types of affine tensors are the points of an affine space and the affine functions on this space, but there are more complex ones which are relevant for mechanics -- torsors and momenta. The essential point is to derive the balance equations of a continuum from a unique principle which claims that these tensors are affine-divergence free.
Galileo Engineer
by Matteo VallerianiThis work systematically investigates and reconstructs the practical knowledge Galileo shared during his lifetime. Galileo shared many aspects of practical knowledge. These included the methods and experience of foremen and engineers active within various frameworks. Galileo did not always react to such scientific impulses in the same way. On the one hand, he not only shared practical knowledge, but also acted as an engineer, especially within the framework of the art of war at the end of the sixteenth century, and more so during the time he spent in Padua. On the other hand, his scientific achievements were largely based on and influenced by aspects of practical knowledge coming from particular disciplines and activities, without him ever becoming an expert in these disciplines. Two case studies, the first concerned with Galileo's theory of the strength of materials and the second with his achievement of an atomistic heat doctrine, enable a focus on the early modern model of generation of new scientific knowledge based on the conflicting interaction between aspects of practical knowledge and Aristotelian theoretical assumptions.
Galois Cohomology and Class Field Theory (Universitext)
by David HarariThis graduate textbook offers an introduction to modern methods in number theory. It gives a complete account of the main results of class field theory as well as the Poitou-Tate duality theorems, considered crowning achievements of modern number theory.Assuming a first graduate course in algebra and number theory, the book begins with an introduction to group and Galois cohomology. Local fields and local class field theory, including Lubin-Tate formal group laws, are covered next, followed by global class field theory and the description of abelian extensions of global fields. The final part of the book gives an accessible yet complete exposition of the Poitou-Tate duality theorems. Two appendices cover the necessary background in homological algebra and the analytic theory of Dirichlet L-series, including the Čebotarev density theorem. Based on several advanced courses given by the author, this textbook has been written for graduate students. Including complete proofs and numerous exercises, the book will also appeal to more experienced mathematicians, either as a text to learn the subject or as a reference.
Galois Covers, Grothendieck-Teichmüller Theory and Dessins d'Enfants: Interactions between Geometry, Topology, Number Theory and Algebra, Leicester, UK, June 2018 (Springer Proceedings in Mathematics & Statistics #330)
by Frank Neumann Sibylle SchrollThis book presents original peer-reviewed contributions from the London Mathematical Society (LMS) Midlands Regional Meeting and Workshop on 'Galois Covers, Grothendieck-Teichmüller Theory and Dessinsd'Enfants', which took place at the University of Leicester, UK, from 4 to 7 June, 2018. Within the theme of the workshop, the collected articles cover a broad range of topics and explore exciting new links between algebraic geometry, representation theory, group theory, number theory and algebraic topology. The book combines research and overview articles by prominent international researchers and provides a valuable resource for researchers and students alike.
Galois Groups and Fundamental Groups
by Tamás SzamuelyEver since the concepts of Galois groups in algebra and fundamental groups in topology emerged during the nineteenth century, mathematicians have known of the strong analogies between the two concepts. This book presents the connection starting at an elementary level, showing how the judicious use of algebraic geometry gives access to the powerful interplay between algebra and topology that underpins much modern research in geometry and number theory. Assuming as little technical background as possible, the book starts with basic algebraic and topological concepts, but already presented from the modern viewpoint advocated by Grothendieck. This enables a systematic yet accessible development of the theories of fundamental groups of algebraic curves, fundamental groups of schemes, and Tannakian fundamental groups. The connection between fundamental groups and linear differential equations is also developed at increasing levels of generality. Key applications and recent results, for example on the inverse Galois problem, are given throughout.
Galois Representations and (φ, Γ)-Modules
by Peter SchneiderUnderstanding Galois representations is one of the central goals of number theory. Around 1990, Fontaine devised a strategy to compare such p-adic Galois representations to seemingly much simpler objects of (semi)linear algebra, the so-called etale (phi, gamma)-modules. This book is the first to provide a detailed and self-contained introduction to this theory. The close connection between the absolute Galois groups of local number fields and local function fields in positive characteristic is established using the recent theory of perfectoid fields and the tilting correspondence. The author works in the general framework of Lubin–Tate extensions of local number fields, and provides an introduction to Lubin–Tate formal groups and to the formalism of ramified Witt vectors. This book will allow graduate students to acquire the necessary basis for solving a research problem in this area, while also offering researchers many of the basic results in one convenient location.
Galois Theory
by Ian StewartGalois theory is a fascinating mixture of classical and modern mathematics, and in fact provided much of the seed from which abstract algebra has grown. It is a showpiece of mathematical unification and of "technology transfer" to a range of modern applications.Galois Theory, Second Edition is a revision of a well-established and popular te
Galois Theory
by Ian StewartSince 1973, Galois theory has been educating undergraduate students on Galois groups and classical Galois theory. In Galois Theory, Fifth Edition, mathematician and popular science author Ian Stewart updates this well-established textbook for today’s algebra students. New to the Fifth Edition Reorganised and revised Chapters 7 and 13 New exercises and examples Expanded, updated references Further historical material on figures besides Galois: Omar Khayyam, Vandermonde, Ruffini, and Abel A new final chapter discussing other directions in which Galois theory has developed: the inverse Galois problem, differential Galois theory, and a (very) brief introduction to p-adic Galois representations This bestseller continues to deliver a rigorous, yet engaging, treatment of the subject while keeping pace with current educational requirements. More than 200 exercises and a wealth of historical notes augment the proofs, formulas, and theorems.
Galois Theory (Dover Books on Mathematics)
by Arthur N. Milgram Emil ArtinIn the nineteenth century, French mathematician Evariste Galois developed the Galois theory of groups-one of the most penetrating concepts in modem mathematics. The elements of the theory are clearly presented in this second, revised edition of a volume of lectures delivered by noted mathematician Emil Artin. The book has been edited by Dr. Arthur N. Milgram, who has also supplemented the work with a Section on Applications.The first section deals with linear algebra, including fields, vector spaces, homogeneous linear equations, determinants, and other topics. A second section considers extension fields, polynomials, algebraic elements, splitting fields, group characters, normal extensions, roots of unity, Noether equations, Jummer's fields, and more.Dr. Milgram's section on applications discusses solvable groups, permutation groups, solution of equations by radicals, and other concepts.
Galois Theory Through Exercises (Springer Undergraduate Mathematics Series)
by Juliusz BrzezińskiProvides a hands-on approach to learning Galois theory, focusing on problem-solving exercises.<P><P> Features almost 500 exercises with hints, answers or solutions.<P> Includes Maple tutorials and exercises.<P> This textbook offers a unique introduction to classical Galois theory through many concrete examples and exercises of varying difficulty (including computer-assisted exercises).<P> In addition to covering standard material, the book explores topics related to classical problems such as Galois’ theorem on solvable groups of polynomial equations of prime degrees, Nagell's proof of non-solvability by radicals of quintic equations, Tschirnhausen's transformations, lunes of Hippocrates, and Galois' resolvents. Topics related to open conjectures are also discussed, including exercises related to the inverse Galois problem and cyclotomic fields. The author presents proofs of theorems, historical comments and useful references alongside the exercises, providing readers with a well-rounded introduction to the subject and a gateway to further reading.<P> A valuable reference and a rich source of exercises with sample solutions, this book will be useful to both students and lecturers. Its original concept makes it particularly suitable for self-study.
Galois Theory and Advanced Linear Algebra
by Rajnikant SinhaThis book discusses major topics in Galois theory and advanced linear algebra, including canonical forms. Divided into four chapters and presenting numerous new theorems, it serves as an easy-to-understand textbook for undergraduate students of advanced linear algebra, and helps students understand other courses, such as Riemannian geometry. The book also discusses key topics including Cayley–Hamilton theorem, Galois groups, Sylvester’s law of inertia, Eisenstein criterion, and solvability by radicals. Readers are assumed to have a grasp of elementary properties of groups, rings, fields, and vector spaces, and familiarity with the elementary properties of positive integers, inner product space of finite dimension and linear transformations is beneficial.
Galois Theory, Coverings, and Riemann Surfaces
by Askold KhovanskiiThe first part of this book provides an elementary and self-contained exposition of classical Galois theory and its applications to questions of solvability of algebraic equations in explicit form. The second part describes a surprising analogy between the fundamental theorem of Galois theory and the classification of coverings over a topological space. The third part contains a geometric description of finite algebraic extensions of the field of meromorphic functions on a Riemann surface and provides an introduction to the topological Galois theory developed by the author. All results are presented in the same elementary and self-contained manner as classical Galois theory, making this book both useful and interesting to readers with a variety of backgrounds in mathematics, from advanced undergraduate students to researchers.
Game Analytics
by Alessandro Canossa Magy Seif El-Nasr Anders DrachenDeveloping a successful game in today's market is a challenging endeavor. Thousands of titles are published yearly, all competing for players' time and attention. Game analytics has emerged in the past few years as one of the main resources for ensuring game quality, maximizing success, understanding player behavior and enhancing the quality of the player experience. It has led to a paradigm shift in the development and design strategies of digital games, bringing data-driven intelligence practices into the fray for informing decision making at operational, tactical and strategic levels. Game Analytics - Maximizing the Value of Player Data is the first book on the topic of game analytics; the process of discovering and communicating patterns in data towards evaluating and driving action, improving performance and solving problems in game development and game research. Written by over 50 international experts from industry and research, it covers a comprehensive range of topics across more than 30 chapters, providing an in-depth discussion of game analytics and its practical applications. Topics covered include monetization strategies, design of telemetry systems, analytics for iterative production, game data mining and big data in game development, spatial analytics, visualization and reporting of analysis, player behavior analysis, quantitative user testing and game user research. This state-of-the-art volume is an essential source of reference for game developers and researchers. Key takeaways include: Thorough introduction to game analytics; covering analytics applied to data on players, processes and performance throughout the game lifecycle.In-depth coverage and advice on setting up analytics systems and developing good practices for integrating analytics in game-development and -management.Contributions by leading researchers and experienced professionals from the industry, including Ubisoft, Sony, EA, Bioware, Square Enix, THQ, Volition, and PlayableGames. Interviews with experienced industry professionals on how they use analytics to create hit games.
Game Changers: Stories of the Revolutionary Minds behind Game Theory
by Rudolf TaschnerIn this lively history of game theory, a gifted math educator and science writer explains for lay readers the uses and value of this innovative yet easy-to-understand approach to mathematical modeling. Essentially, game theory interprets life as a game with mathematical rules. By following the rules, decisions can be calculated that result in the greatest benefit for all participants.The author takes the reader from the 17th century through the Cold War to today's age of turbo capitalism. Along the way he introduces such leading contributors as Blaise Pascal in the 17th century, who invented the theory of probability; Ludwig Wittgenstein in the 20th century, who conceived of the world as a play of words; John Nash (the subject of A Beautiful Mind) in the 1950s, who laid the foundation of modern game theory; and today's practitioners who apply the theory to global finance and military strategy.As the author shows, game theory is more than a type of cost-benefit analysis; ultimately, it is a quest for meaning.
Game Design Theory: A New Philosophy for Understanding Games
by Keith BurgunDespite the proliferation of video games in the twenty-first century, the theory of game design is largely underdeveloped, leaving designers on their own to understand what games really are. Helping you produce better games, Game Design Theory: A New Philosophy for Understanding Games presents a bold new path for analyzing and designing games.
Game Math (Math 24/7)
by James FischerAlmost any game you play needs math. From poker to computer games, from video games to board games, math has a role to play. Game Math will help you understand your favorite games better. You may even find you're a better player when you understand the math behind the rules!
Game Theoretic Analysis of Congestion, Safety and Security
by Kjell Hausken Jun ZhuangMaximizing reader insights into the interactions between game theory, excessive crowding and safety and security elements, this book establishes a new research angle by illustrating linkages between different research approaches and through laying the foundations for subsequent analysis. Congestion (excessive crowding) is defined in this work as all kinds of flows; e. g. , road/sea/air traffic, people, data, information, water, electricity, and organisms. Analysing systems where congestion occurs - which may be in parallel, series, interlinked, or interdependent, with flows one way or both ways - this book puts forward new congestion models, breaking new ground by introducing game theory and safety/security into proceedings. Addressing the multiple actors who may hold different concerns regarding system reliability; e. g. one or several terrorists, a government, various local or regional government agencies, or others with stakes for or against system reliability, this book describes how governments and authorities may have the tools to handle congestion, but that these tools need to be improved whilst additionally ensuring safety and security against various threats. This game-theoretic analysis sets this book apart from the current congestion literature and ensures that the book will be of use to postgraduates, researchers, 3rd/4th-year undergraduates, policy makers, and practitioners.
Game Theoretic Approaches for Spectrum Redistribution
by Fan WuThis brief examines issues of spectrum allocation for the limited resources of radio spectrum. It uses a game-theoretic perspective, in which the nodes in the wireless network are rational and always pursue their own objectives. It provides a systematic study of the approaches that can guarantee the system's convergence at an equilibrium state, in which the system performance is optimal or sub-optimal. The author provides a short tutorial on game theory, explains game-theoretic channel allocation in clique and in multi-hop wireless networks and explores challenges in designing game-theoretic mechanisms for dynamic channel redistribution. Since designing a completely secure mechanism is extremely expensive or impossible in most of distributed autonomous systems, it is more beneficial to study misbehavior of the nodes and develop light-weighted game-theoretic channel allocation mechanisms. With a mix of theoretical and hands-on information, the brief traces the concepts of game theory, the current state of spectrum allocation in wireless networks and future competition for resources. Thorough yet accessible, the content is ideal for researchers and practitioners working on spectrum redistribution. It is also a helpful resource for researchers and advanced-level students interested in game theory and wireless communications.
Game Theory
by E. N. BarronAn exciting new edition of the popular introduction to game theory and its applicationsThe thoroughly expanded Second Edition presents a unique, hands-on approach to game theory. While most books on the subject are too abstract or too basic for mathematicians, Game Theory: An Introduction, Second Edition offers a blend of theory and applications, allowing readers to use theory and software to create and analyze real-world decision-making models.With a rigorous, yet accessible, treatment of mathematics, the book focuses on results that can be used to determine optimal game strategies. Game Theory: An Introduction, Second Edition demonstrates how to use modern software, such as MapleTM, Mathematica®, and Gambit, to create, analyze, and implement effective decision-making models. Coverage includes the main aspects of game theory including the fundamentals of two-person zero-sum games, cooperative games, and population games as well as a large number of examples from various fields, such as economics, transportation, warfare, asset distribution, political science, and biology. The Second Edition features:* A new chapter on extensive games, which greatly expands the implementation of available models* New sections on correlated equilibria and exact formulas for three-player cooperative games* Many updated topics including threats in bargaining games and evolutionary stable strategies* Solutions and methods used to solve all odd-numbered problems* A companion website containing the related Maple and Mathematica data sets and codeA trusted and proven guide for students of mathematics and economics, Game Theory: An Introduction, Second Edition is also an excellent resource for researchers and practitioners in economics, finance, engineering, operations research, statistics, and computer science.
Game Theory
by Michael Maschler Eilon Solan Shmuel ZamirCovering both noncooperative and cooperative games, this comprehensive introduction to game theory also includes some advanced chapters on auctions, games with incomplete information, games with vector payoffs, stable matchings and the bargaining set. Mathematically oriented, the book presents every theorem alongside a proof. The material is presented clearly and every concept is illustrated with concrete examples from a broad range of disciplines. With numerous exercises the book is a thorough and extensive guide to game theory from undergraduate through graduate courses in economics, mathematics, computer science, engineering and life sciences to being an authoritative reference for researchers.
Game Theory
by Hans PetersThis textbook presents the basics of game theory both on an undergraduate level and on a more advanced mathematical level. It is the second, revised version of the successful 2008 edition. The book covers most topics of interest in game theory, including cooperative game theory. Part I presents introductions to all these topics on a basic yet formally precise level. It includes chapters on repeated games, social choice theory, and selected topics such as bargaining theory, exchange economies, and matching. Part II goes deeper into noncooperative theory and treats the theory of zerosum games, refinements of Nash equilibrium in strategic as well as extensive form games, and evolutionary games. Part III covers basic concepts in the theory of transferable utility games, such as core and balancedness, Shapley value and variations, and nucleolus. Some mathematical tools on duality and convexity are collected in Part IV. Every chapter in the book contains a problem section. Hints, answers and solutions are included.
Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Interaction - Second Edition
by Herbert GintisSince its original publication in 2000, Game Theory Evolving has been considered the best textbook on evolutionary game theory. This completely revised and updated second edition of Game Theory Evolving contains new material and shows students how to apply game theory to model human behavior in ways that reflect the special nature of sociality and individuality. The textbook continues its in-depth look at cooperation in teams, agent-based simulations, experimental economics, the evolution and diffusion of preferences, and the connection between biology and economics. Recognizing that students learn by doing, the textbook introduces principles through practice. Herbert Gintis exposes students to the techniques and applications of game theory through a wealth of sophisticated and surprisingly fun-to-solve problems involving human and animal behavior. The second edition includes solutions to the problems presented and information related to agent-based modeling. In addition, the textbook incorporates instruction in using mathematical software to solve complex problems. Game Theory Evolving is perfect for graduate and upper-level undergraduate economics students, and is a terrific introduction for ambitious do-it-yourselfers throughout the behavioral sciences. Revised and updated edition relevant for courses across disciplines Perfect for graduate and upper-level undergraduate economics courses Solutions to problems presented throughout Incorporates instruction in using computational software for complex problem solving Includes in-depth discussions of agent-based modeling
Game Theory and Applications: A Guide for Students and Researchers (Classroom Companion: Economics)
by Florian Bartholomae Marcus WiensThis textbook provides an overview of the fundamentals of game theory and its applications in various fields. It introduces game theory as an established toolkit for the mathematical analysis and evaluation of strategic decisions. Through applied exercises, it introduces the basic concepts of game theory and offers students from various disciplines the opportunity to practice the concepts through in-depth training. The textbook addresses advanced students of economics, business administration, and related disciplines, university graduates with basic mathematical training as well as interested readers from all fields. For this, it provides student-friendly explanations, a variety of exercises and problems, and useful references to further reading. The book is divided into a beginner-friendly theory section, in which the most important aspects are presented in a compact and clear manner, and an application-oriented problem section, in which the readers can directly check what they have learned and find many application examples. The latter can also be used as a source of inspiration for instructors.
Game Theory and Behavior
by Jeffrey Carpenter Andrea RobbettAn introduction to game theory that offers not only theoretical tools but also the intuition and behavioral insights to apply these tools to real-world situations.This introductory text on game theory provides students with both the theoretical tools to analyze situations through the logic of game theory and the intuition and behavioral insights to apply these tools to real-world situations. It is unique among game theory texts in offering a clear, formal introduction to standard game theory while incorporating evidence from experimental data and introducing recent behavioral models. Students will not only learn about incentives, how to represent situations as games, and what agents &“should&” do in these situations, but they will also be presented with evidence that either confirms the theoretical assumptions or suggests a way in which the theory might be updated.Features:Each chapter begins with a motivating example that can be run as an experiment and ends with a discussion of the behavior in the example.Parts I–IV cover the fundamental &“nuts and bolts&” of any introductory game theory course, including the theory of games, simple games with simultaneous decision making by players, sequential move games, and incomplete information in simultaneous and sequential move games.Parts V–VII apply the tools developed in previous sections to bargaining, cooperative game theory, market design, social dilemmas, and social choice and voting.Part VIII offers a more in-depth discussion of behavioral game theory models including evolutionary and psychological game theory.Supplemental material on the book&’s website include solutions to end-of-chapter exercises, a manual for running each chapter&’s experimental games using pencil and paper, and the oTree codes for running the games online.
Game Theory and Climate Change
by Parkash ChanderDespite the growing consensus on the need for action to counteract climate change, complex economic and political forces have so far prevented international actors from making much headway toward resolving the problem. Most approaches to climate change are based in economics and environmental science; in this book, Parkash Chander argues that we can make further progress on the climate change impasse by considering a third approach—game theory.Chander shows that a game-theoretic approach, which offers insight into the nature of interactions between sovereign countries behaving strategically and the kinds of outcomes such interactions produce, can illuminate how best to achieve international agreements in support of climate-change mitigation strategies. Game Theory and Climate Change develops a conceptual framework with which to analyze climate change as a strategic or dynamic game, bringing together cooperative and noncooperative game theory and providing practical analyses of international negotiations. Chander offers economic and game-theoretic interpretations of both the Kyoto Protocol and the Paris Agreement and argues that the Paris Agreement may succeed where the Kyoto Protocol failed. Finally, Chander discusses the policy recommendations his framework generates, including a global agreement to support development of cleaner technologies on a global scale.