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Fy Nodiadau Adolygu: CBAC UG Mathemateg (My Revision Notes: WJEC AS Mathematics Welsh-language edition)
by Sophie Goldie Rose JewellTarget success in the new specification WJEC GCE AS Mathematics with this proven formula for effective, structured revision; key content coverage is combined with full worked examples, diagnostic questions and exam-style questions to create a revision guide that students can rely on to review, strengthen and test their knowledge. Help develop the key skills needed for success with skills-focused questions around problem-solving, proof, modelling and the use of ICT (spreadsheets, graphing software and graphing calculators). Strategically target revision with diagnostic questions to establish which areas need focus. Get assessment-ready with exam-style questions and advice on common examination pitfalls. Develop students' understanding with full worked examples and accompanying solutions, offering detailed, instructive explanations. Consolidate revision with summaries for each topic that focus on what to concentrate on in the buildup to exams, with special focus on common pitfalls such as how to show correct workings. Enable independent learning with access to answers in the back of the book.
Fy Nodiadau Adolygu: CBAC UG Mathemateg (My Revision Notes)
by Sophie Goldie Rose JewellTarget success in the new specification WJEC GCE AS Mathematics with this proven formula for effective, structured revision; key content coverage is combined with full worked examples, diagnostic questions and exam-style questions to create a revision guide that students can rely on to review, strengthen and test their knowledge. Help develop the key skills needed for success with skills-focused questions around problem-solving, proof, modelling and the use of ICT (spreadsheets, graphing software and graphing calculators). Strategically target revision with diagnostic questions to establish which areas need focus. Get assessment-ready with exam-style questions and advice on common examination pitfalls. Develop students' understanding with full worked examples and accompanying solutions, offering detailed, instructive explanations. Consolidate revision with summaries for each topic that focus on what to concentrate on in the buildup to exams, with special focus on common pitfalls such as how to show correct workings. Enable independent learning with access to answers in the back of the book.
G Families of Probability Distributions: Theory and Practices
by Mir Masoom Ali Irfan Ali Haitham M. Yousof Mohamed IbrahimStatistical distributions are essential tools to model the characteristics of datasets, such as right or left skewness, bi-modality or multi-modality observed in different applied sciences, such as engineering, medicine, and finance. The well-known distributions like normal, Weibull, gamma and Lindley are extensively used because of their simple forms and identifiability properties. In the last decade, researchers have focused on the more complex and flexible distributions, referred to as Generalized or simply G families of probability distributions, to increase the modelling capability of these distributions by adding one or more shape parameters.The main aim of this edited book is to present new contributions by researchers in the field of G families of probability distributions. The book will help researchers to: Develop new univariate continuous and discrete G families of probability distributions. Develop new bivariate continuous and discrete G families of probability distributions. Derive beneficial mathematical properties such as ordinary and incomplete moments, moment generating functions, residual life and reversed residual life functions, order statistics, quantile spread ordering and entropies, and some bivariate and multivariate extensions of the new and existing models using a simple-type copula.
G Is for One Gzonk!: An Alpha-number-bet Book
by Tony Diterlizzi Tiny DiterlooneyAges 4-7 Welcome to my silly dilly take on ABC. It's lots of fun and really odd, as you will quickly see. For they're no "leaping lizards" here. No "bears that bounce a ball." In fact, these zany critters have never been seen at all. So turn the page and cast a gaze on this menagerie, but don't forget the beasts within were all made up by me! - Tiny DiTerlooney
G.W. Leibniz, Interrelations between Mathematics and Philosophy
by Norma B. Goethe Philip Beeley David RabouinUp to now there have been scarcely any publications on Leibniz dedicated to investigating the interrelations between philosophy and mathematics in his thought. In part this is due to the previously restricted textual basis of editions such as those produced by Gerhardt. Through recent volumes of the scientific letters and mathematical papers series of the Academy Edition scholars have obtained a much richer textual basis on which to conduct their studies - material which allows readers to see interconnections between his philosophical and mathematical ideas which have not previously been manifested. The present book draws extensively from this recently published material. The contributors are among the best in their fields. Their commissioned papers cover thematically salient aspects of the various ways in which philosophy and mathematics informed each other in Leibniz's thought.
Gaining Skill With Arithmetic: Grade 5 Test Booklet
by Sandra BaumanTest booklet for Grade 5 math. Included in the Mathematics for Christian Living Series.
Gaining Skill with Arithmetic Grade 5 (Mathematics for Christian Living Series)
by Sandra BaumanThis textbook has 170 lessons, counting tests. Lesson concepts are explained in the student text. This book reviews and extends concepts taught in the previous grades. Reading problems are exercised regularly. Covers place value, decimals, factoring and prime numbers, metric system, fractions, ratio and proportion, geometry, percents, and graphs.
Gaṇitānanda: Selected Works of Radha Charan Gupta on History of Mathematics
by K. RamasubramanianThis book includes 58 selected articles that highlight the major contributions of Professor Radha Charan Gupta—a doyen of history of mathematics—written on a variety of important topics pertaining to mathematics and astronomy in India. It is divided into ten parts. Part I presents three articles offering an overview of Professor Gupta’s oeuvre. The four articles in Part II convey the importance of studies in the history of mathematics. Parts III–VII constituting 33 articles, feature a number of articles on a variety of topics, such as geometry, trigonometry, algebra, combinatorics and spherical trigonometry, which not only reveal the breadth and depth of Professor Gupta’s work, but also highlight his deep commitment to the promotion of studies in the history of mathematics. The ten articles of part VIII, present interesting bibliographical sketches of a few veteran historians of mathematics and astronomy in India. Part IX examines the dissemination of mathematical knowledge across different civilisations. The last part presents an up-to-date bibliography of Gupta’s work. It also includes a tribute to him in Sanskrit composed in eight verses.
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 (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
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 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.
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.
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.
A Game- and Decision-Theoretic Approach to Resilient Interdependent Network Analysis and Design (SpringerBriefs in Electrical and Computer Engineering)
by Juntao Chen Quanyan ZhuThis brief introduces game- and decision-theoretical techniques for the analysis and design of resilient interdependent networks. It unites game and decision theory with network science to lay a system-theoretical foundation for understanding the resiliency of interdependent and heterogeneous network systems. The authors pay particular attention to critical infrastructure systems, such as electric power, water, transportation, and communications. They discuss how infrastructure networks are becoming increasingly interconnected as the integration of Internet of Things devices, and how a single-point failure in one network can propagate to other infrastructures, creating an enormous social and economic impact. The specific topics in the book include: · static and dynamic meta-network resilience game analysis and design; · optimal control of interdependent epidemics spreading over complex networks; and · applications to secure and resilient design of critical infrastructures. These topics are supported by up-to-date summaries of the authors’ recent research findings. The authors then discuss the future challenges and directions in the analysis and design of interdependent networks and explain the role of multi-disciplinary research has in computer science, engineering, public policy, and social sciences fields of study. The brief introduces new application areas in mathematics, economics, and system and control theory, and will be of interest to researchers and practitioners looking for new approaches to assess and mitigate risks in their systems and enhance their network resilience. A Game- and Decision-Theoretic Approach to Resilient Interdependent Network Analysis and Design also has self-contained chapters, which allows for multiple levels of reading by anyone with an interest in game and decision theory and network science.
Game-Changer: Game Theory and the Art of Transforming Strategic Situations
by David McadamsA radically new, and easily learned, way to outstrategize your rivals. "The wise win before they fight, while the ignorant fight to win." So wrote Zhuge Liang, the great Chinese military strategist. He was referring to battlefield tactics, but the same can be said about any strategic situation. Even seemingly certain defeat can be turned into victory--whether in battle, business, or life--by those with the strategic vision to recognize how to "change the game" to their own advantage. The aim of David McAdams's Game-Changer is nothing less than to empower you with this wisdom--not just to win in every strategic situation (or "game") you face but to change those games and the ecosystems in which they reside to transform your life and our lives together for the better. Game-Changer develops six basic ways to change games--commitment, regulation, cartelization, retaliation, trust, and relationships--enlivened by countless colorful characters and unforgettable examples from the worlds of business, medicine, finance, military history, crime, sports, and more. The book then digs into several real-world strategic challenges, such as how to keep prices low on the Internet, how to restore the public's lost trust in for-charity telemarketers, and even how to save mankind from looming and seemingly unstoppable drug-resistant disease. In each case, McAdams uses the game-theory approach developed in the book to identify the strategic crux of the problem and then leverages that "game-awareness" to brainstorm ways to change the game to solve or at least mitigate the underlying problem. So get ready for a fascinating journey. You'll emerge a deeper strategic thinker, poised to change and win all the games you play. In doing so, you can also make the world a better place. "Just one Game-Changer [is] enough to seed and transform an entire organization into a more productive, happier, and altogether better place," McAdams writes. Just imagine what we can do together.
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.