A Course in Game Theory presents the main ideas of game theory at a level suitable for graduate students and advanced undergraduates, emphasizing the... theory's foundations and interpretations of its basic concepts. The authors provide precise definitions and full proofs of results, sacrificing generalities and limiting the scope of the material in order to do so. The text is organized in four parts: strategic games, extensive games with perfect information, extensive games with imperfect information, and coalitional games. It includes over 100 exercises.

The classification of the finite simple groups is one of the major intellectual achievements of this century, but it remains almost completely unknown... outside of the mathematics community. This introduction to group theory is also an attempt to make this important work better known. Emphasizing classification themes throughout, the book gives a clear and comprehensive introduction to groups and covers all topics likely to be encountered in an undergraduate course. Introductory chapters explain the concepts of group, subgroup and normal subgroup, and quotient group. The homomorphism and isomorphism theorems are explained, along with an introduction to G-sets. Subsequent chapters deal with finite abelian groups, the Jordan-Holder theorem, soluble groups, p-groups, and group extensions. The numerous worked examples and exercises in this excellent and self-contained introduction will also encourage undergraduates (and first year graduates) to further study.

This program introduces learners to various cultural aspects in Vietnamese life through the use of the Vietnamese language. Further development of the... basic linguistic skills is carried out through conversations, grammar, reading, vocabulary, practice exercises, and writing practice, all at the level beyond the first year of language learning. Each chapter presents a cultural topic, focusing on a particular aspect and offers many opportunities for the students to discuss and elaborate each theme with insights and critical thinking. An appropriate proverb or folk poem accompanies each chapter topic to bring about a sense of reality for the situations under discussion.

This important course provides a comprehensive basic introduction to teaching languages, for use in pre-service or early experience settings. It can be... used by groups of teachers working with a trainer, or as a self-study resource. The Trainee's Book provides all the tasks given in the main book but without background information, bibliographies, notes or solutions. It is suitable for those studying on a trainer-led course, where feedback is readily available.

This important course provides a comprehensive basic introduction to teaching languages, for use in pre-service or early experience settings. It can be... used by groups of teachers working with a trainer, or as a self-study resource. The Trainee's Book provides all the tasks given in the main book but without background information, bibliographies, notes or solutions. It is suitable for those studying on a trainer-led course, where feedback is readily available.

A Course in Large Sample Theory is presented in four parts. The first treats basic probabilistic notions, the second features the basic statistical... tools for expanding the theory, the third contains special topics as applications of the general theory, and the fourth covers more standard statistical topics. Nearly all topics are covered in their multivariate setting.The book is intended as a first year graduate course in large sample theory for statisticians. It has been used by graduate students in statistics, biostatistics, mathematics, and related fields. Throughout the book there are many examples and exercises with solutions. It is an ideal text for self study.

Suitable for advanced undergraduates and graduate students, this text introduces basic concepts of linear algebra. Each chapter contains an... introduction, definitions, and propositions, in addition to multiple examples, lemmas, theorems, corollaries, and proofs. Each chapter features numerous supplemental exercises, and solutions to selected problems appear at the end. 1988 edition.

This is the second edition of the best-selling introduction to linear algebra. Presupposing no knowledge beyond calculus, it provides a thorough... treatment of all the basic concepts, such as vector space, linear transformation and inner product. The concept of a quotient space is introduced and related to solutions of linear system of equations, and a simplified treatment of Jordan normal form is given. Numerous applications of linear algebra are described, including systems of linear recurrence relations, systems of linear differential equations, Markov processes, and the Method of Least Squares. An entirely new chapter on linear programing introduces the reader to the simplex algorithm with emphasis on understanding the theory behind it. The book is addressed to students who wish to learn linear algebra, as well as to professionals who need to use the methods of the subject in their own fields.

This is the only book that teaches all aspects of modern mathematical modeling and that is specifically designed to introduce undergraduate students to... problem solving in the context of biology. Included is an integrated package of theoretical modeling and analysis tools, computational modeling techniques, and parameter estimation and model validation methods, with a focus on integrating analytical and computational tools in the modeling of biological processes. Divided into three parts, it covers basic analytical modeling techniques; introduces computational tools used in the modeling of biological problems; and includes various problems from epidemiology, ecology, and physiology. All chapters include realistic biological examples, including many exercises related to biological questions. In addition, 25 open-ended research projects are provided, suitable for students. An accompanying Web site contains solutions and a tutorial for the implementation of the computational modeling techniques. Calculations can be done in modern computing languages such as Maple, Mathematica, and MATLAB®.

David M. Kreps has developed a text in microeconomics that is both challenging and "user-friendly." The work is designed for the first-year graduate... microeconomic theory course and is accessible to advanced undergraduates as well. Placing unusual emphasis on modern noncooperative game theory, it provides the student and instructor with a unified treatment of modern microeconomic theory--one that stresses the behavior of the individual actor (consumer or firm) in various institutional settings. The author has taken special pains to explore the fundamental assumptions of the theories and techniques studied, pointing out both strengths and weaknesses.The book begins with an exposition of the standard models of choice and the market, with extra attention paid to choice under uncertainty and dynamic choice. General and partial equilibrium approaches are blended, so that the student sees these approaches as points along a continuum. The work then turns to more modern developments. Readers are introduced to noncooperative game theory and shown how to model games and determine solution concepts. Models with incomplete information, the folk theorem and reputation, and bilateral bargaining are covered in depth. Information economics is explored next. A closing discussion concerns firms as organizations and gives readers a taste of transaction-cost economics.

This concise introduction to model theory begins with standard notions and takes the reader through to more advanced topics such as stability,... simplicity and Hrushovski constructions. The authors introduce the classic results, as well as more recent developments in this vibrant area of mathematical logic. Concrete mathematical examples are included throughout to make the concepts easier to follow. The book also contains over 200 exercises, many with solutions, making the book a useful resource for graduate students as well as researchers.

Designed for one-semester courses at the senior undergraduate level, this book is written for mathematics students and teachers, as well as others... needing to learn mathematical analysis for engineering, physics, biology or finance. Nominal divisions between pure and applied mathematics have been merged to provide easier access. Applications are included from differential and integral equations, systems of linear algebraic equations, approximation theory, numerical analysis and quantum mechanics.

Designed for a junior-senior level course for mathematics majors, including those who plan to teach in secondary school. The first chapter presents... several finite geometries in an axiomatic framework, while Chapter 2 continues the synthetic approach in introducing both Euclids and ideas of non-Euclidean geometry. There follows a new introduction to symmetry and hands-on explorations of isometries that precedes an extensive analytic treatment of similarities and affinities. Chapter 4 presents plane projective geometry both synthetically and analytically, and the new Chapter 5 uses a descriptive and exploratory approach to introduce chaos theory and fractal geometry, stressing the self-similarity of fractals and their generation by transformations from Chapter 3. Throughout, each chapter includes a list of suggested resources for applications or related topics in areas such as art and history, plus this second edition points to Web locations of author-developed guides for dynamic software explorations of the Poincaré model, isometries, projectivities, conics and fractals. Parallel versions are available for "Cabri Geometry" and "Geometers Sketchpad".

This is a substantially revised and updated introduction to arithmetic topics, both ancient and modern, that have been at the centre of interest in... applications of number theory, particularly in cryptography. As such, no background in algebra or number theory is assumed, and the book begins with a discussion of the basic number theory that is needed. The approach taken is algorithmic, emphasising estimates of the efficiency of the techniques that arise from the theory, and one special feature is the inclusion of recent applications of the theory of elliptic curves. Extensive exercises and careful answers are an integral part all of the chapters.

The first contemporary textbook on ordinary differential equations (ODEs) to include instructions on MATLAB®, Mathematica®, and Maple™, A Course in... Ordinary Differential Equations focuses on applications and methods of analytical and numerical solutions, emphasizing approaches used in the typical engineering, physics, or mathematics student's field of study.Stressing applications wherever possible, the authors have written this text with the applied math, engineer, or science major in mind. It includes a number of modern topics that are not commonly found in a traditional sophomore-level text. For example, Chapter 2 covers direction fields, phase line techniques, and the Runge-Kutta method; another chapter discusses linear algebraic topics, such as transformations and eigenvalues. Chapter 6 considers linear and nonlinear systems of equations from a dynamical systems viewpoint and uses the linear algebra insights from the previous chapter; it also includes modern applications like epidemiological models. With sufficient problems at the end of each chapter, even the pure math major will be fully challenged. Although traditional in its coverage of basic topics of ODEs, A Course in Ordinary Differential Equations is one of the first texts to provide relevant computer code and instruction in MATLAB, Mathematica, and Maple that will prepare students for further study in their fields.