Written by two of the most prominent figures in the field of graph theory, this comprehensive text provides a remarkably student-friendly approach.... Geared toward undergraduates taking a first course in graph theory, its sound yet accessible treatment emphasizes the history of graph theory and offers unique examples and lucid proofs. 2004 edition.

This innovative, intermediate-level statistics text fills an important gap by presenting the theory of linear statistical models at a level appropriate... for senior undergraduate or first-year graduate students. With an innovative approach, the author's introduces students to the mathematical and statistical concepts and tools that form a foundation for studying the theory and applications of both univariate and multivariate linear modelsA First Course in Linear Model Theory systematically presents the basic theory behind linear statistical models with motivation from an algebraic as well as a geometric perspective. Through the concepts and tools of matrix and linear algebra and distribution theory, it provides a framework for understanding classical and contemporary linear model theory. It does not merely introduce formulas, but develops in students the art of statistical thinking and inspires learning at an intuitive level by emphasizing conceptual understanding.The authors' fresh approach, methodical presentation, wealth of examples, and introduction to topics beyond the classical theory set this book apart from other texts on linear models. It forms a refreshing and invaluable first step in students' study of advanced linear models, generalized linear models, nonlinear models, and dynamic models.

This innovative, intermediate-level statistics text fills an important gap by presenting the theory of linear statistical models at a level appropriate... for senior undergraduate or first-year graduate students. With an innovative approach, the author's introduces students to the mathematical and statistical concepts and tools that form a foundation for studying the theory and applications of both univariate and multivariate linear modelsA First Course in Linear Model Theory systematically presents the basic theory behind linear statistical models with motivation from an algebraic as well as a geometric perspective. Through the concepts and tools of matrix and linear algebra and distribution theory, it provides a framework for understanding classical and contemporary linear model theory. It does not merely introduce formulas, but develops in students the art of statistical thinking and inspires learning at an intuitive level by emphasizing conceptual understanding.The authors' fresh approach, methodical presentation, wealth of examples, and introduction to topics beyond the classical theory set this book apart from other texts on linear models. It forms a refreshing and invaluable first step in students' study of advanced linear models, generalized linear models, nonlinear models, and dynamic models.

This book is intended to provide a foundation in the grammar of classical Chinese on which the student who plans to specialize in classical studies can... build, and to give the student of modern Chinese sufficient knowledge of literary Chinese for his purposes.The material was developed over twenty years for use in the course "Introduction to Classical Chinese," as taught at Cornell University, where students of Chinese history and literature began their study of the literary language after one year of modern Chinese, and students in modern fields after two years. It is therefore assumed that the student can already pronounce Chinese words, use a system of romanization, read and write a few hundred Chinese characters, and understand simple passages of modern Chinese.The language studied in this book took shape in the latter half of the first millennium B.C. and persists as a living medium of expression today. Bernhard Karlgren has said of it: "All grammatical expedients which have been current at any time in the past, can be used promiscuously in the literature of later epochs."Texts 1-22 in Volume I constitute the core of the course. With the accompanying Exercises (also in Volume I), they provide material for about forty class sessions, thus leaving time in a normal academic year to take up a selection from Texts 23-34 and the Additional Texts A-N. (All are included in Volume I.) Most of the first twenty-two texts are from classical works of the formative period when the basic syntax was established. The remaining texts illustrate later grammatical forms and contain subject matter of considerable variety.

This book is intended to provide a foundation in the grammar of classical Chinese on which the student who plans to specialize in classical studies can... build, and to give the student of modern Chinese sufficient knowledge of literary Chinese for his purposes.The material was developed over twenty years for use in the course "Introduction to Classical Chinese," as taught at Cornell University, where students of Chinese history and literature began their study of the literary language after one year of modern Chinese, and students in modern fields after two years. It is therefore assumed that the student can already pronounce Chinese words, use a system of romanization, read and write a few hundred Chinese characters, and understand simple passages of modern Chinese.Volume II of this work consists of vocabularies for all of the texts and exercises in Volume I.

A First Course in Machine Learning covers the core mathematical and statistical techniques needed to understand some of the most popular machine... learning algorithms. The algorithms presented span the main problem areas within machine learning: classification, clustering and projection. The text gives detailed descriptions and derivations for a small number of algorithms rather than cover many algorithms in less detail. Referenced throughout the text and available on a supporting website (http://bit.ly/firstcourseml), an extensive collection of MATLAB®/Octave scripts enables students to recreate plots that appear in the book and investigate changing model specifications and parameter values. By experimenting with the various algorithms and concepts, students see how an abstract set of equations can be used to solve real problems. Requiring minimal mathematical prerequisites, the classroom-tested material in this text offers a concise, accessible introduction to machine learning. It provides students with the knowledge and confidence to explore the machine learning literature and research specific methods in more detail.

Mathematical Analysis (often called Advanced Calculus) is generally found by students to be one of their hardest courses in Mathematics. This text uses... the so-called sequential approach to continuity, differentiability and integration to make it easier to understand the subject.Topics that are generally glossed over in the standard Calculus courses are given careful study here. For example, what exactly is a 'continuous' function? And how exactly can one give a careful definition of 'integral'? The latter question is often one of the mysterious points in a Calculus course - and it is quite difficult to give a rigorous treatment of integration! The text has a large number of diagrams and helpful margin notes; and uses many graded examples and exercises, often with complete solutions, to guide students through the tricky points. It is suitable for self-study or use in parallel with a standard university course on the subject.

This text provides an introduction to the entire modeling process. Throughout the book, students practice key facets of modeling, including creative and... empirical model construction, model analysis, and model research. The authors apply a proven six-step problem solving process to enhance a student's problem solving capabilities. Rather than simply emphasizing the calculation step, the authors first ensure that students learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving students in the mathematical process as early as possible, beginning with short projects, the book facilitates their progressive development and confidence in mathematics and modeling.

Offering a solid introduction to the entire modeling process, A FIRST COURSE IN MATHEMATICAL MODELING, 4th Edition delivers an excellent balance of... theory and practice, and gives you relevant, hands-on experience developing and sharpening your modeling skills. Throughout, the book emphasizes key facets of modeling, including creative and empirical model construction, model analysis, and model research, and provides myriad opportunities for practice. The authors apply a proven six-step problem-solving process to enhance your problem-solving capabilities -- whatever your level. In addition, rather than simply emphasizing the calculation step, the authors first help you learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving you in the mathematical process as early as possible -- beginning with short projects -- this text facilitates your progressive development and confidence in mathematics and modeling.

Aimed at the novice rather than the connoisseur and stressing the role of examples and motivation, this text is suitable not only for use in a graduate... course, but also for self-study in the subject by interested graduate students. More than 400 exercises testing the understanding of the general theory in the text are included in this new edition.

Outstanding text treats numerical analysis with mathematical rigor, but relatively few theorems and proofs. Oriented toward computer solutions of... problems, it stresses errors in methods and computational efficiency. Problems — some strictly mathematical, others requiring a computer — appear at the end of each chapter.

A First Course in Numerical Methods is designed for students and researchers who seek practical knowledge of modern techniques in scientific computing.... Avoiding encyclopedic and heavily theoretical exposition, the book provides an in-depth treatment of fundamental issues and methods, the reasons behind the success and failure of numerical software, and fresh and easy-to-follow approaches and techniques. The authors focus on current methods, issues and software while providing a comprehensive theoretical foundation, enabling those who need to apply the techniques to successfully design solutions to nonstandard problems. The book also illustrates algorithms using the programming environment of MATLAB(r), with the expectation that the reader will gradually become proficient in it while learning the material covered in the book. A variety of exercises are provided within each chapter along with review questions aimed at self-testing. The book takes an algorithmic approach, focusing on techniques that have a high level of applicability to engineering, computer science, and industrial mathematics. Audience: A First Course in Numerical Methods is aimed at undergraduate and beginning graduate students. It may also be appropriate for researchers whose main area of expertise is not scientific computing and who are interested in learning the basic concepts of the field. Contents: Chapter One: Numerical Algorithms; Chapter Two: Roundoff Errors; Chapter Three: Nonlinear Equations in One Variable; Chapter Four: Linear Algebra Background; Chapter Five: Linear Systems: Direct Methods; Chapter Six: Linear Least Squares Problems; Chapter Seven: Linear Systems: Iterative Methods; Chapter Eight: Eigenvalues and Singular Values; Chapter Nine: Nonlinear Systems and Optimization; Chapter Ten: Polynomial Interpolation; Chapter Eleven: Piecewise Polynomial Interpolation; Chapter Twelve: Best Approximation; Chapter Thirteen: Fourier Transform; Chapter Fourteen: Numerical Differentiation; Chapter Fifteen: Numerical Integration; Chapter Sixteen: Differential Equations.

This book introduces students to optimization theory and its use in economics and allied disciplines. The first of its three parts examines the... existence of solutions to optimization problems in Rn, and how these solutions may be identified. The second part explores how solutions to optimization problems change with changes in the underlying parameters, and the last part provides an extensive description of the fundamental principles of finite- and infinite-horizon dynamic programming. A preliminary chapter and three appendices are designed to keep the book mathematically self-contained.

This book introduces students to optimization theory and its use in economics and allied disciplines. The first of its three parts examines the... existence of solutions to optimization problems in Rn, and how these solutions may be identified. The second part explores how solutions to optimization problems change with changes in the underlying parameters, and the last part provides an extensive description of the fundamental principles of finite- and infinite-horizon dynamic programming. A preliminary chapter and three appendices are designed to keep the book mathematically self-contained.