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Presents a useful new technique for analyzing the extreme-value behaviour of random fields

Generating functions, one of the most important tools in enumerative combinatorics, are a bridge between discrete mathematics and continuous analysis. Generating functions have numerous applications in mathematics, especially in - Combinatorics - Probability Theory - Statistics - Theory of Markov Chains - Number Theory One of the most important and relevant recent applications of combinatorics lies in the development of Internet search engines whose incredible capabilities dazzle even the mathematically trained user.

Pure and Applied Mathematics

Figurate numbers have a rich history with many applications. The main purpose of this book is to provide a thorough and complete presentation of the theory of figurate numbers, giving much of their properties, facts and theorems with full proofs. This book is the first of this topic in unified systematic way. It also contains many exercises with solutions.

The first volume (General Theory) differs from most textbooks as it emphasizes the mathematical structure and mathematical rigor, while being adapted to the teaching the first semester of an advanced course in Quantum Mechanics (the content of the book are the lectures of courses actually delivered.). It differs also from the very few texts in Quantum Mechanics that give emphasis to the mathematical aspects because this book, being written as Lecture Notes, has the structure of lectures delivered in a course, namely introduction of the problem, outline of the relevant points, mathematical tools needed, theorems, proofs. This makes this book particularly useful for self-study and for instructors in the preparation of a second course in Quantum Mechanics (after a first basic course). With some minor additions it can be used also as a basis of a first course in Quantum Mechanics for students in mathematics curricula. The second part (Selected Topics) are lecture notes of a more advanced course aimed at giving the basic notions necessary to do research in several areas of mathematical physics connected with quantum mechanics, from solid state to singular interactions, many body theory, semi-classical analysis, quantum statistical mechanics. The structure of this book is suitable for a second-semester course, in which the lectures are meant to provide, in addition to theorems and proofs, an overview of a more specific subject and hints to the direction of research. In this respect and for the width of subjects this second volume differs from other monographs on Quantum Mechanics. The second volume can be useful for students who want to have a basic preparation for doing research and for instructors who may want to use it as a basis for the presentation of selected topics.

With plenty of new material not found in other books, Direct Sum Decompositions of Torsion-Free Finite Rank Groups explores advanced topics in direct sum decompositions of abelian groups and their consequences. The book illustrates a new way of studying these groups while still honoring the rich history of unique direct sum decompositions of groups. Offering a unified approach to theoretic concepts, this reference covers isomorphism, endomorphism, refinement, the Baer splitting property, Gabriel filters, and endomorphism modules. It shows how to effectively study a group G by considering finitely generated projective right End(G)-modules, the left End(G)-module G, and the ring E(G) = End(G)/N(End(G)). For instance, one of the naturally occurring properties considered is when E(G) is a commutative ring. Modern algebraic number theory provides results concerning the isomorphism of locally isomorphic rtffr groups, finitely faithful S-groups that are J-groups, and each rtffr L-group that is a J-group. The book concludes with useful appendices that contain background material and numerous examples.

Pseudolinear Functions and Optimization is the first book to focus exclusively on pseudolinear functions, a class of generalized convex functions. It discusses the properties, characterizations, and applications of pseudolinear functions in nonlinear optimization problems. The book describes the characterizations of solution sets of various optimization problems. It examines multiobjective pseudolinear, multiobjective fractional pseudolinear, static minmax pseudolinear, and static minmax fractional pseudolinear optimization problems and their results. The authors extend these results to locally Lipschitz functions using Clarke subdifferentials. They also present optimality and duality results for h-pseudolinear and semi-infinite pseudolinear optimization problems. The authors go on to explore the relationships between vector variational inequalities and vector optimization problems involving pseudolinear functions. They present characterizations of solution sets of pseudolinear optimization problems on Riemannian manifolds as well as results on pseudolinearity of quadratic fractional functions. The book also extends n-pseudolinear functions to pseudolinear and n-pseudolinear fuzzy mappings and characterizations of solution sets of pseudolinear fuzzy optimization problems and n-pseudolinear fuzzy optimization problems. The text concludes with some applications of pseudolinear optimization problems to hospital management and economics. This book encompasses nearly all the published literature on the subject along with new results on semi-infinite nonlinear programming problems. It will be useful to readers from mathematical programming, industrial engineering, and operations management.

A Classroom-Tested, Alternative Approach to Teaching Math for Liberal Arts Puzzles, Paradoxes, and Problem Solving: An Introduction to Mathematical Thinking uses puzzles and paradoxes to introduce basic principles of mathematical thought. The text is designed for students in liberal arts mathematics courses. Decision-making situations that progress from recreational problems to important contemporary applications develop the critical-thinking skills of non-science and non-technical majors. The logical underpinnings of this textbook were developed and refined throughout many years of classroom feedback and in response to commentary from presentations at national conferences. The text’s five units focus on graphs, logic, probability, voting, and cryptography. The authors also cover related areas, such as operations research, game theory, number theory, combinatorics, statistics, and circuit design. The text uses a core set of common representations, strategies, and algorithms to analyze diverse games, puzzles, and applications. This unified treatment logically connects the topics with a recurring set of solution approaches. Requiring no mathematical prerequisites, this book helps students explore creative mathematical thinking and enhance their own critical-thinking skills. Students will acquire quantitative literacy and appreciation of mathematics through the text’s unified approach and wide range of interesting applications.

A collection of definitions, questions, and theorems edited by M. L. Perez, such as Smarandache type conjectures, problems, numerical bases, T-numbers, progressions, series, functions, Non-Euclidean geometries, paradoxes (such as Smarandache Sorites Paradox that our visible world is composed by a totality of invisible particles), linguistic tautologies, Smarandache hypothesis that there is no speed barrier in the universe - which has been extended to SRM-theory.

This book introduces you to the study of statistics and data analysis by using real data and attention-grabbing examples. The authors guide you through an intuition-based learning process that stresses interpretation and communication of statistical information. They help you grasp concepts and cement your comprehension by using simple notation-frequently substituting words for symbols. You will also find coverage of the graphing calculator as a problem-solving tool, plus hands-on activities in each chapter that allow you to practice statistics firsthand.

Taught at junior level math courses at every university, Linear Algebra is essential for students in almost every technical and analytic discipline.

A Handbook of Statistical Analyses Using SPSS clearly describes how to conduct a range of univariate and multivariate statistical analyses using the latest version of the Statistical Package for the Social Sciences, SPSS 11. Each chapter addresses a different type of analytical procedure applied to one or more data sets, primarily from the social and behavioral sciences areas. Each chapter also contains exercises relating to the data sets introduced, providing readers with a means to develop both their SPSS and statistical skills. Model answers to the exercises are also provided. Readers can download all of the data sets from a companion Web site furnished by the authors.

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