This monograph provides a modern introduction to the theory of quantales. First coined by C.J. Mulvey in 1986, quantales have since developed into a significant topic at the crossroads of algebra and logic, of notable interest to theoretical computer science. This book recasts the subject within the powerful framework of categorical algebra, showcasing its versatility through applications to C*- and MV-algebras, fuzzy sets and automata. With exercises and historical remarks at the end of each chapter, this self-contained book provides readers with a valuable source of references and hints for future research. This book will appeal to researchers across mathematics and computer science with an interest in category theory, lattice theory, and many-valued logic.

Floating-point arithmetic is the most widely used way of implementing real-number arithmetic on modern computers. However, making such an arithmetic reliable and portable, yet fast, is a very difficult task. As a result, floating-point arithmetic is far from being exploited to its full potential. This handbook aims to provide a complete overview of modern floating-point arithmetic. So that the techniques presented can be put directly into practice in actual coding or design, they are illustrated, whenever possible, by a corresponding program. The handbook is designed for programmers of numerical applications, compiler designers, programmers of floating-point algorithms, designers of arithmetic operators, and more generally, students and researchers in numerical analysis who wish to better understand a tool used in their daily work and research.

This visionary and engaging book provides a mathematical perspective on the fundamental ideas of numbers, space, life, evolution, the brain and the mind. The author suggests how a development of mathematical concepts in the spirit of category theory may lead to unravelling the mystery of the human mind and the design of universal learning algorithms. The book is divided into two parts, the first of which describes the ideas of great mathematicians and scientists, those who saw sparks of light in the dark sea of unknown. The second part, Memorandum Ergo, reflects on how mathematics can contribute to the understanding of the mystery of thought. It argues that the core of the human mind is a structurally elaborated object that needs a creation of a broad mathematical context for its understanding. Readers will discover the main properties of the expected mathematical objects within this context, called ERGO-SYSTEMS, and readers will see how these "systems" may serve as prototypes for design of universal learning computer programs. This is a work of great, poetical insight and is richly illustrated. It is a highly attractive read for all those who welcome a mathematical and scientific way of thinking about the world.

Using data from one season of NBA games, Basketball Data Science: With Applications in R is the perfect book for anyone interested in learning and applying data analytics in basketball. Whether assessing the spatial performance of an NBA player's shots or doing an analysis of the impact of high pressure game situations on the probability of scoring, this book discusses a variety of case studies and hands-on examples using a custom R package. The codes are supplied so readers can reproduce the analyses themselves or create their own. Assuming a basic statistical knowledge, Basketball Data Science with R is suitable for students, technicians, coaches, data analysts and applied researchers. Features: * One of the first books to provide statistical and data mining methods for the growing field of analytics in basketball. * Presents tools for modelling graphs and figures to visualize the data. * Includes real world case studies and examples, such as estimations of scoring probability using the Golden State Warriors as a test case. * Provides the source code and data so readers can do their own analyses on NBA teams and players.

In the second edition of this classic monograph, complete with four new chapters and updated references, readers will now have access to content describing and analysing classical and modern methods with emphasis on the algebraic structure of linear iteration, which is usually ignored in other literature. The necessary amount of work increases dramatically with the size of systems, so one has to search for algorithms that most efficiently and accurately solve systems of, e.g., several million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretization of partial differential equations. In this case, the matrices are sparse (i.e., they contain mostly zeroes) and well-suited to iterative algorithms. The first edition of this book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics. The second edition includes quite novel approaches.

This book contains a compendium of 25 papers published since the 1970s dealing with pi and associated topics of mathematics and computer science. The collection begins with a Foreword by Bruce Berndt. Each contribution is preceded by a brief summary of its content as well as a short key word list indicating how the content relates to others in the collection. The volume includes articles on actual computations of pi, articles on mathematical questions related to pi (e.g., "Is pi normal?"), articles presenting new and often amazing techniques for computing digits of pi (e.g., the "BBP" algorithm for pi, which permits one to compute an arbitrary binary digit of pi without needing to compute any of the digits that came before), papers presenting important fundamental mathematical results relating to pi, and papers presenting new, high-tech techniques for analyzing pi (i.e., new graphical techniques that permit one to visually see if pi and other numbers are "normal"). This volume is a companion to Pi: A Source Book whose third edition released in 2004. The present collection begins with 2 papers from 1976, published by Eugene Salamin and Richard Brent, which describe "quadratically convergent" algorithms for pi and other basic mathematical functions, derived from some mathematical work of Gauss. Bailey and Borwein hold that these two papers constitute the beginning of the modern era of computational mathematics. This time period (1970s) also corresponds with the introduction of high-performance computer systems (supercomputers), which since that time have increased relentlessly in power, by approximately a factor of 100,000,000, advancing roughly at the same rate as Moore's Law of semiconductor technology. This book may be of interest to a wide range of mathematical readers; some articles cover more advanced research questions suitable for active researchers in the field, but several are highly accessible to undergraduate mathematics students.

The arrangement of nonzero entries of a matrix, described by the graph of the matrix, limits the possible geometric multiplicities of the eigenvalues, which are far more limited by this information than algebraic multiplicities or the numerical values of the eigenvalues. This book gives a unified development of how the graph of a symmetric matrix influences the possible multiplicities of its eigenvalues. While the theory is richest in cases where the graph is a tree, work on eigenvalues, multiplicities and graphs has provided the opportunity to identify which ideas have analogs for non-trees, and those for which trees are essential. It gathers and organizes the fundamental ideas to allow students and researchers to easily access and investigate the many interesting questions in the subject.

A comprehensive guide to statistics-with information on collecting, measuring, analyzing, and presenting statistical data-continuing the popular 101 series. Data is everywhere. In the age of the internet and social media, we're responsible for consuming, evaluating, and analyzing data on a daily basis. From understanding the percentage probability that it will rain later today, to evaluating your risk of a health problem, or the fluctuations in the stock market, statistics impact our lives in a variety of ways, and are vital to a variety of careers and fields of practice. Unfortunately, most statistics text books just make us want to take a snooze, but with Statistics 101, you'll learn the basics of statistics in a way that is both easy-to-understand and apply. From learning the theory of probability and different kinds of distribution concepts, to identifying data patterns and graphing and presenting precise findings, this essential guide can help turn statistical math from scary and complicated, to easy and fun. Whether you are a student looking to supplement your learning, a worker hoping to better understand how statistics works for your job, or a lifelong learner looking to improve your grasp of the world, Statistics 101 has you covered.

An essential guide to recognizing bogus numbers and misleading data Numbers are often intimidating, confusing, and even deliberately deceptive-especially when they are really big. The media loves to report on millions, billions, and trillions, but frequently makes basic mistakes or presents such numbers in misleading ways. And misunderstanding numbers can have serious consequences, since they can deceive us in many of our most important decisions, including how to vote, what to buy, and whether to make a financial investment. In this short, accessible, enlightening, and entertaining book, Brian Kernighan teaches anyone-even diehard math-phobes-how to demystify the numbers that assault us every day. Giving you the simple tools you need to avoid being fooled by dubious numbers, Millions, Billions, Zillions is an essential survival guide for a world drowning in big-and often bad-data.

The goal of this monograph is to give an accessible introduction to nonstandard methods and their applications, with an emphasis on combinatorics and Ramsey theory. It includes both new nonstandard proofs of classical results and recent developments initially obtained in the nonstandard setting. This makes it the first combinatorics-focused account of nonstandard methods to be aimed at a general (graduate-level) mathematical audience. This book will provide a natural starting point for researchers interested in approaching the rapidly growing literature on combinatorial results obtained via nonstandard methods. The primary audience consists of graduate students and specialists in logic and combinatorics who wish to pursue research at the interface between these areas.

Keeping students involved and actively learning is challenging. Instructors in computer science are aware of the cognitive value of modelling puzzles and often use logical puzzles as an efficient pedagogical instrument to engage students and develop problem-solving skills. This unique book is a comprehensive resource that offers teachers and students fun activities to teach and learn logic. It provides new, complete, and running formalisation in Propositional and First Order Logic for over 130 logical puzzles, including Sudoku-like puzzles, zebra-like puzzles, island of truth, lady and tigers, grid puzzles, strange numbers, or self-reference puzzles. Solving puzzles with theorem provers can be an effective cognitive incentive to motivate students to learn logic. They will find a ready-to-use format which illustrates how to model each puzzle, provides running implementations, and explains each solution. This concise and easy-to-follow textbook is a much-needed support tool for students willing to explore beyond the introductory level of learning logic and lecturers looking for examples to heighten student engagement in their computer science courses.

Absolutely everything you need to get ready for Algebra Scared of square roots? Suspicious of powers of ten? You're not alone. Plenty of school-age students and adult learners don't care for math. But, with the right guide, you can make math basics "click" for you too! In Basic Math & Pre-Algebra All-in-One For Dummies, you'll find everything you need to be successful in your next math class and tackle basic math tasks in the real world. Whether you're trying to get a handle on pre-algebra before moving to the next grade or looking to get more comfortable with everyday math--such as tipping calculations or balancing your checkbook--this book walks you through every step--in plain English, and with clear explanations--to help you build a firm foundation in math. You'll also get: Practice quizzes at the end of each chapter to test your comprehension and understanding A bonus online quiz for each chapter, with answer choices presented in multiple choice format A ton of explanations, examples, and practice problems that prepare you to tackle more advanced algebraic concepts From the different categories of numbers to mathematical operations, fractions, percentages, roots and powers, and a short intro to algebraic expressions and equations, Basic Math & Pre-Algebra All-in-One For Dummies is an essential companion for anyone who wants to get a handle on the foundational math concepts that are the building blocks for Algebra and beyond.

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the eleventh publication in the Perspectives in Logic series, Manuel Lerman presents a systematic study of the interaction between local and global degree theory. He introduces the reader to the fascinating combinatorial methods of recursion theory while simultaneously showing how to use these methods to prove global theorems about degrees. The intended reader will have already taken a graduate-level course in recursion theory, but this book will also be accessible to those with some background in mathematical logic and a feeling for computability. It will prove a key reference to enable readers to easily locate facts about degrees and it will direct them to further results.

This LNCS volume is part of FoLLI book serie and contains the papers presented at the 6th International Workshop on Logic, Rationality and Interaction/ (LORI-VI), held in September 2017 in Sapporo, Japan. The focus of the workshop is on following topics: Agency, Argumentation and Agreement, Belief Revision and Belief Merging, Belief Representation, Cooperation, Decision making and Planning, Natural Language, Philosophy and Philosophical Logic, and Strategic Reasoning.

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the sixth publication in the Perspectives in Logic series, Keith J. Devlin gives a comprehensive account of the theory of constructible sets at an advanced level. The book provides complete coverage of the theory itself, rather than the many and diverse applications of constructibility theory, although applications are used to motivate and illustrate the theory. The book is divided into two parts: Part I (Elementary Theory) deals with the classical definition of the L -hierarchy of constructible sets and may be used as the basis of a graduate course on constructibility theory. and Part II (Advanced Theory) deals with the J -hierarchy and the Jensen 'fine-structure theory'.

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the tenth publication in the Lecture Notes in Logic series, Per Lindstroem presents some of the main topics and results in general metamathematics. In addition to standard results of Goedel et al. on incompleteness, (non-)finite axiomatizability, and interpretability, this book contains a thorough treatment of partial conservativity and degrees of interpretability. It comes complete with exercises, and will be useful as a textbook for graduate students with a background in logic, as well as a valuable resource for researchers.

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. Large cardinal hypotheses play a central role in modern set theory. One important way to understand such hypotheses is to construct concrete, minimal universes, or 'core models', satisfying them. Since Goedel's pioneering work on the universe of constructible sets, several larger core models satisfying stronger hypotheses have been constructed, and these have proved quite useful. In this volume, the eighth publication in the Lecture Notes in Logic series, Steel extends this theory so that it can produce core models having Woodin cardinals, a large cardinal hypothesis that is the focus of much current research. The book is intended for advanced graduate students and researchers in set theory.

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. Admissible set theory is a major source of interaction between model theory, recursion theory and set theory, and plays an important role in definability theory. In this volume, the seventh publication in the Perspectives in Logic series, Jon Barwise presents the basic facts about admissible sets and admissible ordinals in a way that makes them accessible to logic students and specialists alike. It fills the artificial gap between model theory and recursion theory and covers everything the logician should know about admissible sets.

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the third publication in the Perspectives in Logic series, is a much-needed monograph on the metamathematics of first-order arithmetic. The authors pay particular attention to subsystems (fragments) of Peano arithmetic and give the reader a deeper understanding of the role of the axiom schema of induction and of the phenomenon of incompleteness. The reader is only assumed to know the basics of mathematical logic, which are reviewed in the preliminaries. Part I develops parts of mathematics and logic in various fragments. Part II is devoted to incompleteness. Finally, Part III studies systems that have the induction schema restricted to bounded formulas (bounded arithmetic).

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the first publication in the Perspectives in Logic series, Pour-El and Richards present the first graduate-level treatment of computable analysis within the tradition of classical mathematical reasoning. The book focuses on the computability or noncomputability of standard processes in analysis and physics. Topics include classical analysis, Hilbert and Banach spaces, bounded and unbounded linear operators, eigenvalues, eigenvectors, and equations of mathematical physics. The work is self-contained, and although it is intended primarily for logicians and analysts, it should also be of interest to researchers and graduate students in physics and computer science.

The area of coalgebra has emerged within theoretical computer science with a unifying claim: to be the mathematics of computational dynamics. It combines ideas from the theory of dynamical systems and from the theory of state-based computation. Although still in its infancy, it is an active area of research that generates wide interest. Written by one of the founders of the field, this book acts as the first mature and accessible introduction to coalgebra. It provides clear mathematical explanations, with many examples and exercises involving deterministic and non-deterministic automata, transition systems, streams, Markov chains and weighted automata. The theory is expressed in the language of category theory, which provides the right abstraction to make the similarity and duality between algebra and coalgebra explicit, and which the reader is introduced to in a hands-on manner. The book will be useful to mathematicians and (theoretical) computer scientists and will also be of interest to mathematical physicists, biologists and economists.

Providing a timely description of the present state of the art of moduli spaces of curves and their geometry, this volume is written in a way which will make it extremely useful both for young people who want to approach this important field, and also for established researchers, who will find references, problems, original expositions, new viewpoints, etc. The book collects the lecture notes of a number of leading algebraic geometers and in particular specialists in the field of moduli spaces of curves and their geometry. This is an important subject in algebraic geometry and complex analysis which has seen spectacular developments in recent decades, with important applications to other parts of mathematics such as birational geometry and enumerative geometry, and to other sciences, including physics. The themes treated are classical but with a constant look to modern developments (see Cascini, Debarre, Farkas, and Sernesi's contributions), and include very new material, such as Bridgeland stability (see Macri's lecture notes) and tropical geometry (see Chan's lecture notes).

Originally published in 1948, this book was written to provide students with an accessible guide to various elements of mathematics. The text was created for individual working rather than group learning situations. Numerous exercises are included. This book will be of value to anyone with an interest in mathematics and the history of education.

Michael Holzhauser discusses generalizations of well-known network flow and packing problems by additional or modified side constraints. By exploiting the inherent connection between the two problem classes, the author investigates the complexity and approximability of several novel network flow and packing problems and presents combinatorial solution and approximation algorithms.