From Zero to Infinity is a combination of number lore, number history, and sparkling descriptions of the simply stated but exceedingly difficult problems posed by the most ordinary numbers that first appeared in 1955 and has been kept in print continuously ever since. With the fifth edition this classic has been updated to report on advances in number theory over the last 50 years, including the proof of Fermat's Last Theorem. Deceptively simple in style and structure, it is a book to which the reader will return again and again, gaining greater understanding and satisfaction with each reading.

"Among the many expositions of Goedel's incompleteness theorems written for non-specialists, this book stands apart. With exceptional clarity, Franzen gives careful, non-technical explanations both of what those theorems say and, more importantly, what they do not. No other book aims, as his does, to address in detail the misunderstandings and abuses of the incompleteness theorems that are so rife in popular discussions of their significance. As an antidote to the many spurious appeals to incompleteness in theological, anti-mechanist and post-modernist debates, it is a valuable addition to the literature." --- John W. Dawson, author of Logical Dilemmas: The Life and Work of Kurt Goedel

Physics World's 'Book of the Year' for 2016 An Entertaining and Enlightening Guide to the Who, What, and Why of String Theory, now also available in an updated reflowable electronic format compatible with mobile devices and e-readers. During the last 50 years, numerous physicists have tried to unravel the secrets of string theory. Yet why do these scientists work on a theory lacking experimental confirmation? Why String Theory? provides the answer, offering a highly readable and accessible panorama of the who, what, and why of this large aspect of modern theoretical physics. The author, a theoretical physics professor at the University of Oxford and a leading string theorist, explains what string theory is and where it originated. He describes how string theory fits into physics and why so many physicists and mathematicians find it appealing when working on topics from M-theory to monsters and from cosmology to superconductors.

This volume focuses on the important mathematical idea of functions that, with the technology of computers and calculators, can be dynamically represented in ways that have not been possible previously. The book's editors contend that as result of recent technological developments combined with the integrated knowledge available from research on teaching, instruction, students' thinking, and assessment, curriculum developers, researchers, and teacher educators are faced with an unprecedented opportunity for making dramatic changes.
The book presents content considerations that occur when the mathematics of graphs and functions relate to curriculum. It also examines content in a carefully considered integration of research that conveys where the field stands and where it might go. Drawing heavily on their own work, the chapter authors reconceptualize research in their specific areas so that this knowledge is integrated with the others' strands. This model for synthesizing research can serve as a paradigm for how research in mathematics education can -- and probably should -- proceed.

Nonlinear Dynamics of Reservoir Mixtures provides an overview of modeling techniques for solving nonlinear problems in hydrodynamics, with an emphasis on compositional flows in porous reservoirs. The volume focuses on nonlinear wave techniques for simulating and predicting fluid dynamic processes in petroleum reservoirs and discusses general applications of these models for other fluids.
Topics covered include inhomogeneous space structures in reservoir processes, gradient models for analyzing changes in thermodynamic and hydrodynamic fluid properties, phase transition dynamics in fluids and rock minerals, and wetting phenomena. The book also discusses the stages involved in developing compositional simulators for enhanced oil recovery and describes applications used in hydrocarbon fields in the former USSR.
Nonlinear Dynamics of Reservoir Mixtures provides excellent reference material for mathematicians, petroleum engineers, exploration geophysicists, and mechanical engineers. It is also a useful compositional modeling text for graduate students in the earth sciences and in petroleum and chemical engineering.

This text presents methods of modern set theory as tools that can be usefully applied to other areas of mathematics. The author describes numerous applications in abstract geometry and real analysis and, in some cases, in topology and algebra. The book begins with a tour of the basics of set theory, culminating in a proof of Zorn's Lemma and a discussion of some of its applications. The author then develops the notions of transfinite induction and descriptive set theory, with applications to the theory of real functions. The final part of the book presents the tools of "modern" set theory: Martin's Axiom, the Diamond Principle, and elements of forcing. Written primarily as a text for beginning graduate or advanced level undergraduate students, this book should also interest researchers wanting to learn more about set theoretical techniques applicable to their fields.

This graduate level text is distinguished both by the range of topics and the novelty of the material it treats--more than half of the material in it has previously only appeared in research papers. The first half of this book introduces the characteristic and matchings polynomials of a graph. It is instructive to consider these polynomials together because they have a number of properties in common. The matchings polynomial has links with a number of problems in combinatorial enumeration, particularly some of the current work on the combinatorics of orthogonal polynomials. This connection is discussed at some length, and is also in part the stimulus for the inclusion of chapters on orthogonal polynomials and formal power series. Many of the properties of orthogonal polynomials are derived from properties of characteristic polynomials. The second half of the book introduces the theory of polynomial spaces, which provide easy access to a number of important results in design theory, coding theory and the theory of association schemes. This book should be of interest to second year graduate text/reference in mathematics.

Assuming little previous mathematical knowledge, Error Correcting Codes provides a sound introduction to key areas of the subject. Topics have been chosen for their importance and practical significance, which Baylis demonstrates in a rigorous but gentle mathematical style. Coverage includes optimal codes; linear and non-linear codes; general techniques of decoding errors and erasures; error detection; syndrome decoding, and much more. Error Correcting Codes contains not only straight maths, but also exercises on more investigational problem solving. Chapters on number theory and polynomial algebra are included to support linear codes and cyclic codes, and an extensive reminder of relevant topics in linear algebra is given. Exercises are placed within the main body of the text to encourage active participation by the reader, with comprehensive solutions provided. Error Correcting Codes will appeal to undergraduate students in pure and applied mathematical fields, software engineering, communications engineering, computer science and information technology, and to organizations with substantial research and development in those areas.

Computational Thinking (CT) involves fundamental concepts and reasoning, distilled from computer science and other computational sciences, which become powerful general mental tools for solving problems, increasing efficiency, reducing complexity, designing procedures, or interacting with humans and machines. An easy-to-understand guidebook, From Computing to Computational Thinking gives you the tools for understanding and using CT. It does not assume experience or knowledge of programming or of a programming language, but explains concepts and methods for CT with clarity and depth. Successful applications in diverse disciplines have shown the power of CT in problem solving. The book uses puzzles, games, and everyday examples as starting points for discussion and for connecting abstract thinking patterns to real-life situations. It provides an interesting and thought-provoking way to gain general knowledge about modern computing and the concepts and thinking processes underlying modern digital technologies.

Join the Cryptokids as they apply basic mathematics to make and break secret codes. This book has many hands-on activities that have been tested in both classrooms and informal settings. Classic coding methods are discussed, such as Caesar, substitution, Vigen and multiplicative ciphers as well as the modern RSA. Math topics covered include: - Addition and Subtraction with, negative numbers, decimals, and percentages - Factorization - Modular Arithmetic - Exponentiation - Prime Numbers - Frequency Analysis.The accompanying workbook, The Cryptoclub Workbook: Using Mathematics to Make and Break Secret Codes provides students with problems related to each section to help them master the concepts introduced throughout the book. A PDF version of the workbook is available at no charge on the download tab, a printed workbook is available for $19.95 (K00701). The teacher manual can be requested from the publisher by contacting the Academic Sales Manager, Susie Carlisle

Project Origami: Activities for Exploring Mathematics, Second Edition presents a flexible, discovery-based approach to learning origami-math topics. It helps readers see how origami intersects a variety of mathematical topics, from the more obvious realm of geometry to the fields of algebra, number theory, and combinatorics. With over 100 new pages, this updated and expanded edition now includes 30 activities and offers better solutions and teaching tips for all activities. The book contains detailed plans for 30 hands-on, scalable origami activities. Each activity lists courses in which the activity might fit, includes handouts for classroom use, and provides notes for instructors on solutions, how the handouts can be used, and other pedagogical suggestions. The handouts are also available on the book's CRC Press web page. Reflecting feedback from teachers and students who have used the book, this classroom-tested text provides an easy and entertaining way for teachers to incorporate origami into a range of college and advanced high school math courses. Visit the author's website for more information.

The subject of mathematics is not something distant, strange, and abstract that you can only learn about and often dislike in school. It is in everyday situations, such as housekeeping, communications, traffic, and weather reports. Taking you on a trip into the world of mathematics, Do I Count? Stories from Mathematics describes in a clear and captivating way the people behind the numbers and the places where mathematics is made. Written by top scientist and engaging storyteller G nter M. Ziegler and translated by Thomas von Foerster, the book presents mathematics and mathematicians in a manner that you have not previously encountered. It guides you on a scenic tour through the field, pointing out which beds were useful in constructing which theorems and which notebooks list the prizes for solving particular problems. Forgoing esoteric areas, the text relates mathematics to celebrities, history, travel, politics, science and technology, weather, clever puzzles, and the future. Can bees count? Is 13 bad luck? Are there equations for everything? What's the real practical value of the Pythagorean Theorem? Are there Sudoku puzzles with fewer than 17 entries and just one solution? Where and how do mathematicians work? Who invented proofs and why do we need them? Why is there no Nobel Prize for mathematics? What kind of life did Paul Erdos lead? Find out the answers to these and other questions in this entertaining book of stories. You'll see that everyone counts, but no computation is needed.

The magnum opus of one of the worlds leading origami artists, the second edition of Origami Design Secrets reveals the underlying concepts of origami and how to create original origami designs. Containing step-by-step instructions for 26 models, this book is not just an origami cookbook or list of instructions it introduces the fundamental building blocks of origami, building up to advanced methods such as the combination of uniaxial bases, the circle/river method, and tree theory. With corrections and improved illustrations, this new expanded edition also covers uniaxial box pleating, introduces the new design technique of hex pleating, and describes methods of generalizing polygon packing to arbitrary angles. With coverage spanning the foundations of origami construction and advanced methods using both paper and pencil and custom-built free software, Origami Design Secrets helps readers cultivate the intuition and skills necessary to develop their own designs. It takes them beyond merely following a recipe to crafting a work of art.

A day does not go by without a news article reporting some amazing breakthrough in artificial intelligence (AI). Many philosophers, futurists, and AI researchers have conjectured that human-level AI will be developed in the next 20 to 200 years. If these predictions are correct, it raises new and sinister issues related to our future in the age of intelligent machines. Artificial Superintelligence: A Futuristic Approach directly addresses these issues and consolidates research aimed at making sure that emerging superintelligence is beneficial to humanity. While specific predictions regarding the consequences of superintelligent AI vary from potential economic hardship to the complete extinction of humankind, many researchers agree that the issue is of utmost importance and needs to be seriously addressed. Artificial Superintelligence: A Futuristic Approach discusses key topics such as: AI-Completeness theory and how it can be used to see if an artificial intelligent agent has attained human level intelligence Methods for safeguarding the invention of a superintelligent system that could theoretically be worth trillions of dollars Self-improving AI systems: definition, types, and limits The science of AI safety engineering, including machine ethics and robot rights Solutions for ensuring safe and secure confinement of superintelligent systems The future of superintelligence and why long-term prospects for humanity to remain as the dominant species on Earth are not great Artificial Superintelligence: A Futuristic Approach is designed to become a foundational text for the new science of AI safety engineering. AI researchers and students, computer security researchers, futurists, and philosophers should find this an invaluable resource.

A Bridge to Higher Mathematics is more than simply another book to aid the transition to advanced mathematics. The authors intend to assist students in developing a deeper understanding of mathematics and mathematical thought. The only way to understand mathematics is by doing mathematics. The reader will learn the language of axioms and theorems and will write convincing and cogent proofs using quantifiers. Students will solve many puzzles and encounter some mysteries and challenging problems. The emphasis is on proof. To progress towards mathematical maturity, it is necessary to be trained in two aspects: the ability to read and understand a proof and the ability to write a proof. The journey begins with elements of logic and techniques of proof, then with elementary set theory, relations and functions. Peano axioms for positive integers and for natural numbers follow, in particular mathematical and other forms of induction. Next is the construction of integers including some elementary number theory. The notions of finite and infinite sets, cardinality of counting techniques and combinatorics illustrate more techniques of proof. For more advanced readers, the text concludes with sets of rational numbers, the set of reals and the set of complex numbers. Topics, like Zorn's lemma and the axiom of choice are included. More challenging problems are marked with a star. All these materials are optional, depending on the instructor and the goals of the course.

The connections between origami, mathematics, science, technology, and education have been a topic of considerable interest now for several decades. While many individuals have happened upon discrete connections among these fields during the twentieth century, the field really took off when previously isolated individuals began to make stronger connections with each other through a series of conferences exploring the links between origami and "the outside world." The Fourth International Meeting on Origami in Science, Mathematics, and Education (4OSME), held in September, 2006, at the California Institute of Technology in Pasadena, California, brought together an unprecedented number of researchers presenting on topics ranging from mathematics, to technology, to educational uses of origami, to fine art, and to computer programs for the design of origami. Selected papers based on talks presented at that conference make up the book you hold in your hands.

"Ah, I'm Pingree. We meet again. Splendid. Won't you sit down?" I looked around David's room. Short of the library stacks, I had never seen so many books piled into a single room. Where could I sit down? Every square inch of horizontal surface was covered. Books, papers, notes, manuscripts-all congregated in random and chaotic disorder. This small encounter and the snapshot of the protagonist on the cover of this book introduce the reader to David E. Pingree, the eminent classicist, Orientalist, historian of ancient science, and member of the Department of the History of Mathematics at Brown University. This is a book of his stories, retold by Phil Davis, award-winning author and raconteur par excellence, who reconstructs them from letters and many conversations with his friend Pingree. The stories trace connections between ancient characters, historical and mythical, and recreate a world in which the pursuit of knowledge for its own sake leads to unexpected pleasures and associations. They capture a world best described by Saul Lieberman's quip about Gershom Scholem's great work on the Kabala: "Trash is trash; but the study of trash is scholarship," and David Pingree's imagined response, "Yes, but there's always something of value to be learned." The book is dedicated to preserving and promoting the specialized knowledge and thoughts of David Pingree, a truly remarkable person and to inspire readers to follow academic tradition and at the same time explore unusual connections.

It is necessary to practice methodological doubt, like Descartes, in - der to loosen the hold of mental habits; and it is necessary to cultivate logical imagination, in order to have a number of hypotheses at c- mand, and not to be the slave of the one which common sense has r- dered easy to imagine. These two processes, of doubting the familiar and imagining the unfamiliar, are corrective, and form the chief part of the mental training required for a philosopher. Bertrand Russell At every stage and in all circumstances knowledge is incomplete and provisional, conditioned and limited by the historical circumstances under which it was acquired, including the means and methods used for gaining it and the historically conditioned assumptions and categories used in the formulation of ideas and conclusions. Maurice Cornforth This monograph is the second in the series of meta-theoretic analysis of fuzzy paradigm and its contribution and possible contribution to formal reasoning in order to free the knowledge production process from the ridge frame of the classical paradigm that makes its application to soft and inexact sciences d- ficult or irrelevant. The work in the previous monograph was strictly devoted to problems of theory of knowledge and critique of classical, bounded and other rationalities in decision-choice processes regarding the principles of verification, falsification or corroboration in knowledge production. This monograph deals mostly with epistemic decision-choice models and theories and how they are related to both the classical and fuzzy paradigms.

Multiple-Valued Logic Design: An Introduction explains the theory and applications of this increasingly important subject. Written in a clear and understandable style, the author develops the material in a skillful way. Without using a huge mathematical apparatus, he introduces the subject in a general form that includes the well-known binary logic as a special case. The book is further enhanced by more 200 explanatory diagrams and circuits, hardware and software applications with supporting PASCAL programming, and comprehensive exercises with even-numbered answers for every chapter.
Requiring introductory knowledge in Boolean algebra, 2-valued logic, or 2-valued switching theory, Multiple-Valued Logic Design: An Introduction is an ideal book for courses not only in logic design, but also in switching theory, nonclassical logic, and computer arithmetic. Computer scientists, mathematicians, and electronic engineers can also use the book as a basis for research into multiple-valued logic design.

Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations. In the theoretical part of the book, the author discusses the main theorems and results of the stability and consistency analysis for ordinary differential equations. He then presents extensions of the iterative splitting methods to partial differential equations and spatial- and time-dependent differential equations. The practical part of the text applies the methods to benchmark and real-life problems, such as waste disposal, elastics wave propagation, and complex flow phenomena. The book also examines the benefits of equation decomposition. It concludes with a discussion on several useful software packages, including r3t and FIDOS. Covering a wide range of theoretical and practical issues in multiphysics and multiscale problems, this book explores the benefits of using iterative splitting schemes to solve physical problems. It illustrates how iterative operator splitting methods are excellent decomposition methods for obtaining higher-order accuracy.

Examines partitions and covers of graphs and digraphs, latin squares, pairwise balanced designs with prescribed block sizes, ranks and permanents, extremal graph theory, Hadamard matrices and graph factorizations. This book is designed to be of interest to applied mathematicians, computer scientists and communications researchers.

A textbook for either a semester or year course for graduate students of mathematics who have had at least one course in topology. Introduces continuum theory through a combination of classical and modern techniques. Annotation copyright Book News, Inc. Portland, Or.

This book treats bounded arithmetic and propositional proof complexity from the point of view of computational complexity. The first seven chapters include the necessary logical background for the material and are suitable for a graduate course. Associated with each of many complexity classes are both a two-sorted predicate calculus theory, with induction restricted to concepts in the class, and a propositional proof system. The complexity classes range from AC0 for the weakest theory up to the polynomial hierarchy. Each bounded theorem in a theory translates into a family of (quantified) propositional tautologies with polynomial size proofs in the corresponding proof system. The theory proves the soundness of the associated proof system. The result is a uniform treatment of many systems in the literature, including Buss's theories for the polynomial hierarchy and many disparate systems for complexity classes such as AC0, AC0(m), TC0, NC1, L, NL, NC, and P.

In the theory of splines, a function is approximated piece-wise by (usually cubic) polynomials. Quasi-splines is the natural extension of this, allowing us to use any useful class of functions adapted to the problem.
Approximation with Quasi-Splines is a detailed account of this highly useful technique in numerical analysis.
The book presents the requisite approximation theorems and optimization methods, developing a unified theory of one and several variables. The author applies his techniques to the evaluation of definite integrals (quadrature) and its many-variables generalization, which he calls "cubature."
This book should be required reading for all practitioners of the methods of approximation, including researchers, teachers, and students in applied, numerical and computational mathematics.

For many civilian, security, and military applications, distributed and networked coordination offers a more promising alternative to centralized command and control in terms of scalability, flexibility, and robustness. It also introduces its own challenges. Distributed Networks: Intelligence, Security, and Applications brings together scientific research in distributed network intelligence, security, and novel applications. The book presents recent trends and advances in the theory and applications of network intelligence and helps you understand how to successfully incorporate them into distributed systems and services. Featuring contributions by leading scholars and experts from around the world, this collection covers: Approaches for distributed network intelligence Distributed models for distributed enterprises, including forecasting and performance measurement models Security applications for distributed enterprises, including intrusion tackling and peer-to-peer traffic detection Future wireless networking scenarios, including the use of software sensors instead of hardware sensors Emerging enterprise applications and trends such as the smartOR standard and innovative concepts for human-machine interaction in the operating room Several chapters use a tutorial style to emphasize the development process behind complex distributed networked systems and services, which highlights the difficulties of knowledge engineering of such systems. Delving into novel concepts, theories, and advanced technologies, this book offers inspiration for further research and development in distributed computing and networking, especially related to security solutions for distributed environments.