This book unravels the mystery of Geometry in Origami with a unique approach: 64 Polyhedra designs, each made from a single square sheet of paper, no cuts, no glue; each polyhedron the largest possible from the starting size of square and each having an ingenious locking mechanism to hold its shape. The author covers the five Platonic solids (cube, tetrahedron, octahedron, icosahedron and dodecahedron). There are ample variations with different color patterns and sunken sides. Dipyramids and Dimpled Dipyramids, unexplored before this in Origami, are also covered. There are a total of 64 models in the book. All the designs have an interesting look and a pleasing folding sequence and are based on unique mathematical equations.

The classic results obtained by Godel, Tarski, Kleene, and Church in the early thirties are the finest flowers of symbolic logic. They are of fundamental importance to those investigations of the foundations of mathematics via the concept of a formal system that were inaugurated by Frege, and of obvious significance to the mathematical disciplines, such as computability theory, that developed from them.
Derived from courses taught by the author over several years, this new exposition presents all of the results with their original proofs and central concepts in a manner that is unified by a systematic grounding of the notion of effectiveness in the semantics of the existential quantifier. Logicians and non-mathematicians, repelled by detail which is not obviously relevant in the standard textbooks, will be able to reach the heart of the matter with a minimum of fuss.

"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.

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

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.

This book discusses how to design "good" geometric puzzles: two-dimensional dissection puzzles, polyhedral dissections, and burrs. It outlines major categories of geometric puzzles and provides examples, sometimes going into the history and philosophy of those examples. The author presents challenges and thoughtful questions, as well as practical design and woodworking tips to encourage the reader to build his own puzzles and experiment with his own designs. Aesthetics, phychology, and mathematical considerations all factor into the definition of the quality of a puzzle.

Mathematics in Games, Sports, and Gambling: The Games People Play, Second Edition demonstrates how discrete probability, statistics, and elementary discrete mathematics are used in games, sports, and gambling situations. With emphasis on mathematical thinking and problem solving, the text draws on numerous examples, questions, and problems to explain the application of mathematical theory to various real-life games.This updated edition of a widely adopted textbook considers a number of popular games and diversions that are mathematically based or can be studied from a mathematical perspective. Requiring only high school algebra, the book is suitable for use as a textbook in seminars, general education courses, or as a supplement in introductory probability courses.New in this Edition: Many new exercises, including basic skills exercises More answers in the back of the book Expanded summary exercises, including writing exercises More detailed examples, especially in the early chapters An expansion of the discrete adjustment technique for binomial approximation problems New sections on chessboard puzzles that encourage students to develop graph theory ideas New review material on relations and functions Exercises are included in each section to help students understand the various concepts. The text covers permutations in the two-deck matching game so derangements can be counted. It introduces graphs to find matches when looking at extensions of the five-card trick and studies lexicographic orderings and ideas of encoding for card tricks.The text also explores linear and weighted equations in the section on the NFL passer rating formula and presents graphing to show how data can be compared or displayed. For each topic, the author includes exercises based on real games and actual sports data.

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.

Exploring a vast array of topics related to computation, Computing: A Historical and Technical Perspective covers the historical and technical foundation of ancient and modern-day computing. The book starts with the earliest references to counting by humans, introduces various number systems, and discusses mathematics in early civilizations. It guides readers all the way through the latest advances in computer science, such as the design and analysis of computer algorithms. Through historical accounts, brief technical explanations, and examples, the book answers a host of questions, including: Why do humans count differently from the way current electronic computers do? Why are there 24 hours in a day, 60 minutes in an hour, etc.? Who invented numbers, when were they invented, and why are there different kinds? How do secret writings and cryptography date back to ancient civilizations? Innumerable individuals from many cultures have contributed their talents and creativity to formulate what has become our mathematical and computing heritage. By bringing together the historical and technical aspects of computing, this book enables readers to gain a deep appreciation of the long evolutionary processes of the field developed over thousands of years. Suitable as a supplement in undergraduate courses, it provides a self-contained historical reference source for anyone interested in this important and evolving field.

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.

This volume, which ten years ago appeared as the first in the acclaimed series Lecture Notes in Logic, serves as an introduction to recursion theory. The fundamental concept of recursion makes the idea of computability accessible to a mathematical analysis, thus forming one of the pillars on which modern computer science rests. The clarity and focus of this text have established it as a classic instrument for teaching and self-study that prepares its readers for the study of advanced monographs and the current literature on recursion theory.

The Star and the Whole: Gian-Carlo Rota on Mathematics and Phenomenology, authored by Fabrizio Palombi, is the first book to study Rota's philosophical reflection. Rota (1932 1999) was a leading figure in contemporary mathematics and an outstanding philosopher, inspired by phenomenology, who made fundamental contributions to combinatorial analysis, and trained several generations of mathematicians in his long career at the Massachusetts Institute of Technology (MIT) and the Los Alamos National Laboratory. The first chapter of the book reconstructs Rota's cultural biography and examines his philosophical style, his criticisms of analytical philosophy, and his reflection on Heidegger's thought. The second chapter presents a general picture of Rota's re-elaboration of phenomenology examined in the light of the Husserlian notion of Fundierung. This chapter also illustrates how the star-shape becomes a powerful instrument for understanding the properties of Husserl's mereology and the critique of objectivism. The third chapter is a theoretical reflection on the nature of mathematical entities, and the fourth examines the complex relation of mathematical research with technological applicability and scientific progress. The foreword of the text is written by Robert Sokolowski.

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.

Going beyond current books on privacy and security, Unauthorized Access: The Crisis in Online Privacy and Security proposes specific solutions to public policy issues pertaining to online privacy and security. Requiring no technical or legal expertise, the book explains complicated concepts in clear, straightforward language. The authors two renowned experts on computer security and law explore the well-established connection between social norms, privacy, security, and technological structure. This approach is the key to understanding information security and informational privacy, providing a practical framework to address ethical and legal issues. The authors also discuss how rapid technological developments have created novel situations that lack relevant norms and present ways to develop these norms for protecting informational privacy and ensuring sufficient information security. Bridging the gap among computer scientists, economists, lawyers, and public policy makers, this book provides technically and legally sound public policy guidance about online privacy and security. It emphasizes the need to make trade-offs among the complex concerns that arise in the context of online privacy and security.

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.

Paradoxes are poems of science and philosophy that collectively allow us to address broad multidisciplinary issues within a microcosm. A true paradox is a source of creativity and a concise expression that delivers a profound idea and provokes a wild and endless imagination. The study of paradoxes leads to ultimate clarity and, at the same time, indisputably challenges your mind. Paradoxes in Scientific Inference analyzes paradoxes from many different perspectives: statistics, mathematics, philosophy, science, artificial intelligence, and more. The book elaborates on findings and reaches new and exciting conclusions. It challenges your knowledge, intuition, and conventional wisdom, compelling you to adjust your way of thinking. Ultimately, you will learn effective scientific inference through studying the paradoxes.

Proof complexity is a rich subject drawing on methods from logic, combinatorics, algebra and computer science. This self-contained book presents the basic concepts, classical results, current state of the art and possible future directions in the field. It stresses a view of proof complexity as a whole entity rather than a collection of various topics held together loosely by a few notions, and it favors more generalizable statements. Lower bounds for lengths of proofs, often regarded as the key issue in proof complexity, are of course covered in detail. However, upper bounds are not neglected: this book also explores the relations between bounded arithmetic theories and proof systems and how they can be used to prove upper bounds on lengths of proofs and simulations among proof systems. It goes on to discuss topics that transcend specific proof systems, allowing for deeper understanding of the fundamental problems of the subject.

This book comprises five parts. The first three contain ten historical essays on important topics: number theory, calculus/analysis, and proof, respectively. Part four deals with several historically oriented courses, and Part five provides biographies of five mathematicians who played major roles in the historical events described in the first four parts of the work.

"Excursions in the History of Mathematics" was written with several goals in mind: to arouse mathematics teachers' interest in the history of their subject; to encourage mathematics teachers with at least some knowledge of the history of mathematics to offer courses with a strong historical component; and to provide an historical perspective on a number of basic topics taught in mathematics courses."

"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.

This book is a specialized monograph on the development of the mathematical and computational metatheory of reductive logic and proof-search, areas of logic that are becoming important in computer science. A systematic foundational text on these emerging topics, it includes proof-theoretic, semantic/model-theoretic and algorithmic aspects. The scope ranges from the conceptual background to reductive logic, through its mathematical metatheory, to its modern applications in the computational sciences. Suitable for researchers and graduate students in mathematical, computational and philosophical logic, and in theoretical computer science and artificial intelligence, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism (2nd Edition), Dov M. Gabbay, Mark A. Reynolds, and Marcelo Finger's Temporal Logic Mathematical Foundations and Computational Aspects , J. M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and Nonmonotonic Reasoning , and P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2 .

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.

Computer arithmetic has become so fundamentally embedded into digital design that many engineers are unaware of the many research advances in the area. As a result, they are losing out on emerging opportunities to optimize its use in targeted applications and technologies. In many cases, easily available standard arithmetic hardware might not necessarily be the most efficient implementation strategy. Multiple-Base Number System: Theory and Applications stands apart from the usual books on computer arithmetic with its concentration on the uses and the mathematical operations associated with the recently introduced multiple-base number system (MBNS). The book identifies and explores several diverse and never-before-considered MBNS applications (and their implementation issues) to enhance computation efficiency, specifically in digital signal processing (DSP) and public key cryptography. Despite the recent development and increasing popularity of MBNS as a specialized tool for high-performance calculations in electronic hardware and other fields, no single text has compiled all the crucial, cutting-edge information engineers need to optimize its use. The authors' main goal was to disseminate the results of extensive design research-including much of their own-to help the widest possible audience of engineers, computer scientists, and mathematicians. Dedicated to helping readers apply discoveries in advanced integrated circuit technologies, this single reference is packed with a wealth of vital content previously scattered throughout limited-circulation technical and mathematical journals and papers-resources generally accessible only to researchers and designers working in highly specialized fields. Leveling the informational playing field, this resource guides readers through an in-depth analysis of theory, architectural techniques, and the latest research on the subject, subsequently laying the groundwork users require to begin applying MBNS.