Spectral spaces are a class of topological spaces. They are a tool linking algebraic structures, in a very wide sense, with geometry. They were invented to give a functional representation of Boolean algebras and distributive lattices and subsequently gained great prominence as a consequence of Grothendieck's invention of schemes. There are more than 1,000 research articles about spectral spaces, but this is the first monograph. It provides an introduction to the subject and is a unified treatment of results scattered across the literature, filling in gaps and showing the connections between different results. The book includes new research going beyond the existing literature, answering questions that naturally arise from this comprehensive approach. The authors serve graduates by starting gently with the basics. For experts, they lead them to the frontiers of current research, making this book a valuable reference source.

This fourth volume in Vladimir Tkachuk's series on Cp-theory gives reasonably complete coverage of the theory of functional equivalencies through 500 carefully selected problems and exercises. By systematically introducing each of the major topics of Cp-theory, the book is intended to bring a dedicated reader from basic topological principles to the frontiers of modern research. The book presents complete and up-to-date information on the preservation of topological properties by homeomorphisms of function spaces. An exhaustive theory of t-equivalent, u-equivalent and l-equivalent spaces is developed from scratch. The reader will also find introductions to the theory of uniform spaces, the theory of locally convex spaces, as well as the theory of inverse systems and dimension theory. Moreover, the inclusion of Kolmogorov's solution of Hilbert's Problem 13 is included as it is needed for the presentation of the theory of l-equivalent spaces. This volume contains the most important classical results on functional equivalencies, in particular, Gul'ko and Khmyleva's example of non-preservation of compactness by t-equivalence, Okunev's method of constructing l-equivalent spaces and the theorem of Marciszewski and Pelant on u-invariance of absolute Borel sets.

Is college worth the cost? Should I worry about arsenic in my rice? Can we recycle pollution? Real questions of personal finance, public health, and social policy require sober, data-driven analyses. This unique text provides students with the tools of quantitative reasoning to answer such questions. The text models how to clarify the question, recognize and avoid bias, isolate relevant factors, gather data, and construct numerical analyses for interpretation. Themes and techniques are repeated across chapters, with a progression in mathematical sophistication over the course of the book, which helps the student get comfortable with the process of thinking in numbers. This textbook includes references to source materials and suggested further reading, making it user-friendly for motivated undergraduate students. The many detailed problems and worked solutions in the text and extensive appendices help the reader learn mathematical areas such as algebra, functions, graphs, and probability. End-of-chapter problem material provides practice for students, and suggested projects are provided with each chapter. A solutions manual is available online for instructors.

Is college worth the cost? Should I worry about arsenic in my rice? Can we recycle pollution? Real questions of personal finance, public health, and social policy require sober, data-driven analyses. This unique text provides students with the tools of quantitative reasoning to answer such questions. The text models how to clarify the question, recognize and avoid bias, isolate relevant factors, gather data, and construct numerical analyses for interpretation. Themes and techniques are repeated across chapters, with a progression in mathematical sophistication over the course of the book, which helps the student get comfortable with the process of thinking in numbers. This textbook includes references to source materials and suggested further reading, making it user-friendly for motivated undergraduate students. The many detailed problems and worked solutions in the text and extensive appendices help the reader learn mathematical areas such as algebra, functions, graphs, and probability. End-of-chapter problem material provides practice for students, and suggested projects are provided with each chapter. A solutions manual is available online for instructors.

Take an apple and cut it into five pieces. Would you believe that these five pieces can be reassembled in such a fashion so as to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, author of The Pea and the Sun, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Written in an engaging style, The Pea and the Sun catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox. Wapner makes one of the most interesting problems of advanced mathematics accessible to the non-mathematician.

The notion of an ( ,1)-category has become widely used in homotopy theory, category theory, and in a number of applications. There are many different approaches to this structure, all of them equivalent, and each with its corresponding homotopy theory. This book provides a relatively self-contained source of the definitions of the different models, the model structure (homotopy theory) of each, and the equivalences between the models. While most of the current literature focusses on how to extend category theory in this context, and centers in particular on the quasi-category model, this book offers a balanced treatment of the appropriate model structures for simplicial categories, Segal categories, complete Segal spaces, quasi-categories, and relative categories, all from a homotopy-theoretic perspective. Introductory chapters provide background in both homotopy and category theory and contain many references to the literature, thus making the book accessible to graduates and to researchers in related areas.

Descriptive complexity theory establishes a connection between the computational complexity of algorithmic problems (the computational resources required to solve the problems) and their descriptive complexity (the language resources required to describe the problems). This groundbreaking book approaches descriptive complexity from the angle of modern structural graph theory, specifically graph minor theory. It develops a 'definable structure theory' concerned with the logical definability of graph theoretic concepts such as tree decompositions and embeddings. The first part starts with an introduction to the background, from logic, complexity, and graph theory, and develops the theory up to first applications in descriptive complexity theory and graph isomorphism testing. It may serve as the basis for a graduate-level course. The second part is more advanced and mainly devoted to the proof of a single, previously unpublished theorem: properties of graphs with excluded minors are decidable in polynomial time if, and only if, they are definable in fixed-point logic with counting.

Computer users have a significant impact on the security of their computer and personal information as a result of the actions they perform (or do not perform). Helping the average user of computers, or more broadly information technology, make sound security decisions, Computer Security Literacy: Staying Safe in a Digital World focuses on practical security topics that users are likely to encounter on a regular basis. Written for nontechnical readers, the book provides context to routine computing tasks so that readers better understand the function and impact of security in everyday life. The authors offer practical computer security knowledge on a range of topics, including social engineering, email, and online shopping, and present best practices pertaining to passwords, wireless networks, and suspicious emails. They also explain how security mechanisms, such as antivirus software and firewalls, protect against the threats of hackers and malware. While information technology has become interwoven into almost every aspect of daily life, many computer users do not have practical computer security knowledge. This hands-on, in-depth guide helps anyone interested in information technology to better understand the practical aspects of computer security and successfully navigate the dangers of the digital world.

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 eleventh publication in the Lecture Notes in Logic series, collects the proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic, held in 1995. It includes papers in the core areas of set theory, model theory, proof theory and recursion theory, as well as the more recent topics of finite model theory and non-monotonic logic. It also includes a tutorial on interactive proofs, zero-knowledge and computationally sound proofs that reported on recent developments in theoretical computer science, and three plenary lectures dedicated to the foundational and technical evolution of set theory over the past 100 years.

This book constitutes the proceedings of the 12th International Conference on Cellular Automata for Research and Industry, ACRI 2016, held in Fez, Morocco, in September 2014. The 45 full papers and 4 invited talks presented in this volume were carefully reviewed and selected from 59 submissions. This volume contains invited contributions and accepted papers from the main track and from the three organized workshops. The first part is organized according to three topics: (1) Cellular Automata Theory and Implementation (2) Cellular Automata Dynamics and Synchronization, (3) Asynchronous Cellular Automata and Asynchronous Discrete Models - ACA. The second part of the volume contains three topics: (4) Modelling and Sim-ulation with Cellular Automata (5) Crowds, Traffic and Cellular Automata -CT&CA (6) Agent-Based Simulation and Cellular Automata - ABS&CA.

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 fifth publication in the Perspectives in Logic series, studies set-theoretic independence results (independence from the usual set-theoretic ZFC axioms), in particular for problems on the continuum. The author gives a complete presentation of the theory of proper forcing and its relatives, starting from the beginning and avoiding the metamathematical considerations. No prior knowledge of forcing is required. The book will enable a researcher interested in an independence result of the appropriate kind to have much of the work done for them, thereby allowing them to quote general results.

Fascinating connections exist between group theory and automata theory, and a wide variety of them are discussed in this text. Automata can be used in group theory to encode complexity, to represent aspects of underlying geometry on a space on which a group acts, and to provide efficient algorithms for practical computation. There are also many applications in geometric group theory. The authors provide background material in each of these related areas, as well as exploring the connections along a number of strands that lead to the forefront of current research in geometric group theory. Examples studied in detail include hyperbolic groups, Euclidean groups, braid groups, Coxeter groups, Artin groups, and automata groups such as the Grigorchuk group. This book will be a convenient reference point for established mathematicians who need to understand background material for applications, and can serve as a textbook for research students in (geometric) group 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. This volume, the sixth publication in the Lecture Notes in Logic series, collects the proceedings of the conference 'Logical Foundations of Mathematics, Computer Science, and Physics - Kurt Goedel's Legacy', held in Brno, Czech Republic, on the 90th anniversary of Goedel's birth. The broad range of speakers who participated in this event affirms the continuing importance of Goedel's work in logic, physics, and the philosophy and foundations of mathematics and computer science. The papers in this volume range over all these topics and contribute to our present understanding of them.

The logician Kurt Goedel (1906-1978) published a paper in 1931 formulating what have come to be known as his 'incompleteness theorems', which prove, among other things, that within any formal system with resources sufficient to code arithmetic, questions exist which are neither provable nor disprovable on the basis of the axioms which define the system. These are among the most celebrated results in logic today. In this volume, leading philosophers and mathematicians assess important aspects of Goedel's work on the foundations and philosophy of mathematics. Their essays explore almost every aspect of Godel's intellectual legacy including his concepts of intuition and analyticity, the Completeness Theorem, the set-theoretic multiverse, and the state of mathematical logic today. This groundbreaking volume will be invaluable to students, historians, logicians and philosophers of mathematics who wish to understand the current thinking on these issues.

Logic is a field studied mainly by researchers and students of philosophy, mathematics and computing. Inductive logic seeks to determine the extent to which the premisses of an argument entail its conclusion, aiming to provide a theory of how one should reason in the face of uncertainty. It has applications to decision making and artificial intelligence, as well as how scientists should reason when not in possession of the full facts. In this book, Jon Williamson embarks on a quest to find a general, reasonable, applicable inductive logic (GRAIL), all the while examining why pioneers such as Ludwig Wittgenstein and Rudolf Carnap did not entirely succeed in this task. Along the way he presents a general framework for the field, and reaches a new inductive logic, which builds upon recent developments in Bayesian epistemology (a theory about how strongly one should believe the various propositions that one can express). The book explores this logic in detail, discusses some key criticisms, and considers how it might be justified. Is this truly the GRAIL? Although the book presents new research, this material is well suited to being delivered as a series of lectures to students of philosophy, mathematics, or computing and doubles as an introduction to the field of inductive logic

This book constitutes the revised selected papers from the 12th International Conference on Formal Aspects of Component Software, FACS 2015, held in Niteroi, Brazil, in October 2015. The 15 full papers and 2 invited papers presented in this volume were carefully reviewed and selected from 33 submissions. They are organized in topical sections, namely quality of service to withstand faults, component-based software development through research on mathematical models for components, composition and adaptation; rigorous approaches to verification, deployment, testing, and certification.

This book constitutes the proceedings of the 15th International Conference on Relational and Algebraic Methods in Computer Science, RAMiCS 2015, held in Braga, Portugal, in September/October 2015. The 20 revised full papers and 3 invited papers presented were carefully selected from 25 submissions. The papers deal with the theory of relation algebras and Kleene algebras, process algebras; fixed point calculi; idempotent semirings; quantales, allegories, and dynamic algebras; cylindric algebras, and about their application in areas such as verification, analysis and development of programs and algorithms, algebraic approaches to logics of programs, modal and dynamic logics, interval and temporal logics.

This title links two of the most dominant research streams in philosophy of logic, namely game theory and proof theory. As the work's subtitle expresses, the authors will build this link by means of the dialogical approach to logic. One important aspect of the present study is that the authors restrict themselves to the logically valid fragment of Constructive Type Theory (CTT). The reason is that, once that fragment is achieved the result can be extended to cover the whole CTT system. The first chapters in the brief offer overviews on the two frameworks discussed in the book with an emphasis on the dialogical framework. The third chapter demonstrates the left-to-right direction of the equivalence result. This is followed by a chapter that demonstrates the use of the algorithm in showing how to transform a specific winning strategy into a CCT-demonstration of the axiom of choice. The fifth chapter develops the algorithm from CTT-demonstrations to dialogical strategies. This brief concludes by introducing elements of discussion which are to be developed in subsequent work.

This Festschrift is published in honor of Yuri Gurevich's 75th birthday. Yuri Gurevich has made fundamental contributions on the broad spectrum of logic and computer science, including decision procedures, the monadic theory of order, abstract state machines, formal methods, foundations of computer science, security, and much more. Many of these areas are reflected in the 20 articles in this Festschrift and in the presentations at the "Yurifest" symposium, which was held in Berlin, Germany, on September 11 and 12, 2015. The Yurifest symposium was co-located with the 24th EACSL Annual Conference on Computer Science Logic (CSL 2015).

This book constitutes the thoroughly refereed post-workshop proceedings of the 10th International Workshop on Automated Deduction in Geometry, ADG 2014, held in Coimbra, Portugal, in July 2014. The 11 revised full papers presented in this volume were carefully selected from 20 submissions. The papers show the trend set of current research in automated reasoning in geometry.

This book provides an argumentation model for means end-reasoning, a distinctive type of reasoning used for problem-solving and decision-making. Means end-reasoning is modelled as goal-directed argumentation from an agent's goals and known circumstances, and from an action selected as a means, to a decision to carry out the action. Goal-based Reasoning for Argumentation provides an argumentation model of this kind of reasoning showing how it is employed in settings of intelligent deliberation where agents try to collectively arrive at a conclusion on what they should do to move forward in a set of circumstances. The book explains how this argumentation model can help build more realistic computational systems of deliberation and decision-making, and shows how such systems can be applied to solve problems posed by goal-based reasoning in numerous fields, from social psychology and sociology, to law, political science, anthropology, cognitive science, artificial intelligence, multi-agent systems, and robotics.