Programming

Design patterns are the cutting-edge paradigm for programming in C++, and they are here discussed in depth using examples from financial mathematics. Assuming only a basic knowledge of C++ and mathematical finance, the reader learns how to produce well-designed, structured, reusable code via carefully-chosen examples. This new edition includes several new chapters covering topics of increasing robustness in the presence of exceptions, designing a generic factory, interfacing C++ with EXCEL, and improving code design using the idea of decoupling. Complete ANSI/ISO compatible C++ source code is hosted on an accompanying website for the reader to study in detail, and reuse as they see fit. Whether you are a student of financial mathematics, a working quantitative analyst or financial mathematician, you need this book. Offering practical steps for implementing pricing models for complex financial products, it will transform your understanding of how to use C++.

Type theory is one of the most important tools in the design of higher-level programming languages, such as ML. This book introduces and teaches its techniques by focusing on one particularly neat system and studying it in detail. In this way, all the key ideas are covered without getting involved in the complications of more advanced systems, but concentrating rather on the principles that make the theory work in practice. This book takes a type-assignment approach to type theory, and the system considered is the simplest polymorphic one. The author covers all the basic ideas, including the system's relation to propositional logic, and gives a careful treatment of the type-checking algorithm which lies at the heart of every such system. Also featured are two other interesting algorithms that have been buried in inaccessible technical literature. The mathematical presentation is rigorous but clear, making the book at a level which can be used as an introduction to type theory for comp

Power grids, flexible manufacturing, cellular communications: interconnectedness has consequences. This remarkable book gives the tools and philosophy you need to build network models detailed enough to capture essential dynamics but simple enough to expose the structure of effective control solutions. Core chapters assume only exposure to stochastic processes and linear algebra at undergraduate level; later chapters are for advanced graduate students and researchers/practitioners. This gradual development bridges classical theory with the state-of-the-art. The workload model at the heart of traditional analysis of the single queue becomes a foundation for workload relaxations used in the treatment of complex networks. Lyapunov functions and dynamic programming equations lead to the celebrated MaxWeight policy along with many generalizations. Other topics include methods for synthesizing hedging and safety stocks, stability theory for networks, and techniques for accelerated simulation

This book teaches model-based analysis and model-based testing, with important new ways to write and analyze software specifications and designs, generate test cases, and check the results of test runs. These methods increase the automation in each of these steps, making them more timely, more thorough, and more effective. Using a familiar programming language, testers and analysts will learn to write models that describe how a program is supposed to behave. The authors work through several realistic case studies in depth and detail, using a toolkit built on the C# language and the .NET framework. Readers can also apply the methods in analyzing and testing systems in many other languages and frameworks. Intended for professional software developers including testers, and for university students, this book is suitable for courses on software engineering, testing, specification, or applications of formal methods.

This book teaches model-based analysis and model-based testing, with important new ways to write and analyze software specifications and designs, generate test cases, and check the results of test runs. These methods increase the automation in each of these steps, making them more timely, more thorough, and more effective. Using a familiar programming language, testers and analysts will learn to write models that describe how a program is supposed to behave. The authors work through several realistic case studies in depth and detail, using a toolkit built on the C# language and the .NET framework. Readers can also apply the methods in analyzing and testing systems in many other languages and frameworks. Intended for professional software developers including testers, and for university students, this book is suitable for courses on software engineering, testing, specification, or applications of formal methods.

This book/CD bundle of the greatly expanded third edition of Numerical Recipes now has wider coverage than ever before, many new, expanded and updated sections, and two completely new chapters. Co-authored by four leading scientists from academia and industry, Numerical Recipes starts with basic mathematics and computer science and proceeds to complete, working routines. The informal, easy-to-read style that made earlier editions so popular is kept throughout. Highlights of the new material include: a new chapter on classification and inference, Gaussian mixture models, HMMs, hierarchical clustering, and SVMs; a new chapter on computational geometry, covering KD trees, quad- and octrees, Delaunay triangulation, and algorithms for lines, polygons, triangles, and spheres; interior point methods for linear programming; MCMC; an expanded treatment of ODEs with completely new routines; and many new statistical distributions. For support or further licence information please visit www.nr.com

Students of evolutionary and behavioural ecology are often unfamiliar with mathematical techniques, though much of biology relies on mathematics. Evolutionary ideas are often complex, meaning that the logic of hypotheses proposed should not only be tested empirically but also mathematically. There are numerous different modelling tools used by ecologists, ranging from population genetic 'bookkeeping', to game theory and individual-based computer simulations. Due to the many different modelling options available, it is often difficult to know where to start. Hanna Kokko has designed this 2007 book to help with these decisions. Each method described is illustrated with one or two biologically interesting examples that have been chosen to help overcome fears of many biologists when faced with mathematical work, whilst also providing the programming code (Matlab) for each problem. Aimed primarily at students of evolutionary and behavioural ecology, this book will be of interest to any biol

Students of evolutionary and behavioural ecology are often unfamiliar with mathematical techniques, though much of biology relies on mathematics. Evolutionary ideas are often complex, meaning that the logic of hypotheses proposed should not only be tested empirically but also mathematically. There are numerous different modelling tools used by ecologists, ranging from population genetic 'bookkeeping', to game theory and individual-based computer simulations. Due to the many different modelling options available, it is often difficult to know where to start. Hanna Kokko has designed this 2007 book to help with these decisions. Each method described is illustrated with one or two biologically interesting examples that have been chosen to help overcome fears of many biologists when faced with mathematical work, whilst also providing the programming code (Matlab) for each problem. Aimed primarily at students of evolutionary and behavioural ecology, this book will be of interest to any biol

What meanings do buildings and places convey to the people who use and visit them? Too often, design competitions and signature architecture result in costly eyesores that do not work. How can sponsors and clients get more meaningful results? In answer to these questions, Dr Nasar, supported by riveting studies of competitions and Peter Eisenman's competition-winning design for the Wexner Center at the Ohio State University, suggests the use of pre-jury evaluation (PJE). He shows the potential value of this approach as well as visual quality programming for many kinds of environmental design for which the client wants to convey certain desirable meanings. The studies, from those specific to the Wexner Center to those covering the scope of history, point to an alternative method for shaping the visual form of buildings, places and cities.

The core of scientific computing is designing, writing, testing, debugging and modifying numerical software for application to a vast range of areas: from graphics, meteorology and chemistry to engineering, biology and finance. Scientists, engineers and computer scientists need to write good code, for speed, clarity, flexibility and ease of re-use. Oliveira and Stewart's style guide for numerical software points out good practices to follow, and pitfalls to avoid. By following their advice, readers will learn how to write efficient software, and how to test it for bugs, accuracy and performance. Techniques are explained with a variety of programming languages, and illustrated with two extensive design examples, one in Fortran 90 and one in C++: other examples in C, C++, Fortran 90 and Java are scattered throughout the book. This manual of scientific computing style will be an essential addition to the bookshelf and lab of everyone who writes numerical software.

Input-output analysis is the main tool of applied equilibrium analysis. This textbook provides a systematic survey of the most recent developments in input-output analysis and their applications, helping us to examine questions such as: which industries are competitive? What are the multiplier effects of an investment program? How do environmental restrictions impact on prices? Linear programming and national accounting are introduced and used to resolve issues such as the choice of technique, the comparative advantage of a national economy, its efficiency and dynamic performance. Technological and environmental spillovers are analysed, both at the national level (between industries) and the international level (the measurement of globalisation effects). The book is self-contained, but assumes some familiarity with calculus, matrix algebra, and the microeconomic principle of optimizing behaviour. Exercises and review questions are included at the end of each chapter, and solutions at t

The authoritative reference on NEURON, the simulation environment for modeling biological neurons and neural networks that enjoys wide use in the experimental and computational neuroscience communities. This book shows how to use NEURON to construct and apply empirically based models. Written primarily for neuroscience investigators, teachers, and students, it assumes no previous knowledge of computer programming or numerical methods. Readers with a background in the physical sciences or mathematics, who have some knowledge about brain cells and circuits and are interested in computational modeling, will also find it helpful. The NEURON Book covers material that ranges from the inner workings of this program, to practical considerations involved in specifying the anatomical and biophysical properties that are to be represented in models. It uses a problem-solving approach, with many working examples that readers can try for themselves.

This book develops the theory of typed feature structures, a data structure that generalizes both first-order terms and feature structures of unification-based grammars to include inheritance, typing, inequality, cycles and intensionality. The resulting synthesis serves as a logical foundation for grammars, logic programming and constraint-based reasoning systems. A logical perspective is adopted which employs an attribute-value description language along with complete equational axiomatizations of the various systems of feature structures. At the same time, efficiency concerns are kept in mind and complexity and representability results are provided. The application of feature structures to phrase structure grammars is described and completeness results are shown for standard evaluation strategies. Definite clause logic programs are treated as a special case of phrase structure grammars. Constraint systems are introduced and an enumeration technique is developed for solving arbitrary

The B Method is a means for specifying, designing and coding software systems. The long-awaited B-Book is the standard reference for everything concerning this method. It contains the mathematical basis on which it is founded, the precise definitions of the notations used, and a large number of examples illustrating its use in practice. J.-R. Abrial, the inventor of B, has written the book in such a way that it can be used for self-study or for reference. It is in four parts, the first dealing with the mathematical foundations and the definition of the various mathematical structures that are needed to formalise software systems; special emphasis is placed on the notion of proof. The second part contains a presentation of the Generalised Substitution Language and of the Abstract Machine Notation; examples are given to show how large specifications can be constructed systematically. The next part introduces the two basic programming features of sequencing and loop. The last part covers

Seismic Ray Theory presents a comprehensive treatment of the seismic ray method. This method plays an important role in seismology, seismic exploration, and in the interpretation of seismic measurements. Many concepts which extend the possibilities and increase the efficiency of the seismic ray method are included. The book has a tutorial character: derivations start with a relatively simple problem, in which the main ideas are easier to explain, and then advance to more complex problems. Most of the derived equations in the book are expressed in algorithmic form and may be used directly for computer programming. This book will prove to be an invaluable advanced textbook and reference volume in all academic institutions in which seismology is taught or researched. It will also be an invaluable resource in the research and exploration departments of the petroleum industry and in geological surveys.

A central problem in the design of programming systems is to provide methods for verifying that computer code performs to specification. This book presents a rigorous foundation for defining Boolean categories, in which the relationship between specification and behaviour can be explored. Boolean categories provide a rich interface between program constructs and techniques familiar from algebra, for instance matrix- or ideal-theoretic methods. The book's distinction is that the approach relies on only a single program construct (the first-order theory of categories), the others being derived mathematically from four axioms. Development of these axioms (which are obeyed by an abundance of program paradigms) yields Boolean algebras of 'predicates', loop-free constructs, and a calculus of partial and total correctness which is shown to be the standard one of Hoare, Dijkstra, Pratt, and Kozen. The book is based in part on courses taught by the author, and will appeal to graduate students a

Linear logic is a branch of proof theory which provides refined tools for the study of the computational aspects of proofs. These tools include a duality-based categorical semantics, an intrinsic graphical representation of proofs, the introduction of well-behaved non-commutative logical connectives, and the concepts of polarity and focalisation. These various aspects are illustrated here through introductory tutorials as well as more specialised contributions, with a particular emphasis on applications to computer science: denotational semantics, lambda-calculus, logic programming and concurrency theory. The volume is rounded-off by two invited contributions on new topics rooted in recent developments of linear logic. The book derives from a summer school that was the climax of the EU Training and Mobility of Researchers project 'Linear Logic in Computer Science'. It is an excellent introduction to some of the most active research topics in the area.

The book provides a description of the Standard ML (SML) Basis Library, the standard library for the SML language. For programmers using SML, it provides a complete description of the modules, types and functions composing the library, which is supported by all conforming implementations of the language. The book serves as a programmer's reference, providing manual pages with concise descriptions. In addition, it presents the principles and rationales used in designing the library, and relates these to idioms and examples for using the library. A particular emphasis of the library is to encourage the use of SML in serious system programming. Major features of the library include I/O, a large collection of primitive types, support for internationalization, and a portable operating system interface. This manual will be an indispensable reference for students, professional programmers, and language designers.

The book provides a description of the Standard ML (SML) Basis Library, the standard library for the SML language. For programmers using SML, it provides a complete description of the modules, types and functions composing the library, which is supported by all conforming implementations of the language. The book serves as a programmer's reference, providing manual pages with concise descriptions. In addition, it presents the principles and rationales used in designing the library, and relates these to idioms and examples for using the library. A particular emphasis of the library is to encourage the use of SML in serious system programming. Major features of the library include I/O, a large collection of primitive types, support for internationalization, and a portable operating system interface. This manual will be an indispensable reference for students, professional programmers, and language designers.

Recent years have seen the development of powerful tools for verifying hardware and software systems, as companies worldwide realise the need for improved means of validating their products. There is increasing demand for training in basic methods in formal reasoning so that students can gain proficiency in logic-based verification methods. The second edition of this successful textbook addresses both those requirements, by continuing to provide a clear introduction to formal reasoning which is both relevant to the needs of modern computer science and rigorous enough for practical application. Improvements to the first edition have been made throughout, with extra and expanded sections on SAT solvers, existential/universal second-order logic, micro-models, programming by contract and total correctness. The coverage of model-checking has been substantially updated. Further exercises have been added. Internet support for the book includes worked solutions for all exercises for teachers,

This book offers a unique insight into a revolution in software development that allows model specifications to be fully and efficiently translated into code. Using the most widely adopted, industry standard, software modelling language, UML, the reader will learn how to build robust specifications based on OMG's Model Driven Architecture (MDA). From there, the authors describe the steps needed to translate the Executable UML (xUML) models to any platform-specific implementation. The benefits of this approach go well beyond simply reducing or eliminating the coding stage - it also ensures platform independence, avoids obsolescence (programming languages may change, the model doesn't) and allows full verification of the models by executing them in a test and debug xUML environment. This is an excellent reference for anyone embarking on what is surely the future of software development for medium and large scale projects.

The essays in this collection cover the whole range of Irish drama from the late nineteenth-century melodramas which anticipated the rise of the Abbey Theatre to the contemporary Dublin of theatre festivals. A team of international experts from Ireland, the UK, the USA and Europe provide individual studies of internationally known playwrights of the period of the Literary Revival - Yeats, Synge, Lady Gregory, Shaw, Wilde, O'Casey - and contemporary playwrights Brian Friel, Tom Murphy, Frank McGuiness and Sebastian Barry, in addition to emerging playwrights such as Martin McDonagh and Marina Carr. Further to studies of individual playwrights the collection also includes examination of the relationship between the theatre and its political context as this is inflected through its ideology, staging and programming. With a full chronology and bibliography, this collection is an indispensable introduction to one of the world's most vibrant theatre cultures.

This book discusses recent research in the theoretical foundations of several subjects of importance for the design of hardware, and for computer science in general. The physical technologies of very large scale integration (VLSI) are having major effects on the electronic industry. The potential diversity and complexity of digital systems have begun a revolution in the technologies of digital design, involving the application of concepts and methods to do with algorithms and programming. In return, the problems of VLSI design have led to new subjects becoming of importance in computer science. Topics covered in this volume include: models of VLSI complexity; complexity theory; systolic algorithm design; specification theory; verification theory; design by stepwise refinement and transformations. A thorough literature survey with an exhaustive bibliography is also included. The book has grown from a workshop held at the Centre for Theoretical Computer Science at Leeds University and or

In this wide-ranging inside view of the history and practice of conducting, analysis and advice comes directly from working conductors, including Sir Charles Mackerras on opera, Bramwell Tovey on being an Artistic Director, Martyn Brabbins on modern music, Leon Botstein on programming and Vance George on choral conducting, and from those who work closely with conductors: a leading violinist describes working as a soloist with Stokowski, Ormandy and Barbirolli, while Solti and Abbado's studio producer explains orchestral recording, and one of the world's most powerful managers tells all. The book includes advice on how to conduct different types of groups (choral, opera, symphony, early music) and provides a substantial history of conducting as a study of national traditions. It is an unusually honest book about a secretive industry and managers, artistic directors, soloists, players and conductors openly discuss their different perspectives for the first time.

This book describes the use of qualified types to provide a general framework for the combination of polymorphism and overloading. For example, qualified types can be viewed as a generalization of type classes in the functional language Haskell and the theorem prover Isabelle. These in turn are extensions of equality types in Standard ML. Other applications of qualified types include extensible records and subtyping. Using a general formulation of qualified types, the author extends the Damas/Milner type inference algorithm to support qualified types, which in turn specifies the set of all possible types for any term. In addition, he describes a new technique for establishing suitable coherence conditions that guarantee the same semantics for all possible translations of a given term. Practical issues that arise in concrete implementations are also discussed, concentrating in particular on the implementation of overloading in Haskell and Gofer, a small functional programming system dev

Mobile systems, whose components communicate and change their structure, now pervade the informational world and the wider world of which it is a part. The science of mobile systems is as yet immature, however. This book presents the pi-calculus, a theory of mobile systems. The pi-calculus provides a conceptual framework for understanding mobility, and mathematical tools for expressing systems and reasoning about their behaviours. The book serves both as a reference for the theory and as an extended demonstration of how to use pi-calculus to describe systems and analyse their properties. It covers the basic theory of pi-calculus, typed pi-calculi, higher-order processes, the relationship between pi-calculus and lambda-calculus, and applications of pi-calculus to object-oriented design and programming. The book is written at the graduate level, assuming no prior acquaintance with the subject, and is intended for computer scientists interested in mobile systems.

Numerical algorithms, modern programming techniques, and parallel computing are often taught serially across different courses and different textbooks. The need to integrate concepts and tools usually comes only in employment or in research - after the courses are concluded - forcing the student to synthesise what is perceived to be three independent subfields into one. This book provides a seamless approach to stimulate the student simultaneously through the eyes of multiple disciplines, leading to enhanced understanding of scientific computing as a whole. The book includes both basic as well as advanced topics and places equal emphasis on the discretization of partial differential equations and on solvers. Some of the advanced topics include wavelets, high-order methods, non-symmetric systems, and parallelization of sparse systems. The material covered is suited to students from engineering, computer science, physics and mathematics.

Term rewriting systems developed out of mathematical logic and are an important part of theoretical computer science. They consist of sequences of discrete transformation steps where one term is replaced with another and have applications in many areas, from functional programming to automatic theorem proving and computer algebra. This 2003 book starts at an elementary level with the earlier chapters providing a foundation for the rest of the work. Much of the advanced material appeared here for the first time in book form. Subjects treated include orthogonality, termination, completion, lambda calculus, higher-order rewriting, infinitary rewriting and term graph rewriting. Many exercises are included with selected solutions provided on the web. A comprehensive bibliography makes this book ideal both for teaching and research. A chapter is included presenting applications of term rewriting systems, with many pointers to actual implementations.

Information content and programming semantics are just two of the applications of the mathematical concepts of order, continuity and domains. The authors develop the mathematical foundations of partially ordered sets with completeness properties of various degrees, in particular directed complete ordered sets and complete lattices. Uniquely, they focus on partially ordered sets that have an extra order relation, modelling the notion that one element 'finitely approximates' another, something closely related to intrinsic topologies linking order and topology. Extensive use is made of topological ideas, both by defining useful topologies on the structures themselves and by developing close connections with numerous aspects of topology. The theory so developed not only has applications to computer science but also within mathematics to such areas as analysis, the spectral theory of algebras and the theory of computability. This authoritative, comprehensive account of the subject will be e

This book introduces a new, unique, and far-reaching industry technology, Business Service Orchestration (BSO). BSO encompasses the art of orchestrating the interactions between business services. These business services may represent internal business processes of organizations. Integration of many of these internal legacy, custom and COTS applications may, in turn, create these services. This book focuses on the importance of orchestration and how it enables IT professionals to develop and design highly effective and efficient business systems of the future. The book is divided into three major sections. Section I provides a detailed overview of business services and their orchestration and describes an in-depth architecture necessary to provide a web of business services, and orchestration of their interactions, including a methodology for modeling the BSO. Section II focuses on technologies necessary to orchestrate business services, ranging from component models to programming lan

This book explains the financial appraisal of capital budgeting projects. The coverage extends from the development of basic concepts, principles and techniques to the application of them in increasingly complex and real-world situations. Identification and estimation (including forecasting) of cash flows, project appraisal formulae, and the application of net present value (NPV), internal rate of return (IRR) and other project evaluation criteria are illustrated with a variety of calculation examples. Risk analysis is extensively covered by the use of risk adjusted discount rate, certainty equivalent, sensitivity, simulation and Monte Carlo analysis. The NPV and IRR models are further applied to forestry, property and international investments. Resource constraints are introduced to the capital budgeting decisions with a variety of worked examples using linear programming technique. All calculations are extensively supported by Excel workbooks on the Web, and each chapter is well revi

This book explains the financial appraisal of capital budgeting projects. The coverage extends from the development of basic concepts, principles and techniques to the application of them in increasingly complex and real-world situations. Identification and estimation (including forecasting) of cash flows, project appraisal formulae, and the application of net present value (NPV), internal rate of return (IRR) and other project evaluation criteria are illustrated with a variety of calculation examples. Risk analysis is extensively covered by the use of risk adjusted discount rate, certainty equivalent, sensitivity, simulation and Monte Carlo analysis. The NPV and IRR models are further applied to forestry, property and international investments. Resource constraints are introduced to the capital budgeting decisions with a variety of worked examples using linear programming technique. All calculations are extensively supported by Excel workbooks on the Web, and each chapter is well revi

The discrepancy method is the glue that binds randomness and complexity. It is the bridge between randomized computation and discrepancy theory, the area of mathematics concerned with irregularities in distributions. The discrepancy method has played a major role in complexity theory; in particular, it has caused a mini-revolution of sorts in computational geometry. This book tells the story of the discrepancy method in a few short independent vignettes. It is a varied tale which includes such topics as communication complexity, pseudo-randomness, rapidly mixing Markov chains, points on the sphere and modular forms, derandomization, convex hulls, Voronoi diagrams, linear programming and extensions, geometric sampling, VC-dimension theory, minimum spanning trees, linear circuit complexity, and multidimensional searching. The mathematical treatment is thorough and self-contained. In particular, background material in discrepancy theory is supplied as needed. Thus the book should appeal t

This was the first cross-over book into the history of science written by an historian of economics. It shows how 'history of technology' can be integrated with the history of economic ideas. The analysis combines Cold War history with the history of postwar economics in America and later elsewhere, revealing that the Pax Americana had much to do with abstruse and formal doctrines such as linear programming and game theory. It links the literature on 'cyborg' to economics, an element missing in literature to date. The treatment further calls into question the idea that economics has been immune to postmodern currents, arguing that neoclassical economics has participated in the deconstruction of the integral 'self'. Finally, it argues for an alliance of computational and institutional themes, and challenges the widespread impression that there is nothing else besides American neoclassical economic theory left standing after the demise of Marxism.

This was the first cross-over book into the history of science written by an historian of economics. It shows how 'history of technology' can be integrated with the history of economic ideas. The analysis combines Cold War history with the history of postwar economics in America and later elsewhere, revealing that the Pax Americana had much to do with abstruse and formal doctrines such as linear programming and game theory. It links the literature on 'cyborg' to economics, an element missing in literature to date. The treatment further calls into question the idea that economics has been immune to postmodern currents, arguing that neoclassical economics has participated in the deconstruction of the integral 'self'. Finally, it argues for an alliance of computational and institutional themes, and challenges the widespread impression that there is nothing else besides American neoclassical economic theory left standing after the demise of Marxism.

Seismic Ray Theory presents a comprehensive treatment of the seismic ray method. This method plays an important role in seismology, seismic exploration, and in the interpretation of seismic measurements. Many concepts which extend the possibilities and increase the efficiency of the seismic ray method are included. The book has a tutorial character: derivations start with a relatively simple problem, in which the main ideas are easier to explain, and then advance to more complex problems. Most of the derived equations in the book are expressed in algorithmic form and may be used directly for computer programming. This book will prove to be an invaluable advanced textbook and reference volume in all academic institutions in which seismology is taught or researched. It will also be an invaluable resource in the research and exploration departments of the petroleum industry and in geological surveys.

Hardcore JFC is a comprehensive guide to the functionality and practical use of the Java Foundations Classes (JFC), a component library designed for the Java programming language and operating environment. It presents intermediate and advanced techniques in exploiting the power and flexibility of JFC and the Swing component set. The book describes the inner workings of Swing and how its design principles can be used to add tremendous value to Java applications. The important features of JFC components are investigated thoroughly with a focus on the comprehension of fundamentals and the pragmatic application of advanced techniques. Included are concrete illustrations of how to enhance the JFC architecture: leveraging the 'Model/View/Controller' paradigm, customizing and developing new components and techniques for creating 'look and feel' user interface classes. Explanations of design and development techniques are introduced through effective, well-constructed and reusable example code

This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much more complex settings. There are numerous exercises throughout the text. In general, the only prerequisite is a standard course in first-order logic, making the book ideal for graduate students and beginning researchers in mathematical logic, theoretical computer science and artificial intelligence. For the new edition, many sections have been rewritten to improve clarity, new sections have been added on cut elimination, and solutions to sel

The discrepancy method is the glue that binds randomness and complexity. It is the bridge between randomized computation and discrepancy theory, the area of mathematics concerned with irregularities in distributions. The discrepancy method has played a major role in complexity theory; in particular, it has caused a mini-revolution of sorts in computational geometry. This book tells the story of the discrepancy method in a few short independent vignettes. It is a varied tale which includes such topics as communication complexity, pseudo-randomness, rapidly mixing Markov chains, points on the sphere and modular forms, derandomization, convex hulls, Voronoi diagrams, linear programming and extensions, geometric sampling, VC-dimension theory, minimum spanning trees, linear circuit complexity, and multidimensional searching. The mathematical treatment is thorough and self-contained. In particular, background material in discrepancy theory is supplied as needed. Thus the book should appeal t

The pi-calculus differs from other models of communicating behaviour mainly in its treatment of mobility. The movement of a piece of data inside a computer program is treated exactly the same as the transfer of a message - or indeed an entire computer program - across the internet. One can also describe networks which reconfigure themselves. The calculus is very simple but powerful; its most prominent ingredient is the notion of a name. Its theory has two important ingredients: the concept of behavioural (or observational) equivalence, and the use of a new theory of types to classify patterns of interactive behaviour. The internet, and its communication protocols, fall within the scope of the theory just as much as computer programs, data structures, algorithms and programming languages. This book is the first textbook on the subject; it has been long-awaited by professionals and will be welcomed by them, and their students.