# Download Ebook Free Realizability: An Introduction To Its Categorical Side

## Realizability

Publisher : Elsevier

Release Date : 2008-04-10

Category : Mathematics

Total pages :328

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Aimed at starting researchers in the field, Realizability gives a rigorous, yet reasonable introduction to the basic concepts of a field which has passed several successive phases of abstraction. Material from previously unpublished sources such as Ph.D. theses, unpublished papers, etc. has been molded into one comprehensive presentation of the subject area. - The first book to date on this subject area - Provides an clear introduction to Realizability with a comprehensive bibliography - Easy to read and mathematically rigorous - Written by an expert in the field

## Theory and Applications of Models of Computation

Publisher : Springer

Release Date : 2017-04-13

Category : Mathematics

Total pages :698

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This book constitutes the refereed proceedings of the 14th Annual Conference on Theory and Applications of Models of Computation, TAMC 2017, held in Bern, Switzerland, in April 2017. The 45 revised full papers presented together with 4 invited papers were carefully reviewed and selected from 103 submissions. The main themes of TAMC 2017 have been computability, computer science logic, complexity, algorithms, and models of computation and systems theory.

## Joachim Lambek: The Interplay of Mathematics, Logic, and Linguistics

Publisher : Springer Nature

Release Date : 2021-04-21

Category : Philosophy

Total pages :432

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This book is dedicated to the life and work of the mathematician Joachim Lambek (1922–2014). The editors gather together noted experts to discuss the state of the art of various of Lambek’s works in logic, category theory, and linguistics and to celebrate his contributions to those areas over the course of his multifaceted career. After early work in combinatorics and elementary number theory, Lambek became a distinguished algebraist (notably in ring theory). In the 1960s, he began to work in category theory, categorical algebra, logic, proof theory, and foundations of computability. In a parallel development, beginning in the late 1950s and for the rest of his career, Lambek also worked extensively in mathematical linguistics and computational approaches to natural languages. He and his collaborators perfected production and type grammars for numerous natural languages. Lambek grammars form an early noncommutative precursor to Girard’s linear logic. In a surprising development (2000), he introduced a novel and deeper algebraic framework (which he called pregroup grammars) for analyzing natural language, along with algebraic, higher category, and proof-theoretic semantics. This book is of interest to mathematicians, logicians, linguists, and computer scientists.

## A Computable Universe

Publisher : World Scientific

Release Date : 2013

Category : Mathematics

Total pages :810

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This volume discusses the foundations of computation in relation to nature. It focuses on two main questions: What is computation? and How does nature compute?

## Sets, Models and Proofs

Publisher : Springer

Release Date : 2018-11-23

Category : Mathematics

Total pages :141

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This textbook provides a concise and self-contained introduction to mathematical logic, with a focus on the fundamental topics in first-order logic and model theory. Including examples from several areas of mathematics (algebra, linear algebra and analysis), the book illustrates the relevance and usefulness of logic in the study of these subject areas. The authors start with an exposition of set theory and the axiom of choice as used in everyday mathematics. Proceeding at a gentle pace, they go on to present some of the first important results in model theory, followed by a careful exposition of Gentzen-style natural deduction and a detailed proof of Gödel’s completeness theorem for first-order logic. The book then explores the formal axiom system of Zermelo and Fraenkel before concluding with an extensive list of suggestions for further study. The present volume is primarily aimed at mathematics students who are already familiar with basic analysis, algebra and linear algebra. It contains numerous exercises of varying difficulty and can be used for self-study, though it is ideally suited as a text for a one-semester university course in the second or third year.

## Foundations of Secure Computation

Publisher : Unknown

Release Date : 2000

Category : Computer security

Total pages :319

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## Mathematical Reviews

Publisher : Unknown

Release Date : 2003-05

Category : Mathematics

Total pages :129

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## Handbook of Algebraic Topology

Publisher : Elsevier

Release Date : 1995-07-18

Category : Mathematics

Total pages :1324

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Algebraic topology (also known as homotopy theory) is a flourishing branch of modern mathematics. It is very much an international subject and this is reflected in the background of the 36 leading experts who have contributed to the Handbook. Written for the reader who already has a grounding in the subject, the volume consists of 27 expository surveys covering the most active areas of research. They provide the researcher with an up-to-date overview of this exciting branch of mathematics.

## Categories, Types, and Structures

Publisher : Mit Press

Release Date : 1991

Category : Computers

Total pages :306

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Category theory is a mathematical subject whose importance in several areas of computer science, most notably the semantics of programming languages and the design of programmes using abstract data types, is widely acknowledged. This book introduces category theory at a level appropriate for computer scientists and provides practical examples in the context of programming language design.

## An Introduction to Neural Networks

Publisher : CRC Press

Release Date : 2018-10-08

Category : Computers

Total pages :234

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Though mathematical ideas underpin the study of neural networks, the author presents the fundamentals without the full mathematical apparatus. All aspects of the field are tackled, including artificial neurons as models of their real counterparts; the geometry of network action in pattern space; gradient descent methods, including back-propagation; associative memory and Hopfield nets; and self-organization and feature maps. The traditionally difficult topic of adaptive resonance theory is clarified within a hierarchical description of its operation. The book also includes several real-world examples to provide a concrete focus. This should enhance its appeal to those involved in the design, construction and management of networks in commercial environments and who wish to improve their understanding of network simulator packages. As a comprehensive and highly accessible introduction to one of the most important topics in cognitive and computer science, this volume should interest a wide range of readers, both students and professionals, in cognitive science, psychology, computer science and electrical engineering.

## Content Analysis

Publisher : SAGE

Release Date : 2004

Category : Language Arts & Disciplines

Total pages :413

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The Second Edition of Content Analysis: An Introduction to Its Methodology is a definitive sourcebook of the history and core principles of content analysis as well as an essential resource for present and future studies. The book introduces readers to ways of analyzing meaningful matter such as texts, images, voices – that is, data whose physical manifestations are secondary to the meanings that a particular population of people brings to them. Organized into three parts, the book examines the conceptual and methodological aspects of content analysis and also traces several paths through content analysis protocols. The author has completely revised and updated the Second Edition, integrating new information on computer-aided text analysis. The book also includes a practical guide that incorporates experiences in teaching and how to advise academic and commercial researchers. In addition, Krippendorff clarifies the epistemology and logic of content analysis as well as the methods for achieving its aims. Intended as a textbook for advanced undergraduate and graduate students across the social sciences, Content Analysis, Second Edition will also be a valuable resource for practitioners in a variety of disciplines.

## Semihypergroup Theory

Publisher : Academic Press

Release Date : 2016-06-24

Category : Mathematics

Total pages :164

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Semihypergroup Theory is the first book devoted to the semihypergroup theory and it includes basic results concerning semigroup theory and algebraic hyperstructures, which represent the most general algebraic context in which reality can be modelled. Hyperstructures represent a natural extension of classical algebraic structures and they were introduced in 1934 by the French mathematician Marty. Since then, hundreds of papers have been published on this subject. Offers the first book devoted to the semihypergroup theory Presents an introduction to recent progress in the theory of semihypergroups Covers most of the mathematical ideas and techniques required in the study of semihypergroups Employs the notion of fundamental relations to connect semihypergroups to semigroups

## The Optimal Implementation of Functional Programming Languages

Publisher : Cambridge University Press

Release Date : 1998-12-03

Category : Computers

Total pages :392

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First account of the subject by two of its leading exponents. Essentially self-contained.

## Conceptual Mathematics

Publisher : Cambridge University Press

Release Date : 2009-07-30

Category : Mathematics

Total pages :390

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In the last 60 years, the use of the notion of category has led to a remarkable unification and simplification of mathematics. Conceptual Mathematics introduces this tool for the learning, development, and use of mathematics, to beginning students and also to practising mathematical scientists. This book provides a skeleton key that makes explicit some concepts and procedures that are common to all branches of pure and applied mathematics. The treatment does not presuppose knowledge of specific fields, but rather develops, from basic definitions, such elementary categories as discrete dynamical systems and directed graphs; the fundamental ideas are then illuminated by examples in these categories. This second edition provides links with more advanced topics of possible study. In the new appendices and annotated bibliography the reader will find concise introductions to adjoint functors and geometrical structures, as well as sketches of relevant historical developments.

## Equality and Liberty

Publisher : Springer

Release Date : 2016-07-27

Category : Political Science

Total pages :397

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Equality and Liberty: Analysing Rawls and Nozick is an indispensable source for those seriously interested in some rigorous assessments of the ideas of America's two most popular political philosophers. The essays in this volume cover a wide range of topics, some engaging each other in their analyses of particular Rawlsian or Nozickian themes. This collection of recent essays brings the student up-to-date concerning some of the more recent developments and assessments of Rawlsian and Nozickian ideas.