CATEGORY THEORY FOR THE SCIENCES MIT PRESS

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Category Theory For The Sciences

Author : David I. Spivak
ISBN : 9780262028134
Genre : Computers
File Size : 29.23 MB
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An introduction to category theory as a rigorous, flexible, and coherent modeling language that can be used across the sciences.
Category: Computers

Basic Category Theory For Computer Scientists

Author : Benjamin C. Pierce
ISBN : 0262660717
Genre : Computers
File Size : 64.64 MB
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Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts. Contents Tutorial * Applications * Further Reading
Category: Computers

Categories Types And Structures

Author : Andrea Asperti
ISBN : UOM:39015022019742
Genre : Computers
File Size : 75.14 MB
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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.
Category: Computers

Categories And Computer Science

Author : R. F. C. Walters
ISBN : 0521422264
Genre : Computers
File Size : 77.85 MB
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Category Theory has, in recent years, become increasingly important and popular in computer science, and many universities now introduce Category Theory as part of the curriculum for undergraduate computer science students. Here, the theory is developed in a straightforward way, and is enriched with many examples from computer science.
Category: Computers

Category Theory

Author : Steve Awodey
ISBN : 9780191513824
Genre : Mathematics
File Size : 71.63 MB
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This text and reference book on Category Theory, a branch of abstract algebra, is aimed not only at students of Mathematics, but also researchers and students of Computer Science, Logic, Linguistics, Cognitive Science, Philosophy, and any of the other fields that now make use of it. Containing clear definitions of the essential concepts, illuminated with numerous accessible examples, and providing full proofs of all important propositions and theorems, this book aims to make the basic ideas, theorems, and methods of Category Theory understandable to this broad readership. Although it assumes few mathematical pre-requisites, the standard of mathematical rigour is not compromised. The material covered includes the standard core of categories; functors; natural transformations; equivalence; limits and colimits; functor categories; representables; Yoneda's lemma; adjoints; monads.
Category: Mathematics

Linguistic Categories Auxiliaries And Related Puzzles

Author : F. Heny
ISBN : 9789400969896
Genre : Language Arts & Disciplines
File Size : 67.72 MB
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VIrtually all the papers in these volumes originated in presentations at the Fourth Groningen Round Table, held in July 1980. That conference, organ ized by the Institute for General linguistics of Groningen University was the fourth in an irregular series of meetings devoted to issues of topical interest to linguists. Its predecessor, the Third Round Table, was held in June 1976, and dealt with the semantics of natural language. A selection of the papers was published as Syntax and Semantics 10, Selections from the Third Groningen Round Table, ed. by F. Heny and H. Schnelle, Academic Press, 1979. This fourth meeting was more narrowly focussed. The original intention was to examine the hypothesis of Akrnajian, Steele and Wasow in their paper 'The Category AUX in Universal Grammar', Linguistic Inquiry 10, 1-64. Ultimately the topic was broadened considerably to encompass not only the syntax, semantics and morphology of auxiliaries and related elements, but to tackle the problem (implicit in the original work of Akmajian, Steele and Wasow) of justifying the selection of categories for the analysis of natural language. In the summer of 1979, a workshop and short, informal conference were held at the University of Salzburg, in preparation for the Round Table. These were organized in conjunction with the Summer Institute of the linguistic Society of America. The cooperation of the LSA and of the University of Salzburg, and in particular of the Director of that Institute, Professor Gaberell Drachman, is hereby gratefully acknowledged.
Category: Language Arts & Disciplines

Innovative Assessment For The 21st Century

Author : Valerie J. Shute
ISBN : 1441965300
Genre : Education
File Size : 87.26 MB
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In today’s rapidly changing and information-rich world, students are not acquiring adequate knowledge and skills to prepare them for careers in mathematics, science, and technology with the traditional approach to assessment and instruction. New competencies (e.g., information communication and technology skills) are needed to deal successfully with the deluge of data. In order to accomplish this, new "educationally valuable" skills must be acknowledged and assessed. Toward this end, the skills we value and support for a society producing knowledge workers, not simply service workers, must be identified, together with methods for their measurement. Innovative Assessment for the 21st Century explores the faces of future assessment—and ask hard questions, such as: What would an assessment that captures all of the above attributes look like? Should it be standardized? What is the role of the professional teacher?
Category: Education

Sorting Things Out

Author : Geoffrey C. Bowker
ISBN : 026226160X
Genre : Science
File Size : 24.28 MB
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A revealing and surprising look at how classification systems can shape both worldviews and social interactions. What do a seventeenth-century mortality table (whose causes of death include "fainted in a bath," "frighted," and "itch"); the identification of South Africans during apartheid as European, Asian, colored, or black; and the separation of machine- from hand-washables have in common? All are examples of classification—the scaffolding of information infrastructures. In Sorting Things Out, Geoffrey C. Bowker and Susan Leigh Star explore the role of categories and standards in shaping the modern world. In a clear and lively style, they investigate a variety of classification systems, including the International Classification of Diseases, the Nursing Interventions Classification, race classification under apartheid in South Africa, and the classification of viruses and of tuberculosis. The authors emphasize the role of invisibility in the process by which classification orders human interaction. They examine how categories are made and kept invisible, and how people can change this invisibility when necessary. They also explore systems of classification as part of the built information environment. Much as an urban historian would review highway permits and zoning decisions to tell a city's story, the authors review archives of classification design to understand how decisions have been made. Sorting Things Out has a moral agenda, for each standard and category valorizes some point of view and silences another. Standards and classifications produce advantage or suffering. Jobs are made and lost; some regions benefit at the expense of others. How these choices are made and how we think about that process are at the moral and political core of this work. The book is an important empirical source for understanding the building of information infrastructures.
Category: Science

A New Foundation For Representation In Cognitive And Brain Science

Author : Jaime Gómez-Ramirez
ISBN : 9789400777385
Genre : Medical
File Size : 51.96 MB
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The purpose of the book is to advance in the understanding of brain function by defining a general framework for representation based on category theory. The idea is to bring this mathematical formalism into the domain of neural representation of physical spaces, setting the basis for a theory of mental representation, able to relate empirical findings, uniting them into a sound theoretical corpus. The innovative approach presented in the book provides a horizon of interdisciplinary collaboration that aims to set up a common agenda that synthesizes mathematical formalization and empirical procedures in a systemic way. Category theory has been successfully applied to qualitative analysis, mainly in theoretical computer science to deal with programming language semantics. Nevertheless, the potential of category theoretic tools for quantitative analysis of networks has not been tackled so far. Statistical methods to investigate graph structure typically rely on network parameters. Category theory can be seen as an abstraction of graph theory. Thus, new categorical properties can be added into network analysis and graph theoretic constructs can be accordingly extended in more fundamental basis. By generalizing networks using category theory we can address questions and elaborate answers in a more fundamental way without waiving graph theoretic tools. The vital issue is to establish a new framework for quantitative analysis of networks using the theory of categories, in which computational neuroscientists and network theorists may tackle in more efficient ways the dynamics of brain cognitive networks. The intended audience of the book is researchers who wish to explore the validity of mathematical principles in the understanding of cognitive systems. All the actors in cognitive science: philosophers, engineers, neurobiologists, cognitive psychologists, computer scientists etc. are akin to discover along its pages new unforeseen connections through the development of concepts and formal theories described in the book. Practitioners of both pure and applied mathematics e.g., network theorists, will be delighted with the mapping of abstract mathematical concepts in the terra incognita of cognition.
Category: Medical

Interactive Learning For Innovation

Author : B. Asheim
ISBN : 9780230362420
Genre : Business & Economics
File Size : 82.38 MB
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This volume highlights the importance of interactive, practice-based learning as a means to promote more thorough innovation dynamics in regional and national economies. Successful experiences in Scandanavia and southern European countries are examined, with insightful policy lessons extracted from each case.
Category: Business & Economics