Category Theory For The Sciences Mit Press

Author: David I. Spivak
Publisher: The MIT Press
ISBN: 0262028131
Size: 43.20 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 theory was invented in the 1940s to unify and synthesize different areas in mathematics, and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics. This book shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences. Information is inherently dynamic; the same ideas can be organized and reorganized in countless ways, and the ability to translate between such organizational structures is becoming increasingly important in the sciences. Category theory offers a unifying framework for information modeling that can facilitate the translation of knowledge between disciplines. Written in an engaging and straightforward style, and assuming little background in mathematics, the book is rigorous but accessible to non-mathematicians. Using databases as an entry to category theory, it begins with sets and functions, then introduces the reader to notions that are fundamental in mathematics: monoids, groups, orders, and graphs -- categories in disguise. After explaining the "big three" concepts of category theory -- categories, functors, and natural transformations -- the book covers other topics, including limits, colimits, functor categories, sheaves, monads, and operads. The book explains category theory by examples and exercises rather than focusing on theorems and proofs. It includes more than 300 exercises, with solutions. Category Theory for the Sciences is intended to create a bridge between the vast array of mathematical concepts used by mathematicians and the models and frameworks of such scientific disciplines as computation, neuroscience, and physics.


An Introduction To Functional Programming Through Lambda Calculus Dover Books On Mathematics

Author: Greg Michaelson
Publisher: Dover Publications
ISBN: 0486478831
Size: 44.45 MB
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Functional programming is rooted in lambda calculus, which constitutes the world's smallest programming language. This well-respected text offers an accessible introduction to functional programming concepts and techniques for students of mathematics and computer science. The treatment is as nontechnical as possible, and it assumes no prior knowledge of mathematics or functional programming. Cogent examples illuminate the central ideas, and numerous exercises appear throughout the text, offering reinforcement of key concepts. All problems feature complete solutions.

The Structural Transformation Of The Public Sphere An Inquiry Into A Category Of Bourgeois Society Studies In Contemporary German Social Thought

Author: Jürgen Habermas
Publisher: The MIT Press
ISBN: 0262581086
Size: 39.58 MB
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This is Jürgen Habermas's most concrete historical-sociological book and one of the key contributions to political thought in the postwar period. It will be a revelation to those who have known Habermas only through his theoretical writing to find his later interests in problems of legitimation and communication foreshadowed in this lucid study of the origins, nature, and evolution of public opinion in democratic societies.


Basic Category Theory For Computer Scientists Foundations Of Computing

Author: Benjamin C. Pierce
Publisher: The MIT Press
ISBN: 0262660717
Size: 18.35 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. Benjamin C. Pierce received his doctoral degree from Carnegie Mellon University.Contents : Tutorial. Applications. Further Reading.


Categories Types And Structures An Introduction To Category Theory For The Working Computer Scientist Foundations Of Computing Series

Author: Andrea Asperti
Publisher: The MIT Press
ISBN: 0262011255
Size: 71.47 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. "Categories, Types and structures" provides a self-contained introduction to general category theory and explains the mathematical structures that have been the foundation of language design for the past two decades. The authors observe that the language of categories could provide a powerful means of standardizing of methods and language, and offer examples ranging from the early dialects of LISP, to Edinburgh ML, to work in polymorphisms and modularity. The book familiarizes readers with categorical concepts through examples based on elementary mathematical notions such as monoids, groups and toplogical spaces, as well as elementary notions from programming-language semantics such as partial orders and categories of domains in denotational semantics. It then pursues the more complex mathematical semantics of data types and programs as objects and morphisms of categories.

A Course In Gb Syntax Lectures On Binding And Empty Categories Current Studies In Linguistics

Author: Howard Lasnik
Publisher: The MIT Press
ISBN: 026262060X
Size: 34.47 MB
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A Course in GB Syntax is a new kind of linguistics textbook. It presents the fundamental concepts of the Government-Binding approach to syntax in a lecture-dialogue format that conveys the sense of a changing field, with live issues under debate.Students and professionals seeking a lucid introduction to the complexities of GB syntax will have the experience of participating in an actual course taught by a major practitioner. The presentation of fundamentals is followed by further examples, easily understandable discussion of technical questions, and alternative analyses within the same basic framework.The book fits welI between a more general introduction like van Riemsdijk and Williams' Introduction to the Theory of Grammar and the major GB literature. While it has been designed for use by graduate students in a second semester syntax course, it can serve as a reader's companion to important but sometimes forbidding texts like Noam Chomsky's Lectures on Government and Binding and Some Concepts and Consequences of the Theory of Government and Binding.The informal tone makes the subject more approachable; examples are worked out more slowly and in greater detail than is possible in the primary sources; and the definitions and notational devices are carefully explained. Finally, many of the questions that the student might want to raise are raised (in fact, by students) and answers and alternatives are explored.The lectures give an overview of the modular GB model and cover in detail Case theory; Binding Theory; the determination of "empty categories," parasitic gaps, and the Empty Category Principle; extensions and alternatives, such as Aoun's "Generalized Binding Theory" and Higginbotham's "linking" analysis, and various open questions, such as the nature of the Case filter, tough movement, weak crossover, illicit NP-movement, and topicalization.Howard Lasnik is Professor of Linguistics at the University of Connecticut. Juan Uriagereka, one of his graduate students, transcribed and did the initial editing of the tapes of the original lectures. Current Studies in Linguistics.


Category Theory For The Sciences

Author: David I. Spivak
Publisher: MIT Press
ISBN: 0262028131
Size: 25.40 MB
Format: PDF, ePub
View: 7765
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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 Theory For The Sciences

Author: David I. Spivak
Publisher: MIT Press
ISBN: 0262320533
Size: 17.50 MB
Format: PDF, ePub, Docs
View: 6079
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This book shows that category theory can be useful outside of mathematics as a rigorous, flexible, and coherent modeling language throughout the sciences.

Basic Category Theory For Computer Scientists

Author: Benjamin C. Pierce
Publisher: MIT Press
ISBN: 9780262660716
Size: 61.98 MB
Format: PDF, ePub, Docs
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Basic Category Theory for Computer Scientists provides a straightforward presentationof the basic constructions and terminology of category theory, including limits, functors, naturaltransformations, adjoints, and cartesian closed ...

Inventing The Medium

Author: Janet H. Murray
Publisher: MIT Press
ISBN: 0262302802
Size: 58.19 MB
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With Inventing the Medium, Janet Murray provides a unified vocabulary and a common methodology for the design of digital objects and environments.

Conceptual Mathematics

Author: F. William Lawvere
Publisher: Cambridge University Press
ISBN: 0521894859
Size: 70.30 MB
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This book provides a skeleton key that makes explicit some concepts and procedures that are common to all branches of pure and applied mathematics.

Category Theory In Context

Author: Emily Riehl
Publisher: Courier Dover Publications
ISBN: 0486820807
Size: 68.58 MB
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This concise, original text for a one-semester course on the subject is derived from courses that author Emily Riehl taught at Harvard and Johns Hopkins Universities.

Categories For The Working Mathematician

Author: Saunders Mac Lane
Publisher: Springer Science & Business Media
ISBN: 1475747217
Size: 54.49 MB
Format: PDF
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An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality.

An Introduction To Category Theory

Author: Harold Simmons
Publisher: Cambridge University Press
ISBN: 1139503324
Size: 80.72 MB
Format: PDF
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Beginning postgraduate mathematicians will find this book an excellent introduction to all of the basics of category theory.