Theoretical Computer Science For The Working Category Theorist

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Theoretical Computer Science for the Working Category Theorist

Author : Noson S. Yanofsky
Publisher : Cambridge University Press
ISBN 13 : 1108890679
Total Pages : 148 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis Theoretical Computer Science for the Working Category Theorist by : Noson S. Yanofsky

Download or read book Theoretical Computer Science for the Working Category Theorist written by Noson S. Yanofsky and published by Cambridge University Press. This book was released on 2022-03-03 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using basic category theory, this Element describes all the central concepts and proves the main theorems of theoretical computer science. Category theory, which works with functions, processes, and structures, is uniquely qualified to present the fundamental results of theoretical computer science. In this Element, readers will meet some of the deepest ideas and theorems of modern computers and mathematics, such as Turing machines, unsolvable problems, the P=NP question, Kurt Gödel's incompleteness theorem, intractable problems, cryptographic protocols, Alan Turing's Halting problem, and much more. The concepts come alive with many examples and exercises.

Basic Category Theory for Computer Scientists

Author : Benjamin C. Pierce
Publisher : MIT Press
ISBN 13 : 0262326450
Total Pages : 117 pages
Book Rating : 4.2/5 (623 download)

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Book Synopsis Basic Category Theory for Computer Scientists by : Benjamin C. Pierce

Download or read book Basic Category Theory for Computer Scientists written by Benjamin C. Pierce and published by MIT Press. This book was released on 1991-08-07 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Theory for Computing Science

Author : Michael Barr
Publisher :
ISBN 13 :
Total Pages : 352 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Category Theory for Computing Science by : Michael Barr

Download or read book Category Theory for Computing Science written by Michael Barr and published by . This book was released on 1995 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: A wide coverage of topics in category theory and computer science is developed in this text, including introductory treatments of cartesian closed categories, sketches and elementary categorical model theory, and triples. Over 300 exercises are included.

An Invitation to Applied Category Theory

Author : Brendan Fong
Publisher : Cambridge University Press
ISBN 13 : 1108582249
Total Pages : 351 pages
Book Rating : 4.1/5 (85 download)

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Book Synopsis An Invitation to Applied Category Theory by : Brendan Fong

Download or read book An Invitation to Applied Category Theory written by Brendan Fong and published by Cambridge University Press. This book was released on 2019-07-18 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Category theory is unmatched in its ability to organize and layer abstractions and to find commonalities between structures of all sorts. No longer the exclusive preserve of pure mathematicians, it is now proving itself to be a powerful tool in science, informatics, and industry. By facilitating communication between communities and building rigorous bridges between disparate worlds, applied category theory has the potential to be a major organizing force. This book offers a self-contained tour of applied category theory. Each chapter follows a single thread motivated by a real-world application and discussed with category-theoretic tools. We see data migration as an adjoint functor, electrical circuits in terms of monoidal categories and operads, and collaborative design via enriched profunctors. All the relevant category theory, from simple to sophisticated, is introduced in an accessible way with many examples and exercises, making this an ideal guide even for those without experience of university-level mathematics.

Category Theory in Context

Author : Emily Riehl
Publisher : Courier Dover Publications
ISBN 13 : 0486820807
Total Pages : 272 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Category Theory in Context by : Emily Riehl

Download or read book Category Theory in Context written by Emily Riehl and published by Courier Dover Publications. This book was released on 2017-03-09 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.

Computability

Author : Nigel Cutland
Publisher : Cambridge University Press
ISBN 13 : 9780521294652
Total Pages : 268 pages
Book Rating : 4.2/5 (946 download)

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Book Synopsis Computability by : Nigel Cutland

Download or read book Computability written by Nigel Cutland and published by Cambridge University Press. This book was released on 1980-06-19 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: What can computers do in principle? What are their inherent theoretical limitations? The theoretical framework which enables such questions to be answered has been developed over the last fifty years from the idea of a computable function - a function whose values can be calculated in an automatic way.

Categories and Computer Science

Author : R. F. C. Walters
Publisher : Cambridge University Press
ISBN 13 : 9780521422260
Total Pages : 180 pages
Book Rating : 4.4/5 (222 download)

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Book Synopsis Categories and Computer Science by : R. F. C. Walters

Download or read book Categories and Computer Science written by R. F. C. Walters and published by Cambridge University Press. This book was released on 1991 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Category theory has become increasingly important and popular in computer science, and many universities now have introductions to category theory as part of their courses for undergraduate computer scientists. The author is a respected category theorist and has based this textbook on a course given over the last few years at the University of Sydney. The theory is developed in a straightforward way, and is enriched with many examples from computer science. Thus this book meets the needs of undergradute computer scientists, and yet retains a level of mathematical correctness that will broaden its appeal to include students of mathematics new to category theory.

Category Theory for Programmers (New Edition, Hardcover)

Author : Bartosz Milewski
Publisher :
ISBN 13 : 9780464243878
Total Pages : pages
Book Rating : 4.2/5 (438 download)

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Book Synopsis Category Theory for Programmers (New Edition, Hardcover) by : Bartosz Milewski

Download or read book Category Theory for Programmers (New Edition, Hardcover) written by Bartosz Milewski and published by . This book was released on 2019-08-24 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Category Theory is one of the most abstract branches of mathematics. It is usually taught to graduate students after they have mastered several other branches of mathematics, like algebra, topology, and group theory. It might, therefore, come as a shock that the basic concepts of category theory can be explained in relatively simple terms to anybody with some experience in programming.That's because, just like programming, category theory is about structure. Mathematicians discover structure in mathematical theories, programmers discover structure in computer programs. Well-structured programs are easier to understand and maintain and are less likely to contain bugs. Category theory provides the language to talk about structure and learning it will make you a better programmer.

Categories for the Working Philosopher

Author : Elaine M. Landry
Publisher : Oxford University Press
ISBN 13 : 019874899X
Total Pages : 486 pages
Book Rating : 4.1/5 (987 download)

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Book Synopsis Categories for the Working Philosopher by : Elaine M. Landry

Download or read book Categories for the Working Philosopher written by Elaine M. Landry and published by Oxford University Press. This book was released on 2017 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book on category theory for a broad philosophical readership. There is no other discussion of category theory comparable in its scope. It is designed to show the interest and significant of category theory for philosophers working in a range of areas, including mathematics, proof theory, computer science, ontology, physics, biology, cognition, mathematical modelling, the structure of scientific theories, and the structure of the world. Moreover, it does this in a way that is accessible to non specialists. Each chapter is written by either a category-theorist or a philosopher working in one of the represented fields, in a way that builds on the concepts already familiar to philosophers working in these areas. The book is split into two halves. The 'pure' chapters focus on the use of category theory for mathematical, foundational, and logical purposes, while the 'applied' chapters consider the use of category theory for representational purposes, investigating category theory as a framework for theories of physics and biology, for mathematical modelling more generally, and for the structure of scientific theories. Book jacket.

Basic Category Theory

Author : Tom Leinster
Publisher : Cambridge University Press
ISBN 13 : 1107044243
Total Pages : 193 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Basic Category Theory by : Tom Leinster

Download or read book Basic Category Theory written by Tom Leinster and published by Cambridge University Press. This book was released on 2014-07-24 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: A short introduction ideal for students learning category theory for the first time.

Quantum Computing for Computer Scientists

Author : Noson S. Yanofsky
Publisher :
ISBN 13 : 9781316086513
Total Pages : 384 pages
Book Rating : 4.0/5 (865 download)

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Book Synopsis Quantum Computing for Computer Scientists by : Noson S. Yanofsky

Download or read book Quantum Computing for Computer Scientists written by Noson S. Yanofsky and published by . This book was released on 2008 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The multidisciplinary field of quantum computing strives to exploit some of the uncanny aspects of quantum mechanics to expand our computational horizons. Quantum Computing for Computer Scientists takes readers on a tour of this fascinating area of cutting-edge research. Written in an accessible yet rigorous fashion, this book employs ideas and techniques familiar to every student of computer science. The reader is not expected to have any advanced mathematics or physics background. After presenting the necessary prerequisites, the material is organized to look at different aspects of quantum computing from the specific standpoint of computer science. There are chapters on computer architecture, algorithms, programming languages, theoretical computer science, cryptography, information theory, and hardware. The text has step-by-step examples, more than two hundred exercises with solutions, and programming drills that bring the ideas of quantum computing alive for today's computer science students and researchers. --from publisher description.

Categories for the Working Mathematician

Author : Saunders Mac Lane
Publisher : Springer Science & Business Media
ISBN 13 : 1475747217
Total Pages : 320 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Categories for the Working Mathematician by : Saunders Mac Lane

Download or read book Categories for the Working Mathematician written by Saunders Mac Lane and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. It then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterised by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.

Introduction to Coalgebra

Author : Bart Jacobs
Publisher : Cambridge University Press
ISBN 13 : 1107177898
Total Pages : 495 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Introduction to Coalgebra by : Bart Jacobs

Download or read book Introduction to Coalgebra written by Bart Jacobs and published by Cambridge University Press. This book was released on 2017 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to coalgebra, with clear mathematical explanations and numerous examples and exercises.

Software Development and Reality Construction

Author : Christiane Floyd
Publisher : Springer Science & Business Media
ISBN 13 : 3642768172
Total Pages : 484 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis Software Development and Reality Construction by : Christiane Floyd

Download or read book Software Development and Reality Construction written by Christiane Floyd and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book is based on the conference Software Development and Reality Construction held at SchloB Eringerfeld in Germany, September 25 - 30, 1988. This was organized by the Technical University of Berlin (TUB) in cooperation with the German National Research Center for Computer Science (GMD), Sankt Augustin, and sponsored by the Volkswagen Foundation whose financial support we gratefully acknowledge. The conference was an interdisciplinary scientific and cultural event aimed at promoting discussion on the nature of computer science as a scientific discipline and on the theoretical foundations and systemic practice required for human-oriented system design. In keeping with the conversational style of the conference, the book comprises a series of individual contributions, arranged so as to form a coherent whole. Some authors reflect on their practice in computer science and system design. Others start from approaches developed in the humanities and the social sciences for understanding human learning and creativity, individual and cooperative work, and the interrelation between technology and organizations. Thus, each contribution makes its specific point and can be read on its own merit. But, at the same time, it takes its place as a chapter in the book, along with all the other contributions, to give what seemed to us a meaningful overall line of argumentation. This required careful editorial coordination, and we are grateful to all the authors for bearing with us throughout the slow genesis of the book and for complying with our requests for extensive revision of some of the manuscripts.

The Outer Limits of Reason

Author : Noson S. Yanofsky
Publisher : MIT Press
ISBN 13 : 026252984X
Total Pages : 419 pages
Book Rating : 4.2/5 (625 download)

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Book Synopsis The Outer Limits of Reason by : Noson S. Yanofsky

Download or read book The Outer Limits of Reason written by Noson S. Yanofsky and published by MIT Press. This book was released on 2016-11-04 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This exploration of the scientific limits of knowledge challenges our deep-seated beliefs about our universe, our rationality, and ourselves. “A must-read for anyone studying information science.” —Publishers Weekly, starred review Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own intuitions about the world—including our ideas about space, time, and motion, and the complex relationship between the knower and the known. Yanofsky describes simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve: • perfectly formed English sentences that make no sense • different levels of infinity • the bizarre world of the quantum • the relevance of relativity theory • the causes of chaos theory • math problems that cannot be solved by normal means • statements that are true but cannot be proven Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there.

Category Theory

Author : Steve Awodey
Publisher : Oxford University Press
ISBN 13 : 0199587361
Total Pages : 328 pages
Book Rating : 4.1/5 (995 download)

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Book Synopsis Category Theory by : Steve Awodey

Download or read book Category Theory written by Steve Awodey and published by Oxford University Press. This book was released on 2010-06-17 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive reference to category theory for students and researchers in mathematics, computer science, logic, cognitive science, linguistics, and philosophy. Useful for self-study and as a course text, the book includes all basic definitions and theorems (with full proofs), as well as numerous examples and exercises.

Picturing Quantum Processes

Author : Bob Coecke
Publisher : Cambridge University Press
ISBN 13 : 1108107710
Total Pages : 847 pages
Book Rating : 4.1/5 (81 download)

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Book Synopsis Picturing Quantum Processes by : Bob Coecke

Download or read book Picturing Quantum Processes written by Bob Coecke and published by Cambridge University Press. This book was released on 2017-03-16 with total page 847 pages. Available in PDF, EPUB and Kindle. Book excerpt: The unique features of the quantum world are explained in this book through the language of diagrams, setting out an innovative visual method for presenting complex theories. Requiring only basic mathematical literacy, this book employs a unique formalism that builds an intuitive understanding of quantum features while eliminating the need for complex calculations. This entirely diagrammatic presentation of quantum theory represents the culmination of ten years of research, uniting classical techniques in linear algebra and Hilbert spaces with cutting-edge developments in quantum computation and foundations. Written in an entertaining and user-friendly style and including more than one hundred exercises, this book is an ideal first course in quantum theory, foundations, and computation for students from undergraduate to PhD level, as well as an opportunity for researchers from a broad range of fields, from physics to biology, linguistics, and cognitive science, to discover a new set of tools for studying processes and interaction.