Category Theory for the Sciences

Category Theory for the Sciences

Author: David I. Spivak

Publisher: MIT Press

Published: 2014-10-17

Total Pages: 495

ISBN-13: 0262320533

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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.


Book Synopsis Category Theory for the Sciences by : David I. Spivak

Download or read book Category Theory for the Sciences written by David I. Spivak and published by MIT Press. This book was released on 2014-10-17 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Books and the Sciences in History

Books and the Sciences in History

Author: Marina Frasca-Spada

Publisher: Cambridge University Press

Published: 2000-11-02

Total Pages: 460

ISBN-13: 9780521659390

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This book, published in 2000, examines the intersection between science and books from early medieval times to the nineteenth century.


Book Synopsis Books and the Sciences in History by : Marina Frasca-Spada

Download or read book Books and the Sciences in History written by Marina Frasca-Spada and published by Cambridge University Press. This book was released on 2000-11-02 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, published in 2000, examines the intersection between science and books from early medieval times to the nineteenth century.


The Sciences of the Artificial

The Sciences of the Artificial

Author: Herbert Alexander Simon

Publisher: MIT Press (MA)

Published: 1969

Total Pages: 156

ISBN-13:

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The Sciences of the Artificialreveals the design of an intellectual structure aimed at accommodating those empirical phenomena that are "artificial" rather than "natural." The goal is to show how empirical sciences of artificial systems are possible, even in the face of the contingent and teleological character of the phenomena, their attributes of choice and purpose. Developing in some detail two specific examples—human psychology and engineering design—Professor Simon describes the shape of these sciences as they are emerging from developments of the past 25 years. "Artificial" is used here in a very specific sense: to denote systems that have a given form and behavior only because they adapt (or are adapted), in reference to goals or purposes, to their environment. Thus, both man-made artifacts and man himself, in terms of his behavior, are artificial. Simon characterizes an artificial system as an interface between two environments—inner and outer. These environments lie in the province of "natural science," but the interface, linking them, is the realm of "artificial science." When an artificial system adapts successfully, its behavior shows mostly the shape of the outer environment and reveals little of the structure or mechanisms of the inner. The inner environment becomes significant for behavior only when a system reaches the limits of its rationality and adaptability, and contingency degenerates into necessity.


Book Synopsis The Sciences of the Artificial by : Herbert Alexander Simon

Download or read book The Sciences of the Artificial written by Herbert Alexander Simon and published by MIT Press (MA). This book was released on 1969 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Sciences of the Artificialreveals the design of an intellectual structure aimed at accommodating those empirical phenomena that are "artificial" rather than "natural." The goal is to show how empirical sciences of artificial systems are possible, even in the face of the contingent and teleological character of the phenomena, their attributes of choice and purpose. Developing in some detail two specific examples—human psychology and engineering design—Professor Simon describes the shape of these sciences as they are emerging from developments of the past 25 years. "Artificial" is used here in a very specific sense: to denote systems that have a given form and behavior only because they adapt (or are adapted), in reference to goals or purposes, to their environment. Thus, both man-made artifacts and man himself, in terms of his behavior, are artificial. Simon characterizes an artificial system as an interface between two environments—inner and outer. These environments lie in the province of "natural science," but the interface, linking them, is the realm of "artificial science." When an artificial system adapts successfully, its behavior shows mostly the shape of the outer environment and reveals little of the structure or mechanisms of the inner. The inner environment becomes significant for behavior only when a system reaches the limits of its rationality and adaptability, and contingency degenerates into necessity.


A History of the Sciences

A History of the Sciences

Author:

Publisher:

Published: 1977

Total Pages: 638

ISBN-13:

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Book Synopsis A History of the Sciences by :

Download or read book A History of the Sciences written by and published by . This book was released on 1977 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt:


From Natural Philosophy to the Sciences

From Natural Philosophy to the Sciences

Author: David Cahan

Publisher: University of Chicago Press

Published: 2003-09-15

Total Pages: 480

ISBN-13: 9780226089270

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During the 19th century, much of the modern scientific enterprise took shape: scientific disciplines were formed, institutions and communities were founded and unprecedented applications to and interactions with other aspects of society and culture occurred. taught us about this exciting time and identify issues that remain unexamined or require reconsideration. They treat scientific disciplines - biology, physics, chemistry, the earth sciences, mathematics and the social sciences - in their specific intellectual and sociocultural contexts as well as the broader topics of science and medicine; science and religion; scientific institutions and communities; and science, technology and industry. From Natural Philosophy to the Sciences should be valuable for historians of science, but also of great interest to scholars of all aspects of 19th-century life and culture.


Book Synopsis From Natural Philosophy to the Sciences by : David Cahan

Download or read book From Natural Philosophy to the Sciences written by David Cahan and published by University of Chicago Press. This book was released on 2003-09-15 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the 19th century, much of the modern scientific enterprise took shape: scientific disciplines were formed, institutions and communities were founded and unprecedented applications to and interactions with other aspects of society and culture occurred. taught us about this exciting time and identify issues that remain unexamined or require reconsideration. They treat scientific disciplines - biology, physics, chemistry, the earth sciences, mathematics and the social sciences - in their specific intellectual and sociocultural contexts as well as the broader topics of science and medicine; science and religion; scientific institutions and communities; and science, technology and industry. From Natural Philosophy to the Sciences should be valuable for historians of science, but also of great interest to scholars of all aspects of 19th-century life and culture.


Writing in the Sciences

Writing in the Sciences

Author: Ann M. Penrose

Publisher: Longman Publishing Group

Published: 2004

Total Pages: 0

ISBN-13: 9780321112040

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This rhetorical, multi-disciplinary guide discusses the major genres of science writing including research reports, grant proposals, conference presentations, and a variety of forms of public communication. Writing in the Sciences combines a descriptive approach helping students to recognize distinctive features of common genres in their fields with a rhetorical focus helping them to analyze how, why, and for whom texts are created by scientists. Multiple samples from real research cases illustrate a range of scientific disciplines and audiences for scientific research along with the corresponding differences in focus, arrangement, style, and other rhetorical dimensions. Comparisons among disciplines provide the opportunity for students to identify common conventions in science and investigate variation across fields.


Book Synopsis Writing in the Sciences by : Ann M. Penrose

Download or read book Writing in the Sciences written by Ann M. Penrose and published by Longman Publishing Group. This book was released on 2004 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This rhetorical, multi-disciplinary guide discusses the major genres of science writing including research reports, grant proposals, conference presentations, and a variety of forms of public communication. Writing in the Sciences combines a descriptive approach helping students to recognize distinctive features of common genres in their fields with a rhetorical focus helping them to analyze how, why, and for whom texts are created by scientists. Multiple samples from real research cases illustrate a range of scientific disciplines and audiences for scientific research along with the corresponding differences in focus, arrangement, style, and other rhetorical dimensions. Comparisons among disciplines provide the opportunity for students to identify common conventions in science and investigate variation across fields.


The Logic of the Sciences and the Humanities

The Logic of the Sciences and the Humanities

Author: Filmer Stuart Cuckow Northrop

Publisher:

Published: 1959

Total Pages: 402

ISBN-13:

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Book Synopsis The Logic of the Sciences and the Humanities by : Filmer Stuart Cuckow Northrop

Download or read book The Logic of the Sciences and the Humanities written by Filmer Stuart Cuckow Northrop and published by . This book was released on 1959 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt:


What Are the Arts and Sciences?

What Are the Arts and Sciences?

Author: Dan Rockmore

Publisher: Dartmouth College Press

Published: 2017-06-06

Total Pages: 378

ISBN-13: 1512601039

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What constitutes the study of philosophy or physics? What exactly does an anthropologist do, or a geologist or historian? In short, what are the arts and sciences? While many of us have been to college and many aspire to go, we may still wonder just what the various disciplines represent and how they interact. What are their origins, methods, applications, and unique challenges? What kind of people elect to go into each of these fields, and what are the big issues that motivate them? Curious to explore these questions himself, Dartmouth College professor and mathematician Dan Rockmore asked his colleagues to explain their fields and what it is that they do. The result is an accessible, entertaining, and enlightening survey of the ideas and subjects that contribute to a liberal education. The book offers a doorway to the arts and sciences for anyone intrigued by the vast world of ideas.


Book Synopsis What Are the Arts and Sciences? by : Dan Rockmore

Download or read book What Are the Arts and Sciences? written by Dan Rockmore and published by Dartmouth College Press. This book was released on 2017-06-06 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: What constitutes the study of philosophy or physics? What exactly does an anthropologist do, or a geologist or historian? In short, what are the arts and sciences? While many of us have been to college and many aspire to go, we may still wonder just what the various disciplines represent and how they interact. What are their origins, methods, applications, and unique challenges? What kind of people elect to go into each of these fields, and what are the big issues that motivate them? Curious to explore these questions himself, Dartmouth College professor and mathematician Dan Rockmore asked his colleagues to explain their fields and what it is that they do. The result is an accessible, entertaining, and enlightening survey of the ideas and subjects that contribute to a liberal education. The book offers a doorway to the arts and sciences for anyone intrigued by the vast world of ideas.


The Story-book of Science

The Story-book of Science

Author: Jean-Henri Fabre

Publisher:

Published: 1917

Total Pages: 426

ISBN-13:

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A book about metals, plants, animals, and planets.


Book Synopsis The Story-book of Science by : Jean-Henri Fabre

Download or read book The Story-book of Science written by Jean-Henri Fabre and published by . This book was released on 1917 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: A book about metals, plants, animals, and planets.


Encyclopedia of the Sciences of Learning

Encyclopedia of the Sciences of Learning

Author: Norbert M. Seel

Publisher: Springer Science & Business Media

Published: 2011-10-05

Total Pages: 3643

ISBN-13: 1441914277

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Over the past century, educational psychologists and researchers have posited many theories to explain how individuals learn, i.e. how they acquire, organize and deploy knowledge and skills. The 20th century can be considered the century of psychology on learning and related fields of interest (such as motivation, cognition, metacognition etc.) and it is fascinating to see the various mainstreams of learning, remembered and forgotten over the 20th century and note that basic assumptions of early theories survived several paradigm shifts of psychology and epistemology. Beyond folk psychology and its naïve theories of learning, psychological learning theories can be grouped into some basic categories, such as behaviorist learning theories, connectionist learning theories, cognitive learning theories, constructivist learning theories, and social learning theories. Learning theories are not limited to psychology and related fields of interest but rather we can find the topic of learning in various disciplines, such as philosophy and epistemology, education, information science, biology, and – as a result of the emergence of computer technologies – especially also in the field of computer sciences and artificial intelligence. As a consequence, machine learning struck a chord in the 1980s and became an important field of the learning sciences in general. As the learning sciences became more specialized and complex, the various fields of interest were widely spread and separated from each other; as a consequence, even presently, there is no comprehensive overview of the sciences of learning or the central theoretical concepts and vocabulary on which researchers rely. The Encyclopedia of the Sciences of Learning provides an up-to-date, broad and authoritative coverage of the specific terms mostly used in the sciences of learning and its related fields, including relevant areas of instruction, pedagogy, cognitive sciences, and especially machine learning and knowledge engineering. This modern compendium will be an indispensable source of information for scientists, educators, engineers, and technical staff active in all fields of learning. More specifically, the Encyclopedia provides fast access to the most relevant theoretical terms provides up-to-date, broad and authoritative coverage of the most important theories within the various fields of the learning sciences and adjacent sciences and communication technologies; supplies clear and precise explanations of the theoretical terms, cross-references to related entries and up-to-date references to important research and publications. The Encyclopedia also contains biographical entries of individuals who have substantially contributed to the sciences of learning; the entries are written by a distinguished panel of researchers in the various fields of the learning sciences.


Book Synopsis Encyclopedia of the Sciences of Learning by : Norbert M. Seel

Download or read book Encyclopedia of the Sciences of Learning written by Norbert M. Seel and published by Springer Science & Business Media. This book was released on 2011-10-05 with total page 3643 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past century, educational psychologists and researchers have posited many theories to explain how individuals learn, i.e. how they acquire, organize and deploy knowledge and skills. The 20th century can be considered the century of psychology on learning and related fields of interest (such as motivation, cognition, metacognition etc.) and it is fascinating to see the various mainstreams of learning, remembered and forgotten over the 20th century and note that basic assumptions of early theories survived several paradigm shifts of psychology and epistemology. Beyond folk psychology and its naïve theories of learning, psychological learning theories can be grouped into some basic categories, such as behaviorist learning theories, connectionist learning theories, cognitive learning theories, constructivist learning theories, and social learning theories. Learning theories are not limited to psychology and related fields of interest but rather we can find the topic of learning in various disciplines, such as philosophy and epistemology, education, information science, biology, and – as a result of the emergence of computer technologies – especially also in the field of computer sciences and artificial intelligence. As a consequence, machine learning struck a chord in the 1980s and became an important field of the learning sciences in general. As the learning sciences became more specialized and complex, the various fields of interest were widely spread and separated from each other; as a consequence, even presently, there is no comprehensive overview of the sciences of learning or the central theoretical concepts and vocabulary on which researchers rely. The Encyclopedia of the Sciences of Learning provides an up-to-date, broad and authoritative coverage of the specific terms mostly used in the sciences of learning and its related fields, including relevant areas of instruction, pedagogy, cognitive sciences, and especially machine learning and knowledge engineering. This modern compendium will be an indispensable source of information for scientists, educators, engineers, and technical staff active in all fields of learning. More specifically, the Encyclopedia provides fast access to the most relevant theoretical terms provides up-to-date, broad and authoritative coverage of the most important theories within the various fields of the learning sciences and adjacent sciences and communication technologies; supplies clear and precise explanations of the theoretical terms, cross-references to related entries and up-to-date references to important research and publications. The Encyclopedia also contains biographical entries of individuals who have substantially contributed to the sciences of learning; the entries are written by a distinguished panel of researchers in the various fields of the learning sciences.