Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Category Theory for the Sciences PDF full book. Access full book title Category Theory for the Sciences by David I. Spivak. Download full books in PDF and EPUB format.
Author: David I. Spivak Publisher: MIT Press ISBN: 0262320533 Category : Mathematics Languages : en Pages : 495
Book Description
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.
Author: David I. Spivak Publisher: MIT Press ISBN: 0262320533 Category : Mathematics Languages : en Pages : 495
Book Description
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.
Author: Marina Frasca-Spada Publisher: Cambridge University Press ISBN: 9780521659390 Category : History Languages : en Pages : 460
Book Description
This book, published in 2000, examines the intersection between science and books from early medieval times to the nineteenth century.
Author: Eric Watkins Publisher: Oxford University Press ISBN: 0195133056 Category : Philosophy Languages : en Pages : 305
Book Description
Kant and the Sciences aims to reveal the deep unity of Kant's conception of science as it bears on the particular sciences of his day and on his conception of philosophy's function with respect to these sciences. It brings together for the first time twelve essays by leading Kant scholars that take into account Kant's conception of a wide variety of scientific disciplines, including physics, chemistry, biology, psychology, and anthropology.
Author: Fernando Vidal Publisher: University of Chicago Press ISBN: 0226855880 Category : Science Languages : en Pages : 429
Book Description
Fernando Vidal’s trailblazing text on the origins of psychology traces the development of the discipline from its appearance in the late sixteenth century to its redefinition at the end of the seventeenth and its emergence as an institutionalized field in the eighteenth. Originally published in 2011, The Sciences of the Soul continues to be of wide importance in the history and philosophy of psychology, the history of the human sciences more generally, and in the social and intellectual history of eighteenth-century Europe.
Author: Geoffrey C. Bowker Publisher: MIT Press ISBN: 0262524899 Category : Science Languages : en Pages : 275
Book Description
How the way we hold knowledge about the past—in books, in file folders, in databases—affects the kind of stories we tell about the past. The way we record knowledge, and the web of technical, formal, and social practices that surrounds it, inevitably affects the knowledge that we record. The ways we hold knowledge about the past—in handwritten manuscripts, in printed books, in file folders, in databases—shape the kind of stories we tell about that past. In this lively and erudite look at the relation of our information infrastructures to our information, Geoffrey Bowker examines how, over the past two hundred years, information technology has converged with the nature and production of scientific knowledge. His story weaves a path between the social and political work of creating an explicit, indexical memory for science—the making of infrastructures—and the variety of ways we continually reconfigure, lose, and regain the past. At a time when memory is so cheap and its recording is so protean, Bowker reminds us of the centrality of what and how we choose to forget. In Memory Practices in the Sciences he looks at three "memory epochs" of the nineteenth, twentieth, and twenty-first centuries and their particular reconstructions and reconfigurations of scientific knowledge. The nineteenth century's central science, geology, mapped both the social and the natural world into a single time package (despite apparent discontinuities), as, in a different way, did mid-twentieth-century cybernetics. Both, Bowker argues, packaged time in ways indexed by their information technologies to permit traffic between the social and natural worlds. Today's sciences of biodiversity, meanwhile, "database the world" in a way that excludes certain spaces, entities, and times. We use the tools of the present to look at the past, says Bowker; we project onto nature our modes of organizing our own affairs.
Author: Simone Rödder Publisher: Springer Science & Business Media ISBN: 9400720858 Category : Social Science Languages : en Pages : 375
Book Description
The Yearbook addresses the overriding question: what are the effects of the ‘opening up’ of science to the media? Theoretical considerations and a host of empirical studies covering different configurations provide an in-depth analysis of the sciences’ media connection and its repercussions on science itself. They help to form a sound judgement on this recent development.
Author: Herbert Alexander Simon Publisher: MIT Press (MA) ISBN: Category : Science Languages : en Pages : 156
Book Description
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.
Author: David I. Spivak
Author: David I. Spivak
Author: Marina Frasca-Spada
Author: F. S. C. Northrop
Author: Stephen Finney Mason
Author: Eric Watkins
Author: Fernando Vidal
Author: Geoffrey C. Bowker
Author: Simone Rödder
Author: Paul Tillich
Author: Herbert Alexander Simon