An Invitation To Applied Category Theory
DOWNLOAD
Download An Invitation To Applied Category Theory PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get An Invitation To Applied Category Theory book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
An Invitation To Applied Category Theory
DOWNLOAD
Author : Brendan Fong
language : en
Publisher: Cambridge University Press
Release Date : 2019-07-18
An Invitation To Applied Category Theory written by Brendan Fong and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-18 with Computers categories.
Category theory reveals commonalities between structures of all sorts. This book shows its potential in science, engineering, and beyond.
An Invitation To Applied Category Theory
DOWNLOAD
Author : Brendan Fong
language : en
Publisher: Cambridge University Press
Release Date : 2019-07-18
An Invitation To Applied Category Theory written by Brendan Fong and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-18 with Mathematics categories.
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 For The Sciences
DOWNLOAD
Author : David I. Spivak
language : en
Publisher: MIT Press
Release Date : 2014-10-17
Category Theory For The Sciences written by David I. Spivak and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-17 with Mathematics categories.
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.
Tool And Object
DOWNLOAD
Author : Ralph Krömer
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-25
Tool And Object written by Ralph Krömer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-25 with Mathematics categories.
Category theory is a general mathematical theory of structures and of structures of structures. It occupied a central position in contemporary mathematics as well as computer science. This book describes the history of category theory whereby illuminating its symbiotic relationship to algebraic topology, homological algebra, algebraic geometry and mathematical logic and elaboratively develops the connections with the epistemological significance.
Basic Category Theory
DOWNLOAD
Author : Tom Leinster
language : en
Publisher: Cambridge University Press
Release Date : 2014-07-24
Basic Category Theory written by Tom Leinster and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-24 with Mathematics categories.
A short introduction ideal for students learning category theory for the first time.
An Introduction To Category Theory
DOWNLOAD
Author : Harold Simmons
language : en
Publisher: Cambridge University Press
Release Date : 2011-09-22
An Introduction To Category Theory written by Harold Simmons and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-22 with Mathematics categories.
Category theory provides a general conceptual framework that has proved fruitful in subjects as diverse as geometry, topology, theoretical computer science and foundational mathematics. Here is a friendly, easy-to-read textbook that explains the fundamentals at a level suitable for newcomers to the subject. Beginning postgraduate mathematicians will find this book an excellent introduction to all of the basics of category theory. It gives the basic definitions; goes through the various associated gadgetry, such as functors, natural transformations, limits and colimits; and then explains adjunctions. The material is slowly developed using many examples and illustrations to illuminate the concepts explained. Over 200 exercises, with solutions available online, help the reader to access the subject and make the book ideal for self-study. It can also be used as a recommended text for a taught introductory course.
Theoretical Computer Science For The Working Category Theorist
DOWNLOAD
Author : Noson S. Yanofsky
language : en
Publisher: Cambridge University Press
Release Date : 2022-03-03
Theoretical Computer Science For The Working Category Theorist written by Noson S. Yanofsky and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-03 with Mathematics categories.
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.
Category Theory In Context
DOWNLOAD
Author : Emily Riehl
language : en
Publisher: Courier Dover Publications
Release Date : 2017-03-09
Category Theory In Context written by Emily Riehl and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-09 with Mathematics categories.
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.
Conceptual Mathematics
DOWNLOAD
Author : F. William Lawvere
language : en
Publisher: Cambridge University Press
Release Date : 2009-07-30
Conceptual Mathematics written by F. William Lawvere and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-30 with Mathematics categories.
This truly elementary book on categories introduces retracts, graphs, and adjoints to students and scientists.
An Invitation To Applied Mathematics
DOWNLOAD
Author : Carmen Chicone
language : en
Publisher: Academic Press
Release Date : 2016-09-24
An Invitation To Applied Mathematics written by Carmen Chicone and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-24 with Mathematics categories.
An Invitation to Applied Mathematics: Differential Equations, Modeling, and Computation introduces the reader to the methodology of modern applied mathematics in modeling, analysis, and scientific computing with emphasis on the use of ordinary and partial differential equations. Each topic is introduced with an attractive physical problem, where a mathematical model is constructed using physical and constitutive laws arising from the conservation of mass, conservation of momentum, or Maxwell's electrodynamics. Relevant mathematical analysis (which might employ vector calculus, Fourier series, nonlinear ODEs, bifurcation theory, perturbation theory, potential theory, control theory, or probability theory) or scientific computing (which might include Newton's method, the method of lines, finite differences, finite elements, finite volumes, boundary elements, projection methods, smoothed particle hydrodynamics, or Lagrangian methods) is developed in context and used to make physically significant predictions. The target audience is advanced undergraduates (who have at least a working knowledge of vector calculus and linear ordinary differential equations) or beginning graduate students. Readers will gain a solid and exciting introduction to modeling, mathematical analysis, and computation that provides the key ideas and skills needed to enter the wider world of modern applied mathematics. Presents an integrated wealth of modeling, analysis, and numerical methods in one volume Provides practical and comprehensible introductions to complex subjects, for example, conservation laws, CFD, SPH, BEM, and FEM Includes a rich set of applications, with more appealing problems and projects suggested