Download or read book Categories for Types written by Roy L. Crole and published by Cambridge University Press. This book was released on 1993 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook explains the basic principles of categorical type theory and the techniques used to derive categorical semantics for specific type theories. It introduces the reader to ordered set theory, lattices and domains, and this material provides plenty of examples for an introduction to category theory, which covers categories, functors, natural transformations, the Yoneda lemma, cartesian closed categories, limits, adjunctions and indexed categories. Four kinds of formal system are considered in detail, namely algebraic, functional, polymorphic functional, and higher order polymorphic functional type theory. For each of these the categorical semantics are derived and results about the type systems are proved categorically. Issues of soundness and completeness are also considered. Aimed at advanced undergraduates and beginning graduates, this book will be of interest to theoretical computer scientists, logicians and mathematicians specializing in category theory.
Download or read book Categories Types and Structures written by Andrea Asperti and published by MIT Press (MA). This book was released on 1991 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Discipline of Organizing Professional Edition written by Robert J. Glushko and published by "O'Reilly Media, Inc.". This book was released on 2014-08-25 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: Note about this ebook: This ebook exploits many advanced capabilities with images, hypertext, and interactivity and is optimized for EPUB3-compliant book readers, especially Apple's iBooks and browser plugins. These features may not work on all ebook readers. We organize things. We organize information, information about things, and information about information. Organizing is a fundamental issue in many professional fields, but these fields have only limited agreement in how they approach problems of organizing and in what they seek as their solutions. The Discipline of Organizing synthesizes insights from library science, information science, computer science, cognitive science, systems analysis, business, and other disciplines to create an Organizing System for understanding organizing. This framework is robust and forward-looking, enabling effective sharing of insights and design patterns between disciplines that weren’t possible before. The Professional Edition includes new and revised content about the active resources of the "Internet of Things," and how the field of Information Architecture can be viewed as a subset of the discipline of organizing. You’ll find: 600 tagged endnotes that connect to one or more of the contributing disciplines Nearly 60 new pictures and illustrations Links to cross-references and external citations Interactive study guides to test on key points The Professional Edition is ideal for practitioners and as a primary or supplemental text for graduate courses on information organization, content and knowledge management, and digital collections. FOR INSTRUCTORS: Supplemental materials (lecture notes, assignments, exams, etc.) are available at http://disciplineoforganizing.org. FOR STUDENTS: Make sure this is the edition you want to buy. There's a newer one and maybe your instructor has adopted that one instead.
Download or read book Categories and Types in Logic Language and Physics written by Claudia Casadio and published by Springer. This book was released on 2014-04-03 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: For more than 60 years, Jim Lambek has been a profoundly inspirational mathematician, with groundbreaking contributions to algebra, category theory, linguistics, theoretical physics, logic and proof theory. This Festschrift was put together on the occasion of his 90th birthday. The papers in it give a good picture of the multiple research areas where the impact of Jim Lambek's work can be felt. The volume includes contributions by prominent researchers and by their students, showing how Jim Lambek's ideas keep inspiring upcoming generations of scholars.
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.
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.
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 273 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.
Download or read book Homotopy Type Theory Univalent Foundations of Mathematics written by and published by Univalent Foundations. This book was released on with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Handbook of Categorization in Cognitive Science written by Henri Cohen and published by Elsevier. This book was released on 2017-06-03 with total page 1277 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Categorization in Cognitive Science, Second Edition presents the study of categories and the process of categorization as viewed through the lens of the founding disciplines of the cognitive sciences, and how the study of categorization has long been at the core of each of these disciplines. The literature on categorization reveals there is a plethora of definitions, theories, models and methods to apprehend this central object of study. The contributions in this handbook reflect this diversity. For example, the notion of category is not uniform across these contributions, and there are multiple definitions of the notion of concept. Furthermore, the study of category and categorization is approached differently within each discipline. For some authors, the categories themselves constitute the object of study, whereas for others, it is the process of categorization, and for others still, it is the technical manipulation of large chunks of information. Finally, yet another contrast has to do with the biological versus artificial nature of agents or categorizers. Defines notions of category and categorization Discusses the nature of categories: discrete, vague, or other Explores the modality effects on categories Bridges the category divide - calling attention to the bridges that have already been built, and avenues for further cross-fertilization between disciplines
Download or read book Tensor Categories written by Pavel Etingof and published by American Mathematical Soc.. This book was released on 2016-08-05 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Is there a vector space whose dimension is the golden ratio? Of course not—the golden ratio is not an integer! But this can happen for generalizations of vector spaces—objects of a tensor category. The theory of tensor categories is a relatively new field of mathematics that generalizes the theory of group representations. It has deep connections with many other fields, including representation theory, Hopf algebras, operator algebras, low-dimensional topology (in particular, knot theory), homotopy theory, quantum mechanics and field theory, quantum computation, theory of motives, etc. This book gives a systematic introduction to this theory and a review of its applications. While giving a detailed overview of general tensor categories, it focuses especially on the theory of finite tensor categories and fusion categories (in particular, braided and modular ones), and discusses the main results about them with proofs. In particular, it shows how the main properties of finite-dimensional Hopf algebras may be derived from the theory of tensor categories. Many important results are presented as a sequence of exercises, which makes the book valuable for students and suitable for graduate courses. Many applications, connections to other areas, additional results, and references are discussed at the end of each chapter.
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.
Download or read book Advanced R written by Hadley Wickham and published by CRC Press. This book was released on 2015-09-15 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Essential Reference for Intermediate and Advanced R Programmers Advanced R presents useful tools and techniques for attacking many types of R programming problems, helping you avoid mistakes and dead ends. With more than ten years of experience programming in R, the author illustrates the elegance, beauty, and flexibility at the heart of R. The book develops the necessary skills to produce quality code that can be used in a variety of circumstances. You will learn: The fundamentals of R, including standard data types and functions Functional programming as a useful framework for solving wide classes of problems The positives and negatives of metaprogramming How to write fast, memory-efficient code This book not only helps current R users become R programmers but also shows existing programmers what’s special about R. Intermediate R programmers can dive deeper into R and learn new strategies for solving diverse problems while programmers from other languages can learn the details of R and understand why R works the way it does.
Download or read book The Big Book of Concepts written by Gregory Murphy and published by MIT Press. This book was released on 2004-01-30 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concepts embody our knowledge of the kinds of things there are in the world. Tying our past experiences to our present interactions with the environment, they enable us to recognize and understand new objects and events. Concepts are also relevant to understanding domains such as social situations, personality types, and even artistic styles. Yet like other phenomenologically simple cognitive processes such as walking or understanding speech, concept formation and use are maddeningly complex. Research since the 1970s and the decline of the "classical view" of concepts have greatly illuminated the psychology of concepts. But persistent theoretical disputes have sometimes obscured this progress. The Big Book of Concepts goes beyond those disputes to reveal the advances that have been made, focusing on the major empirical discoveries. By reviewing and evaluating research on diverse topics such as category learning, word meaning, conceptual development in infants and children, and the basic level of categorization, the book develops a much broader range of criteria than is usual for evaluating theories of concepts.
Download or read book Lambda Calculus with Types written by Henk Barendregt and published by Cambridge University Press. This book was released on 2013-06-20 with total page 969 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook with exercises reveals in formalisms, hitherto mainly used for hardware and software design and verification, unexpected mathematical beauty. The lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and was treated in the first author's classic The Lambda Calculus (1984). The formalism has since been extended with types and used in functional programming (Haskell, Clean) and proof assistants (Coq, Isabelle, HOL), used in designing and verifying IT products and mathematical proofs. In this book, the authors focus on three classes of typing for lambda terms: simple types, recursive types and intersection types. It is in these three formalisms of terms and types that the unexpected mathematical beauty is revealed. The treatment is authoritative and comprehensive, complemented by an exhaustive bibliography, and numerous exercises are provided to deepen the readers' understanding and increase their confidence using types.
Download or read book Design User Experience and Usability Practice and Case Studies written by Aaron Marcus and published by Springer. This book was released on 2019-07-10 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: The four-volume set LNCS 11583, 11584, 11585, and 11586 constitutes the proceedings of the 8th International Conference on Design, User Experience, and Usability, DUXU 2019, held as part of the 21st International Conference, HCI International 2019, which took place in Orlando, FL, USA, in July 2019. The total of 1274 papers and 209 posters included in the 35 HCII 2019 proceedings volumes was carefully reviewed and selected from 5029 submissions. DUXU 2019 includes a total of 167 regular papers, organized in the following topical sections: design philosophy; design theories, methods, and tools; user requirements, preferences emotions and personality; visual DUXU; DUXU for novel interaction techniques and devices; DUXU and robots; DUXU for AI and AI for DUXU; dialogue, narrative, storytelling; DUXU for automated driving, transport, sustainability and smart cities; DUXU for cultural heritage; DUXU for well-being; DUXU for learning; user experience evaluation methods and tools; DUXU practice; DUXU case studies.
Download or read book Expansion in Finite Simple Groups of Lie Type written by Terence Tao and published by American Mathematical Soc.. This book was released on 2015-04-16 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expander graphs are an important tool in theoretical computer science, geometric group theory, probability, and number theory. Furthermore, the techniques used to rigorously establish the expansion property of a graph draw from such diverse areas of mathematics as representation theory, algebraic geometry, and arithmetic combinatorics. This text focuses on the latter topic in the important case of Cayley graphs on finite groups of Lie type, developing tools such as Kazhdan's property (T), quasirandomness, product estimates, escape from subvarieties, and the Balog-Szemerédi-Gowers lemma. Applications to the affine sieve of Bourgain, Gamburd, and Sarnak are also given. The material is largely self-contained, with additional sections on the general theory of expanders, spectral theory, Lie theory, and the Lang-Weil bound, as well as numerous exercises and other optional material.
