mathematics in computing an accessible guide to historical foundational and application contexts

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Mathematics In Computing

Author : Gerard O’Regan
ISBN : 9781447145349
Genre : Computers
File Size : 80. 89 MB
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This clearly written and enlightening textbook provides a concise, introductory guide to the key mathematical concepts and techniques used by computer scientists. Topics and features: ideal for self-study, offering many pedagogical features such as chapter-opening key topics, chapter introductions and summaries, review questions, and a glossary; places our current state of knowledge within the context of the contributions made by early civilizations, such as the ancient Babylonians, Egyptians and Greeks; examines the building blocks of mathematics, including sets, relations and functions; presents an introduction to logic, formal methods and software engineering; explains the fundamentals of number theory, and its application in cryptography; describes the basics of coding theory, language theory, and graph theory; discusses the concept of computability and decideability; includes concise coverage of calculus, probability and statistics, matrices, complex numbers and quaternions.

Encyclopedia Of Information Science And Technology Fourth Edition

Author : Khosrow-Pour, D.B.A., Mehdi
ISBN : 9781522522560
Genre : Computers
File Size : 55. 67 MB
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In recent years, our world has experienced a profound shift and progression in available computing and knowledge sharing innovations. These emerging advancements have developed at a rapid pace, disseminating into and affecting numerous aspects of contemporary society. This has created a pivotal need for an innovative compendium encompassing the latest trends, concepts, and issues surrounding this relevant discipline area. During the past 15 years, the Encyclopedia of Information Science and Technology has become recognized as one of the landmark sources of the latest knowledge and discoveries in this discipline. The Encyclopedia of Information Science and Technology, Fourth Edition is a 10-volume set which includes 705 original and previously unpublished research articles covering a full range of perspectives, applications, and techniques contributed by thousands of experts and researchers from around the globe. This authoritative encyclopedia is an all-encompassing, well-established reference source that is ideally designed to disseminate the most forward-thinking and diverse research findings. With critical perspectives on the impact of information science management and new technologies in modern settings, including but not limited to computer science, education, healthcare, government, engineering, business, and natural and physical sciences, it is a pivotal and relevant source of knowledge that will benefit every professional within the field of information science and technology and is an invaluable addition to every academic and corporate library.

Advanced Methodologies And Technologies In Network Architecture Mobile Computing And Data Analytics

Author : Khosrow-Pour, D.B.A., Mehdi
ISBN : 9781522575993
Genre : Computers
File Size : 78. 40 MB
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From cloud computing to data analytics, society stores vast supplies of information through wireless networks and mobile computing. As organizations are becoming increasingly more wireless, ensuring the security and seamless function of electronic gadgets while creating a strong network is imperative. Advanced Methodologies and Technologies in Network Architecture, Mobile Computing, and Data Analytics highlights the challenges associated with creating a strong network architecture in a perpetually online society. Readers will learn various methods in building a seamless mobile computing option and the most effective means of analyzing big data. This book is an important resource for information technology professionals, software developers, data analysts, graduate-level students, researchers, computer engineers, and IT specialists seeking modern information on emerging methods in data mining, information technology, and wireless networks.

A Brief History Of Computing

Author : Gerard O'Regan
ISBN : 9781447123590
Genre : Computers
File Size : 90. 29 MB
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This lively and fascinating text traces the key developments in computation – from 3000 B.C. to the present day – in an easy-to-follow and concise manner. Topics and features: ideal for self-study, offering many pedagogical features such as chapter-opening key topics, chapter introductions and summaries, exercises, and a glossary; presents detailed information on major figures in computing, such as Boole, Babbage, Shannon, Turing, Zuse and Von Neumann; reviews the history of software engineering and of programming languages, including syntax and semantics; discusses the progress of artificial intelligence, with extension to such key disciplines as philosophy, psychology, linguistics, neural networks and cybernetics; examines the impact on society of the introduction of the personal computer, the World Wide Web, and the development of mobile phone technology; follows the evolution of a number of major technology companies, including IBM, Microsoft and Apple.

Quantum Theory For Mathematicians

Author : Brian C. Hall
ISBN : 9781461471165
Genre : Science
File Size : 83. 65 MB
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Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Theorem for bounded and unbounded self-adjoint operators; the Stone–von Neumann Theorem; the Wentzel–Kramers–Brillouin approximation; the role of Lie groups and Lie algebras in quantum mechanics; and the path-integral approach to quantum mechanics. The numerous exercises at the end of each chapter make the book suitable for both graduate courses and independent study. Most of the text is accessible to graduate students in mathematics who have had a first course in real analysis, covering the basics of L2 spaces and Hilbert spaces. The final chapters introduce readers who are familiar with the theory of manifolds to more advanced topics, including geometric quantization.

The Foundations Of Computability Theory

Author : Borut Robič
ISBN : 9783662448083
Genre : Computers
File Size : 63. 56 MB
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This book offers an original and informative view of the development of fundamental concepts of computability theory. The treatment is put into historical context, emphasizing the motivation for ideas as well as their logical and formal development. In Part I the author introduces computability theory, with chapters on the foundational crisis of mathematics in the early twentieth century, and formalism; in Part II he explains classical computability theory, with chapters on the quest for formalization, the Turing Machine, and early successes such as defining incomputable problems, c.e. (computably enumerable) sets, and developing methods for proving incomputability; in Part III he explains relative computability, with chapters on computation with external help, degrees of unsolvability, the Turing hierarchy of unsolvability, the class of degrees of unsolvability, c.e. degrees and the priority method, and the arithmetical hierarchy. This is a gentle introduction from the origins of computability theory up to current research, and it will be of value as a textbook and guide for advanced undergraduate and graduate students and researchers in the domains of computability theory and theoretical computer science.

Roads To Infinity

Author : John C. Stillwell
ISBN : 9781439865507
Genre : Mathematics
File Size : 34. 82 MB
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Winner of a CHOICE Outstanding Academic Title Award for 2011! This book offers an introduction to modern ideas about infinity and their implications for mathematics. It unifies ideas from set theory and mathematical logic, and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics. The treatment is historical and partly informal, but with due attention to the subtleties of the subject. Ideas are shown to evolve from natural mathematical questions about the nature of infinity and the nature of proof, set against a background of broader questions and developments in mathematics. A particular aim of the book is to acknowledge some important but neglected figures in the history of infinity, such as Post and Gentzen, alongside the recognized giants Cantor and Gödel.

Plato S Ghost

Author : Jeremy Gray
ISBN : 1400829046
Genre : Mathematics
File Size : 52. 94 MB
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Plato's Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions. Plato's Ghost evokes Yeats's lament that any claim to worldly perfection inevitably is proven wrong by the philosopher's ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincaré, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of naïve set theory and the revived axiomatic method--debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism. Plato's Ghost is essential reading for mathematicians and historians, and will appeal to anyone interested in the development of modern mathematics.

The Sage Guide To Curriculum In Education

Author : Ming Fang He
ISBN : 9781506328867
Genre : Education
File Size : 56. 15 MB
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The SAGE Guide to Curriculum in Education integrates, summarizes, and explains, in highly accessible form, foundational knowledge and information about the field of curriculum with brief, simply written overviews for people outside of or new to the field of education. This Guide supports study, research, and instruction, with content that permits quick access to basic information, accompanied by references to more in-depth presentations in other published sources. This Guide lies between the sophistication of a handbook and the brevity of an encyclopedia. It addresses the ties between and controversies over public debate, policy making, university scholarship, and school practice. While tracing complex traditions, trajectories, and evolutions of curriculum scholarship, the Guide illuminates how curriculum ideas, issues, perspectives, and possibilities can be translated into public debate, school practice, policy making, and life of the general public focusing on the aims of education for a better human condition. 55 topical chapters are organized into four parts: Subject Matter as Curriculum, Teachers as Curriculum, Students as Curriculum, and Milieu as Curriculum based upon the conceptualization of curriculum commonplaces by Joseph J. Schwab: subject matter, teachers, learners, and milieu. The Guide highlights and explicates how the four commonplaces are interdependent and interconnected in the decision-making processes that involve local and state school boards and government agencies, educational institutions, and curriculum stakeholders at all levels that address the central curriculum questions: What is worthwhile? What is worth knowing, needing, experiencing, doing, being, becoming, overcoming, sharing, contributing, wondering, and imagining? The Guide benefits undergraduate and graduate students, curriculum professors, teachers, teacher educators, parents, educational leaders, policy makers, media writers, public intellectuals, and other educational workers. Key Features: Each chapter inspires readers to understand why the particular topic is a cutting edge curriculum topic; what are the pressing issues and contemporary concerns about the topic; what historical, social, political, economic, geographical, cultural, linguistic, ecological, etc. contexts surrounding the topic area; how the topic, relevant practical and policy ramifications, and contextual embodiment can be understood by theoretical perspectives; and how forms of inquiry and modes of representation or expression in the topic area are crucial to develop understanding for and make impact on practice, policy, context, and theory. Further readings and resources are provided for readers to explore topics in more details.

Erfindung Des Computers Elektronenrechner Entwicklungen In Deutschland England Und Der Schweiz

Author : Herbert Bruderer
ISBN : 9783110602616
Genre : Computers
File Size : 54. 92 MB
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Das preisgekrönte Werk „Meilensteine der Rechentechnik" liegt in der 2., völlig neu bearbeiteten und stark erweiterten Auflage vor. Die beiden Bände, die im Ganzen rund 1600 Seiten umfassen, sind ein Gesamtwerk, lassen sich aber auch einzeln nutzen. Diese Schrift behandelt sowohl analoge wie digitale Geräte und geht auf benachbarte Bereiche wie Automatenbau (z.B. Figuren- und Musikautomaten) sowie wissenschaftliche Instrumente (z.B. Himmelskunde, Vermessungswesen, Uhrmacherkunst) ein. Gestreift werden zudem frühe Schreibmaschinen und programmgesteuerte mechanische Webstühle. Schwerpunkte des ersten Bandes sind: Grundlagen, mechanische Rechenmaschinen, Rechenschieber, historische Automaten, Entwicklung der Rechenkunst, Schritt-für-Schritt-Anleitungen für analoge und digitale Rechengeräte. Alle wichtigen Fachbegriffe werden erklärt. Die weltweit prachtvollsten Rundbaurechenmaschinen und Androiden werden in Wort und Bild vorgestellt. Das Buch enthält ferner grundsätzliche Betrachtungen zu Themen wie Digitalisierung und künstliche Intelligenz sowie zur Rolle der Technikgeschichte und der Erhaltung des technischen Kulturguts. Der zweite Band widmet sich überwiegend den Elektronenrechnern: Erfindung des Computers, weltweite Entwicklung der Rechentechnik, insbesondere in Deutschland, England und der Schweiz. Er schließt überdies je ein Fachwörterbuch Deutsch-Englisch und Englisch-Deutsch ein. Die sollen das Lesen anspruchsvoller fremdsprachiger Texte und Übersetzungen fördern. Hinzu kommt eine umfassende weltweite Bibliografie. Beide Bände berichten über aufsehenerregende neue Funde von Dokumenten und Gegenständen (u.a. weltgrößte serienmäßig gefertigte Rechenwalze, weltweit kleinster mechanischer Parallelrechner, erster mechanischer Prozessrechner), sie eignen sich auch als Nachschlagewerke. Sie sind allgemein verständlich und richten sich an alle, die Freude haben an Technik-, Mathematik-, Informatik- und Kunstgeschichte. Mehrsprachige Bibliografie zur Mathematik-, Informatik, Technik- und Naturwissenschaftsgeschichte mit über 5000 Einträgen, Fachwörterbuch Deutsch-Englisch und Englisch-Deutsch mit je 4000 Einträgen, 18 Schritt-für-Schritt-Anleitungen für die Bedienung historischer analoger und digitaler Geräte, 100 tabellarische Übersichten, zahlreiche Zeittafeln, ausführliches Personen-, Orts- und Sachverzeichnis. Herbert Bruderer ist Dozent i.R. am Departement für Informatik der Eidgenössischen Technischen Hochschule (ETH) Zürich und Technikhistoriker. Er hat zahlreiche Bücher zur Informatik verfasst und ist mehrfacher Preisträger.

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