Topos Theory

Author: P.T. Johnstone

Publisher: Courier Corporation

ISBN: 0486493369

Category: Mathematics

Page: 400

View: 1563

Focusing on topos theory's integration of geometric and logical ideas into the foundations of mathematics and theoretical computer science, this volume explores internal category theory, topologies and sheaves, geometric morphisms, and other subjects. 1977 edition.

Toposes and Local Set Theories

An Introduction

Author: John L. Bell

Publisher: Courier Corporation

ISBN: 0486462862

Category: Mathematics

Page: 267

View: 6912

This text introduces topos theory, a development in category theory that unites important but seemingly diverse notions from algebraic geometry, set theory, and intuitionistic logic. Topics include local set theories, fundamental properties of toposes, sheaves, local-valued sets, and natural and real numbers in local set theories. 1988 edition.

Einführung in die Kategorientheorie

Mit ausführlichen Erklärungen und zahlreichen Beispielen

Author: Martin Brandenburg

Publisher: Springer-Verlag

ISBN: 3662535211

Category: Mathematics

Page: 343

View: 5719

Die Kategorientheorie deckt die innere Architektur der Mathematik auf. Dabei werden die strukturellen Gemeinsamkeiten zwischen mathematischen Disziplinen und ihren spezifischen Konstruktionen herausgearbeitet. Dieses Buch gibt eine systematische Einführung in die Grundbegriffe der Kategorientheorie. Zahlreiche ausführliche Erklärungstexte sowie die große Menge an Beispielen helfen beim Einstieg in diese verhältnismäßig abstrakte Theorie. Es werden viele konkrete Anwendungen besprochen, welche die Nützlichkeit der Kategorientheorie im mathematischen Alltag belegen. Jedes Kapitel wird mit einem motivierenden Text eingeleitet und mit einer großen Aufgabensammlung abgeschlossen. An Vorwissen muss der Leser lediglich ein paar Grundbegriffe des Mathematik-Studiums mitbringen. Die vorliegende zweite vollständig durchgesehene Auflage ist um ausführliche Lösungen zu ausgewählten Aufgaben ergänzt.

Topoi

The Categorial Analysis of Logic

Author: Robert Goldblatt

Publisher: Courier Corporation

ISBN: 048631796X

Category: Mathematics

Page: 576

View: 8241

A classic exposition of a branch of mathematical logic that uses category theory, this text is suitable for advanced undergraduates and graduate students and accessible to both philosophically and mathematically oriented readers.

Number Theory

Author: George E. Andrews

Publisher: Courier Corporation

ISBN: 9780486682525

Category: Mathematics

Page: 259

View: 5369

Written by a distinguished mathematician and teacher, this undergraduate text uses a combinatorial approach to accommodate both math majors and liberal arts students. In addition to covering the basics of number theory, it offers an outstanding introduction to partitions, plus chapters on multiplicativity-divisibility, quadratic congruences, additivity, and more.

Category Theory in Context

Author: Emily Riehl

Publisher: Courier Dover Publications

ISBN: 0486820807

Category: Mathematics

Page: 272

View: 2864

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.

A Book of Set Theory

Author: Charles C Pinter

Publisher: Courier Corporation

ISBN: 0486497089

Category: Mathematics

Page: 256

View: 5343

"This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--

Satan, Cantor und die Unendlichkeit

und 200 weitere verblüffende Tüfteleien

Author: Raymond Smullyan

Publisher: Springer-Verlag

ISBN: 3034862318

Category: Juvenile Nonfiction

Page: 232

View: 3488

Einführung in die Modelltheorie

Vorlesungen

Author: Philipp Rothmaler

Publisher: Spektrum Akademischer Verlag

ISBN: 9783860254615

Category: Model theory

Page: 331

View: 4135

New Structures for Physics

Author: Bob Coecke

Publisher: Springer

ISBN: 3642128211

Category: Science

Page: 1031

View: 7732

This volume provides a series of tutorials on mathematical structures which recently have gained prominence in physics, ranging from quantum foundations, via quantum information, to quantum gravity. These include the theory of monoidal categories and corresponding graphical calculi, Girard’s linear logic, Scott domains, lambda calculus and corresponding logics for typing, topos theory, and more general process structures. Most of these structures are very prominent in computer science; the chapters here are tailored towards an audience of physicists.

Philosophical Introduction to Set Theory

Author: Stephen Pollard

Publisher: Courier Dover Publications

ISBN: 0486797147

Category: Mathematics

Page: 192

View: 9832

This unique approach maintains that set theory is the primary mechanism for ideological and theoretical unification in modern mathematics, and its technically informed discussion covers a variety of philosophical issues. 1990 edition.

Kategorien und Funktoren

Author: Bodo Pareigis

Publisher: N.A

ISBN: N.A

Category: Categories (Mathematics)

Page: 192

View: 6523

Die Welt des Lichtes

The Universe of Light

Author: William Henry Bragg

Publisher: Springer-Verlag

ISBN: 3663022749

Category: Juvenile Nonfiction

Page: 222

View: 6545

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Abstract Analytic Number Theory

Author: John Knopfmacher

Publisher: Courier Dover Publications

ISBN: 0486663442

Category: Mathematics

Page: 336

View: 1911

John Knopfmacher (1937-99) was a Professor of Mathematics at the University of the Witwatersrand in Johannesburg, South Africa. ...

Spieltheorie

Author: Ken Binmore

Publisher: N.A

ISBN: 9783150185902

Category:

Page: 272

View: 1519

Principia Mathematica.

Author: Alfred North Whitehead,Bertrand Russell

Publisher: N.A

ISBN: N.A

Category: Logic, Symbolic and mathematical

Page: 167

View: 3699

Geometrie und Erfahrung

Erweiterte Fassung des Festvortrages Gehalten an der Preussischen Akademie der Wissenschaften zu Berlin am 27. Januar 1921

Author: Albert Einstein

Publisher: Springer-Verlag

ISBN: 3642499031

Category: Mathematics

Page: N.A

View: 5930

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Elementary Topology

Author: Michael C. Gemignani

Publisher: Courier Corporation

ISBN: 9780486665221

Category: Mathematics

Page: 270

View: 5523

Topology is one of the most rapidly expanding areas of mathematical thought: while its roots are in geometry and analysis, topology now serves as a powerful tool in almost every sphere of mathematical study. This book is intended as a first text in topology, accessible to readers with at least three semesters of a calculus and analytic geometry sequence. In addition to superb coverage of the fundamentals of metric spaces, topologies, convergence, compactness, connectedness, homotopy theory, and other essentials, Elementary Topology gives added perspective as the author demonstrates how abstract topological notions developed from classical mathematics. For this second edition, numerous exercises have been added as well as a section dealing with paracompactness and complete regularity. The Appendix on infinite products has been extended to include the general Tychonoff theorem; a proof of the Tychonoff theorem which does not depend on the theory of convergence has also been added in Chapter 7.

Shape Theory

Categorical Methods of Approximation

Author: J. M. Cordier,T. Porter

Publisher: Courier Corporation

ISBN: 0486783472

Category: Science

Page: 208

View: 7933

This in-depth treatment uses shape theory as a "case study" to illustrate situations common to many areas of mathematics, including the use of archetypal models as a basis for systems of approximations. It offers students a unified and consolidated presentation of extensive research from category theory, shape theory, and the study of topological algebras. A short introduction to geometric shape explains specifics of the construction of the shape category and relates it to an abstract definition of shape theory. Upon returning to the geometric base, the text considers simplical complexes and numerable covers, in addition to Morita's form of shape theory. Subsequent chapters explore Bénabou's theory of distributors, the theory of exact squares, Kan extensions, the notion of a stable object, and stability in an Abelian context. The text concludes with a brief description of derived functors of the limit functor theory—the concept that leads to movability and strong movability of systems—and illustrations of the equivalence of strong movability and stability in many contexts.