Towards Higher Categories

Author: John C. Baez,J. Peter May

Publisher: Springer Science & Business Media

ISBN: 1441915249

Category: Mathematics

Page: 283

View: 6568

This IMA Volume in Mathematics and its Applications TOWARDS HIGHER CATEGORIES contains expository and research papers based on a highly successful IMA Summer Program on n-Categories: Foundations and Applications. We are grateful to all the participants for making this occasion a very productive and stimulating one. We would like to thank John C. Baez (Department of Mathematics, University of California Riverside) and J. Peter May (Department of Ma- ematics, University of Chicago) for their superb role as summer program organizers and editors of this volume. We take this opportunity to thank the National Science Foundation for its support of the IMA. Series Editors Fadil Santosa, Director of the IMA Markus Keel, Deputy Director of the IMA v PREFACE DEDICATED TO MAX KELLY, JUNE 5 1930 TO JANUARY 26 2007. This is not a proceedings of the 2004 conference “n-Categories: Fo- dations and Applications” that we organized and ran at the IMA during the two weeks June 7–18, 2004! We thank all the participants for helping make that a vibrant and inspiring occasion. We also thank the IMA sta? for a magni?cent job. There has been a great deal of work in higher c- egory theory since then, but we still feel that it is not yet time to o?er a volume devoted to the main topic of the conference.

Higher Structures in Geometry and Physics

In Honor of Murray Gerstenhaber and Jim Stasheff

Author: Alberto S. Cattaneo,Anthony Giaquinto,Ping Xu

Publisher: Springer Science & Business Media

ISBN: 9780817647353

Category: Mathematics

Page: 362

View: 6229

This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics— such as algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics— and in theoretical physics such as quantum field theory and string theory. These higher algebraic structures provide a common language essential in the study of deformation quantization, theory of algebroids and groupoids, symplectic field theory, and much more. Each contribution in this volume expands on the ideas of Gerstenhaber and Stasheff. The volume is intended for post-graduate students, mathematical and theoretical physicists, and mathematicians interested in higher structures.

Homotopy Type Theory

Univalent Foundations of Mathematics

Author: Univalent Foundations Program

Publisher: Univalent Foundations


Category: Homotopy theory

Page: 589

View: 7077

Homotopy type theory is a new branch of mathematics that combines aspects of several different fields in a surprising way. It is based on a recently discovered connection between homotopy theory and type theory. It touches on topics as seemingly distant as the homotopy groups of spheres, the algorithms for type checking, and the definition of weak $\infty$-groupoids. Homotopy type theory brings new ideas into the very foundation of mathematics. On the one hand, there is Voevodsky's subtle and beautiful univalence axiom. The univalence axiom implies, in particular, that isomorphic structures can be identified, a principle that mathematicians have been happily using on workdays, despite its incompatibility with the "official" doctrines of conventional foundations. On the other hand, we have higher inductive types, which provide direct, logical descriptions of some of the basic spaces and constructions of homotopy theory: spheres, cylinders, truncations, localizations, etc. Both ideas are impossible to capture directly in classical set-theoretic foundations, but when combined in homotopy type theory, they permit an entirely new kind of "logic of homotopy types". This suggests a new conception of foundations of mathematics, with intrinsic homotopical content, an "invariant" conception of the objects of mathematics - and convenient machine implementations, which can serve as a practical aid tothe working mathematician. This is the Univalent Foundations program. The present book is intended as a first systematic exposition of the basics of univalent foundations, and a collection of examples of this new style of reasoning - but without requiring the reader to know or learn any formal logic, or to use any computer proof assistant. We believe that univalent foundations will eventually become a viable alternative to set theory as the "implicit foundation" for the unformalized mathematics done by most mathematicians.

Category Theory in Context

Author: Emily Riehl

Publisher: Courier Dover Publications

ISBN: 0486820807

Category: Mathematics

Page: 272

View: 6791

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.

Analytic and Algebraic Geometry

Author: Anilatmaja Aryasomayajula,Indranil Biswas,Archana S. Morye,A. J. Parameswaran

Publisher: Springer

ISBN: 981105648X

Category: Mathematics

Page: 292

View: 9692

This volume is an outcome of the International conference held in Tata Institute of Fundamental Research and the University of Hyderabad. There are fifteen articles in this volume. The main purpose of the articles is to introduce recent and advanced techniques in the area of analytic and algebraic geometry. This volume attempts to give recent developments in the area to target mainly young researchers who are new to this area. Also, some research articles have been added to give examples of how to use these techniques to prove new results.

Unglaubliche Zahlen

Author: Ian Stewart

Publisher: Rowohlt Verlag GmbH

ISBN: 3644564310

Category: Mathematics

Page: 448

View: 7687

In diesem Buch nimmt der britische Mathe-Guru seine Leser mit auf eine Reise durch das Reich der Zahlen – reelle, rationale, irrationale, komplexe; ganz, ganz kleine und unendlich große, Fraktale, Logarithmen, Hochzahlen, Primzahlen, Kusszahlen und viele mehr. Jedes Kapitel konzentriert sich auf eine Zahl oder Zahlengruppe und erläutert, warum sie so interessant ist. «Jede Zahl hat ihre eigene Geschichte zu erzählen», heißt es im Vorwort. Stewart erzählt sie mit Begeisterung und versteht es geschickt, diese Geschichten miteinander zu verweben, ob es um die Zahl Pi geht oder zum Schluss auch um Geheimcodes, den Rubikwürfel und Sudoku. Darüber hinaus erfährt man viel über die Geschichte der Mathematik und die Rolle, die sie für unsere Entwicklung spielt. Schließlich waren es die Zahlen, so der Autor, «die es der Menschheit ermöglicht haben, sich aus dem Schlamm zu ziehen und nach den Sternen zu greifen».

Operations Research


Author: Frederick S. Hillier,Gerald J. Liebermann

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3486792083

Category: Business & Economics

Page: 868

View: 2087

Aus dem Inhalt: Was ist Operations Research? Überblick über die Modellierungsgrundsätze des Operations Research. Einführung in die lineare Programmierung. Die Lösung linearer Programmierungsprobleme: Das Simplexverfahren. Stochastische Prozesse. Warteschlangentheorie. Lagerhaltungstheorie. Prognoseverfahren. Markov-Entscheidungsprozesse. Reliabilität. Entscheidungstheorie. Die Theorie des Simplexverfahrens Qualitätstheorie und Sensitivitätsanalyse Spezialfälle linearer Programmierungsprobleme. Die Formulierung linearer Programmierungsmodelle und Goal-Programmierung. Weitere Algorithmen der linearen Programmierung. Netzwerkanalyse einschließlich PERT-CPM. Dynamische Optimierung. Spieltheorie. Ganzzahlige Programmierung. Nichtlineare Programmierung Simulation. Anhang. Lösungen für ausgewählte Übungsaufgaben.

Amorphous Polymers and Non-Newtonian Fluids

Author: Constantine Dafermos,J.L. Ericksen,David Kinderlehrer

Publisher: Springer

ISBN: 0387965564

Category: Science

Page: 202

View: 9496

This IMA Volume in Mathematics and its Applications AMORPHOUS POLYMERS AND NON-NEWTONIAN FLUIDS is in part the proceedings of a workshop which was an integral part of the 1984-85 IMA program on CONTINUUM PHYSICS AND PARTIAL DIFFERENTIAL EQUATIONS We are grateful to the Scientific Committee: Haim Brezis Constantine Dafermos Jerry Ericksen David Kinderlehrer for planning and implementing an exciting and stimulating year-long program. We espe cially thank the Program Organizers, Jerry Ericksen, David Kinderlehrer, Stephen Prager and Matthew Tirrell for organizing a workshop which brought together scientists and mathematicians in a variety of areas for a fruitful exchange of ideas. George R. Sell Hans Weinberger Preface Experiences with amorphous polymers have supplied much of the motivation for developing novel kinds of molecular theory, to try to deal with the more significant features of systems involving very large molecules with many degrees offreedom. Similarly, the observations of many unusual macroscopic phenomena has stimulated efforts to develop linear and nonlinear theories of viscoelasticity to describe them. In either event, we are confronted not with a well-established, specific set of equations, but with a variety of equations, conforming to a loose pattern and suggested by general kinds of reasoning. One challenge is to devise techniques for finding equations capable of delivering definite and reliable predictions. Related to this is the issue of discovering ways to better grasp the nature of solutions ofthose equations showing some promise.

Zeitschrift für angewandte Mathematik und Mechanik

Author: N.A

Publisher: N.A


Category: Engineering

Page: N.A

View: 2294

Vols. 41-44, 46-50 include Sonderheft: Vorträge der wissenschaftlichen Jahrestagung der Gesellschaft für Angewandte Mathematik und Mechanik (v. 44, Vorträge der Tagung für Angewandte Mathematik und Mechanik).

Linear Algebra for Signal Processing

Author: Adam Bojanczyk,George Cybenko

Publisher: Springer Science & Business Media

ISBN: 9780387944913

Category: Technology & Engineering

Page: 184

View: 8188

Signal processing applications have burgeoned in the past decade. During the same time, signal processing techniques have matured rapidly and now include tools from many areas of mathematics, computer science, physics, and engineering. This trend will continue as many new signal processing applications are opening up in consumer products and communications systems. In particular, signal processing has been making increasingly sophisticated use of linear algebra on both theoretical and algorithmic fronts. This volume gives particular emphasis to exposing broader contexts of the signal processing problems so that the impact of algorithms and hardware can be better understood; it brings together the writings of signal processing engineers, computer engineers, and applied linear algebraists in an exchange of problems, theories, and techniques. This volume will be of interest to both applied mathematicians and engineers.

Amstat News

Author: N.A

Publisher: N.A


Category: Statistics

Page: N.A

View: 2340

Mathematical Reviews

Author: N.A

Publisher: N.A


Category: Mathematics

Page: N.A

View: 8818

Instrumentelle Analytik

Grundlagen - Geräte - Anwendungen

Author: Douglas A. Skoog,James J. Leary

Publisher: Springer-Verlag

ISBN: 366207916X

Category: Science

Page: 900

View: 6784

Mit der deutschsprachigen Ausgabe des Standard-Lehrbuchs zur Instrumentellen Analytik von Skoog und Leary schließt sich endlich eine Lücke im Buchangebot für fortgeschrittene Studenten der Chemie an Universitäten und Fachhochschulen. Aufgrund des multidisziplinären Eindringens der Analytischen Chemie in andere Bereiche richtet sich das Buch auch an Physiker, Ingenieure und Biochemiker. Das Buch führt aktuell und kompetent in die Grundzüge und Feinheiten der heutigen Instrumentellen Analytischen Chemie ein. Über 530 detailreiche, selbsterklärende Abbildungen, Anhänge zu Statistik und Elektronik, Übungsaufgaben mit Lösungen und viele wichtige Originalzitate ergänzen dieses moderne Lehrbuch für Studierende und Praktiker.

The 10th IEEE International Conference on Fuzzy Systems

Meeting the Grand Challenge : Machines that Serve People, December 2-5, 2001, University of Melbourne, Australia

Author: Zhi-Qiang Liu,Institute of Electrical and Electronics Engineers,IEEE Neural Networks Council

Publisher: N.A

ISBN: 9780780372931


Page: N.A

View: 8940

Annual Report

Author: Iowa State University. Statistical Laboratory

Publisher: N.A


Category: Statistics

Page: N.A

View: 2442