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SPIRES-BOOKS: FIND KEYWORD CATEGORY THEORY MATHEMATICS *END*INIT* use /tmp/qspiwww.webspi1/13323.59 QRY 131.225.70.96 . find keyword "category theory mathematics" ( in books using www

 Call number: 9780465051694:ONLINE Show nearby items on shelf Title: How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics Author(s): Eugenia Cheng Date: 2015 Publisher: New York, NY: Basic Books Size: 1 online resource (288 p) Contents: Math. What is math?, Abstraction, Principles, Process, Generalization, Internal vs. external, Axiomatization, What mathematics is -- Category theory. What is category theory?, Context, Relationships, Structure, Sameness, Universal properties, What category theory is. ISBN: 9780465051717 Series: eBooks Series: EBL eBook Keywords: Mathematics. Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: NEW

 Call number: SPRINGER-2011-9783034604055:ONLINE Show nearby items on shelf Title: From Past to Future: Gramann's Work in Context [electronic resource] : Gramann Bicentennial Conference, September 2009 Author(s): Hans-Joachim Petsche Albert C Lewis Jrg Liesen Steve Russ Date: 2011 Publisher: Basel : Springer Basel Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: On the occasion of the 200th anniversary of the birth of Hermann Gramann (1809-1877), an interdisciplinary conference was held in Potsdam, Germany, and in Gramann's hometown Szczecin, Poland. The idea of the conference was topresent a multi-faceted p icture of Gramann, and to uncover the complexity of the factors that were responsible for his creativity. The conference demonstrated not only the very influential reception of his work at the turn of the20th century, but also the unexpected modernity of his ideas, and their continuing development in the 21st century. This book contains 37 papers presented at the conference. They investigate the significance of Gramann's work forphilosophical as well as for scientific and methodological questions, for com parative philology in general and for Indology in particular, for psychology, physiology, religious studies, musicology, didactics, and, last but not least,mathematics. In addition, the book contains numerous illustrations and English translations of orig inal sources, which are published here for the first time. These include life histories of Gramann (written by his son Justus) and ofhis brother Robert (written by Robert himself), as well as the paper On the concept and extent of pure theory of number'' by Justus Gramann (the father). In November 2010 the capital of the federal state of Brandenburg (Germany)chose the Gramann Conference as the first-time winner of the Potsdam Conference-Award in the category Innovative and/or exceptional events Note: Springer eBooks ISBN: 9783034604055 Series: e-books Series: SpringerLink (Online service) Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Mathematics_$xHistory Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE  Call number: SPRINGER-2010-9783034800525:ONLINE Show nearby items on shelf Title: Simplicial Methods for Operads and Algebraic Geometry [electronic resource] Author(s): Ieke Moerdijk Bertrand Ton Date: 2010 Publisher: Basel : Springer Basel Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: This book is an introduction to two higher-categorical topics in algebraic topology and algebraic geometry relying on simplicial methods. Moerdijks lectures offer a detailed introduction to dendroidal sets, which wereintroduced by himself and Weiss a s a foundation for the homotopy theory of operads. The theory of dendroidal sets is based on trees instead of linear orders and has many features analogous to the theory of simplicial sets, but it alsoreveals new phenomena. For example, dendroidal sets ad mit a closed symmetric monoidal structure related to the BoardmanVogt tensor product of operads. The lecture notes start with the combinatorics of trees and culminate with asuitable model structure on the category of dendroidal sets. Important concepts ar e illustrated with pictures and examples. The lecture series by Ton presents derived algebraic geometry. While classical algebraic geometry studiesfunctors from the category of commutative rings to the category of sets, derived algebraic geometry is conce rned with functors from simplicial commutative rings (to allow derived tensor products) to simplicial sets (to allow derivedquotients). The central objects are derived (higher) stacks, which are functors satisfying a certain up-to-homotopy descent conditi on. These lectures provide a concise and focused introduction to this vast subject, glossing over manyof the technicalities that make the subjects research literature so overwhelming. Both sets of lectures assume a working knowledge of model categories in the sense of Quillen. For Tons lectures, some background in algebraicgeometry is also necessary Note: Springer eBooks ISBN: 9783034800525 Series: e-books Series: SpringerLink (Online service) Series: Advanced Courses in Mathematics - CRM Barcelona Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Algebra , Algebraic topology Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE  Call number: SPRINGER-2010-9783034604369:ONLINE Show nearby items on shelf Title: Homological Algebra of Semimodules and Semicontramodules [electronic resource] : Semi-infinite Homological Algebra of Associative Algebraic Structures Author(s): Leonid Positselski Date: 2010 Publisher: Basel : Springer Basel Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: This monograph deals with semi-infinite homological algebra. Intended as the definitive treatment of the subject of semi-infinite homology and cohomology of associative algebraic structures, it also contains material on thesemi-infinite (co)homology of Lie algebras and topological groups, the derived comodule-contramodule correspondence, its application to the duality between representations of infinite-dimensional Lie algebras with complementary centralcharges, and relative non-homogeneous Koszul du ality. The book explains with great clarity what the associative version of semi-infinite cohomology is, why it exists, and for what kind of objects it is defined. Semialgebras,contramodules, exotic derived categories, Tate Lie algebras, algebraic Harish- Chandra pairs, and locally compact totally disconnected topological groups all interplay in the theories developed in this monograph. Contramodules,introduced originally by Eilenberg and Moore in the 1960s but almost forgotten for four decades, are featur ed prominently in this book, with many versions of them introduced and discussed. Rich in new ideas on homological algebra andthe theory of corings and their analogues, this book also makes a contribution to the foundational aspects of representation theo ry. In particular, it will be a valuable addition to the algebraic literature available to mathematicalphysicists Note: Springer eBooks Contents: Preface Introduction 0 Preliminaries and Summary 1 Semialgebras and Semitensor Product 2 Derived Functor SemiTor 3 Semicontramodules and Semihomomorphisms 4 Derived Functor SemiExt 5 Comodule Contramodule Correspondence 6 Semimodule Semicontramodule Correspondence 7 Functoriality in the Coring 8 Functoriality in the Semialgebra 9 Closed Model Category Structures 10 A Construction of Semialgebras 11 Relative Nonhomogeneous Koszul Duality Appendix A Contramodules over Coalgebras over Fields Appendix B Comparison with Arkhipov's Ext^{\infty/2+*} and Se ISBN: 9783034604369 Series: e-books Series: SpringerLink (Online service) Series: Monografie Matematyczne : v70 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Global analysis , Global differential geometry Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE  Call number: SPRINGER-2010-9781849962513:ONLINE Show nearby items on shelf Title: Mathematica: A Problem-Centered Approach [electronic resource] Author(s): Roozbeh Hazrat Date: 2010 Publisher: London : Springer London Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: Mathematica: A Problem-Centered Approach introduces the vast array of features and powerful mathematical functions of Mathematica using a multitude of clearly presented examples and worked- out problems. Each section startswith a description of a new topic and some basic examples. The author then demonstrates the use of new commands through three categories of problems - the first category highlights those essential parts of the text that demonstrate theuse of new commands in Mathematica whilst solvi ng each problem presented - the second comprises problems that further demonstrate the use of commands previously introduced to tackle different situations and - the third presents morechallenging problems for further study. The intention is to enable the reader to learn from the codes, thus avoiding long and exhausting explanations. While based on a computer algebra course taught to undergraduate students ofmathematics, science, engineering and finance, the book also includes chapters on calculus and sol ving equations, and graphics, thus covering all the basic topics in Mathematica. With its strong focus upon programming and problemsolving, and an emphasis on using numerical problems that do not need any particular background in mathematics, this book is also ideal for self-study and as an introduction to researchers who wish to use Mathematica as a computationaltool. Mathematica: A Problem-Centered Approach comes with a free 30 day trial of the Wolfram Mathematica(R) software Note: Springer eBooks Contents: 1. Introduction 1.1 Mathematica as a calculator 1.2 Numbers 1.3 Algebraic computations 1.4 Trigonometric computations 1.5 Variables 1.6 Equalities =, :=, == 1.7 Dynamic variables 2. Defining functions 2.1 Formulas as functions 2.2 Anonymous functions 3. Lists 3.1 Functions producing lists 3.2 Listable functions 3.3 Selecting from a list 4. Changing heads! 5. A bit of logic and set theory 5.1 Being logical 5.2 Handling sets 5.3 Decision making, If and Which 6. Sums and products 6.1 Sum 6.2 Product 7. Loops and repetitions 7 ISBN: 9781849962513 Series: e-books Series: SpringerLink (Online service) Series: Springer Undergraduate Mathematics Series, 1615-2085 : v53 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Computer science , Algebra Data processing , Computer software Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE  Call number: SPRINGER-2010-9781441917218:ONLINE Show nearby items on shelf Title: Lattice-ordered Rings and Modules [electronic resource] Author(s): Stuart A Steinberg Date: 2010 Edition: First Publisher: New York, NY : Springer New York Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: This book provides an exposition of the algebraic aspects of the theory of lattice-ordered rings and lattice-ordered modules. All of the background material on rings, modules, and lattice-ordered groups necessary to make the workself-contained and ac cessible to a variety of readers is included. Steinberg includes in his presentation of the material 800+ extensive exercises of varying levels of difficulty at the end of each of the sections. The first twochapters of the book provide a thorough introduc tion to the material, while the following four chapters delve into more specific topics. Key topics include: *lattice-ordered groups, rings, and fields *archimedean$l$-groups *f-ringsand larger varieties of$l$-rings *the category of f-modules *various c ommutativity results. Filling a gap in the literature, Lattice-Ordered Rings and Modules may be used as a textbook or for self-study by graduate students andresearchers studying lattice-ordered rings and lattice-ordered modules Note: Springer eBooks Contents: Partially Ordered Sets and Lattices Lattice ordered Groups Lattice ordered Rings The Category of Modules Lattice ordered Fields Additional Topics ISBN: 9781441917218 Series: e-books Series: SpringerLink (Online service) Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Algebra Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE  Call number: SPRINGER-2010-9781441915245:ONLINE Show nearby items on shelf Title: Towards Higher Categories [electronic resource] Author(s): John C Baez J. Peter May Date: 2010 Publisher: New York, NY : Springer New York Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: The purpose of this book is to give background for those who would like to delve into some higher category theory. It is not a primer on higher category theory itself. It begins with a paper by John Baez and Michael Shulman whichexplores informally, by analogy and direct connection, how cohomology and other tools of algebraic topology are seen through the eyes of n-category theory. The idea is to give some of the motivations behind this subject. There are thentwo survey articles, by Julie Bergner and Simona Paoli, about (infinity,1) categories and about the algebraic modelling of homotopy n-types. These are areas that are particularly well understood, and where a fully integrated theoryexists. The main focus of the book is on the richness to be found in the theory of bicategories, which gives the essential starting point towards the understanding of higher categorical structures. An article by Stephen Lack gives athorough, but informal, guide to this theory. A paper by Larry Breen on the theory of ge rbes shows how such categorical structures appear in differential geometry. This book is dedicated to Max Kelly, the founder of the Australianschool of category theory, and an historical paper by Ross Street describes its development Note: Springer eBooks Contents: Foreword Preface Lectures on n categories and cohomology A survey of (1, 1) categories Internal categorical structures in homotopical algebra A 2 categories companion Notes on 1 and 2 gerbes An Australian conspectus of higher categories IMA summer program participants ISBN: 9781441915245 Series: e-books Series: SpringerLink (Online service) Series: The IMA Volumes in Mathematics and its Applications, 0940-6573 : v152 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Algebra , Topology , Algebraic topology Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE  Call number: SPRINGER-2009-9783764399986:ONLINE Show nearby items on shelf Title: Frobenius Categories versus Brauer Blocks [electronic resource] : The Grothendieck Group of the Frobenius Category of a Brauer Block Author(s): Llus Puig Date: 2009 Publisher: Basel : Birkhuser Basel Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: This book contributes to important questions in the representation theory of finite groups over fields of positive characteristic an area of research initiated by Richard Brauer sixty years ago with the introduction of theblocks of characters. On th e one hand, it introduces and develops the abstract setting of the Frobenius categories also called the Saturated fusion systems in the literature created by the author fifteen years ago for a betterunderstanding of what was loosely called the local the ory of a finite group around a prime number p or, later, around a Brauer block, and for the purpose of an eventual classification a reasonable concept of simple Frobeniuscategory arises. On the other hand, the book develops this abstract setting in paral lel with its application to the Brauer blocks, giving the detailed translation of any abstract concept in the particular context of the blocks. One ofthe new features in this direction is a framework for a deeper understanding of one of the central open p roblems in modular representation theory, known as Alperins Weight Conjecture (AWC). Actually, this new framework suggests amore general form of AWC, and a significant result of the book is a reduction theorem of this form of AWC to quasi-simple groups. A lthough this book is a research monograph, all the arguments are widely developed to make it accessibleto the interested graduate students and, at the same time, to put them on the verge of the research on this new subject: the third part of the book on t he localities associated to a Frobenius category gives some insight on the openquestion about the existence and the uniquenes of a perfect locality also called centric linking system in the literature. We have developed a long introduction to explain our purpose and to provide a guideline for the readerthroughout the twenty four sections. A systematic appendix on the cohomology of categories completes the book Note: Springer eBooks ISBN: 9783764399986 Series: e-books Series: SpringerLink (Online service) Series: Progress in Mathematics : v274 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Group theory , Algebraic topology Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE  Call number: SPRINGER-2009-9783764399900:ONLINE Show nearby items on shelf Title: Regularity and Substructures of Hom [electronic resource] Author(s): Friedrich Kasch Adolf Mader Date: 2009 Publisher: Basel : Birkhuser Basel Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: The book generalizes the well-known regularity of ring elements to regularity of homomorphisms in module categories, and further to regularity of morphisms in any category. Regular homomorphisms are characterized in terms ofdecompositions of domain a nd codomain, and numerous other results are presented. While the theory is well developed in module categories many questions remain about generalizations and extensions to other categories. The book onlyrequires the knowledge of a basic course in modern algebra. It is written clearly, with great detail, and is accessible to students and researchers alike Note: Springer eBooks ISBN: 9783764399900 Series: e-books Series: SpringerLink (Online service) Series: Frontiers in Mathematics, 1660-8046 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Algebra , Group theory Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE  Call number: SPRINGER-2009-9783764387365:ONLINE Show nearby items on shelf Title: Quantum Field Theory [electronic resource] : Competitive Models Author(s): Bertfried Fauser Jrgen Tolksdorf Eberhard Zeidler Date: 2009 Publisher: Basel : Birkhuser Basel Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: For more than 70 years, quantum field theory (QFT) can be seen as a driving force in the development of theoretical physics. Equally fascinating is the fruitful impact which QFT had in rather remote areas of mathematics. Thepresent book features some of the different approaches, different physically viewpoints and techniques used to make the notion of quantum field theory more precise. For example, the present book contains a discussion including generalconsiderations, stochastic methods, deformation theory and the holographic AdS/CFT correspondence. It also contains a discussion of more recent developments like the use of category theory and topos theoretic methods to describe QFT.The present volume emerged from the 3rd 'Blaubeuren Workshop: Recent Developments in Quantum Field Theory', held in July 2007 at the Max Planck Institute of Mathematics in the Sciences in Leipzig/Germany. All of the contributions arecommitted to the idea of this workshop series: 'To bring together outstanding experts worki ng in the field of mathematics and physics to discuss in an open atmosphere the fundamental questions at the frontier of theoretical physics' Note: Springer eBooks Contents: Constructive Use of Holographic Projections Topos Theory and Neo Realist Quantum Theory A Survey on Mathematical Feynman Path Integrals: Construction, Asymptotics, Applications A Comment on the Infra Red Problem in the AdS/CFT Correspondence Some Steps Towards Noncommutative Mirror Symmetry on the Torus Wittens Volume Formula, Cohomological Pairings of Moduli Space of Flat Connections and Applications of Multiple Zeta Functions Noncommutative Field Theories from a Deformation Point of View Renormalization of Gauge Fields using Hopf Algebras Not so Non Renormali ISBN: 9783764387365 Series: e-books Series: SpringerLink (Online service) Series: Physics and Astronomy (Springer-11651) Keywords: Quantum theory , Mathematical physics Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE  Call number: SPRINGER-2009-9783642001482:ONLINE Show nearby items on shelf Title: The Rubato Composer Music Software [electronic resource] Component-Based Implementation of a Functorial Concept Architecture Author(s): Grard Milmeister Date: 2009 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: Both modern mathematical music theory and computer science are strongly influenced by the theory of categories and functors. One outcome of this research is the data format of denotators, which is based on set-valued presheavesover the category of mo dules and diaffine homomorphisms. The functorial approach of denotators deals with generalized points in the form of arrows and allows the construction of a universal concept architecture. This architecture isideal for handling all aspects of music, espec ially for the analysis and composition of highly abstract musical works. This book presents an introduction to the theory of module categories and the theory of denotators, as well as thedesign of a software system, called Rubato Composer, which is an imp lementation of the category-theoretic concept framework. The application is written in portable Java and relies on plug-in components, so-called rubettes, which may becombined in data flow networks for the generation and manipulation of denotators. The Ru bato Composer system is open to arbitrary extension and is freely available under the GPL license. It allows the developer to build specializedrubettes for tasks that are of interest to composers, who in turn combine them to create music. It equally serve s music theorists, who use them to extract information from and manipulate musical structures. They may even develop newtheories by experimenting with the many parameters that are at their disposal thanks to the increased flexibility of the functorial con cept architecture. Two contributed chapters by Guerino Mazzola and Florian Thalmann illustrate theapplication of the theory as well as the software in the development of compositional tools and the creation of a musical work with the help of the Rubato fr amework Note: Springer eBooks Contents: Concepts and Theory Overview of Music Theories The Representation of Music Architecture of Concepts I: Principles The Category of Modules Architecture of Concepts II: Forms and Denotators Software Components for Computational Theories Historical Overview The Implementation Overview Architecture Modules and Morphisms Forms and Denotators Tools and Utilities Rubato Composer GUI Rubato Composer in Practice Overview A Tutorial First Applications in Rubette Construction The BigBang Rubette Creative Analysis of Boulezs Conclusion and ISBN: 9783642001482 Series: e-books Series: SpringerLink (Online service) Series: Computational Music Science, 1868-0305 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Information systems , Computer science , Algebra , Music Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE  Call number: SPRINGER-2009-9783540890560:ONLINE Show nearby items on shelf Title: Modules over Operads and Functors [electronic resource] Author(s): Benoit Fresse Date: 2009 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: The notion of an operad supplies both a conceptual and effective device to handle a variety of algebraic structures in various situations. Operads were introduced 40 years ago in algebraic topology in order to model the structureof iterated loop spac es. Since then, operads have been used fruitfully in many fields of mathematics and physics. This monograph begins with a review of the basis of operad theory. The main purpose is to study structures of modulesover operads as a new device to model functor s between categories of algebras as effectively as operads model categories of algebras Note: Springer eBooks Contents: Categorical and operadic background Symmetric monoidal categories for operads Symmetric objects and functors Operads and algebras in symmetric monoidal categories Miscellaneous structures associated to algebras over operads The category of right modules over operads and functors Definitions and basic constructions Tensor products Universal constructions on right modules over operads Adjunction and embedding properties Algebras in right modules over operads Miscellaneous examples Homotopical background Symmetric monoidal model categories for operads The ISBN: 9783540890560 Series: e-books Series: SpringerLink (Online service) Series: Lecture Notes in Mathematics, 0075-8434 : v1967 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Algebra , Algebraic topology Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE  Call number: SPRINGER-2009-9783034601894:ONLINE Show nearby items on shelf Title: Simplicial Homotopy Theory [electronic resource] Author(s): Paul G Goerss John F Jardine Date: 2009 Publisher: Basel : Birkhuser Basel Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: Since the beginning of the modern era of algebraic topology, simplicial methods have been used systematically and effectively for both computation and basic theory. With the development of Quillen's concept of a closed modelcategory and, in particula r, a simplicial model category, this collection of methods has become the primary way to describe non-abelian homological algebra and to address homotopy-theoretical issues in a variety of fields, includingalgebraic K-theory. This book supplies a modern e xposition of these ideas, emphasizing model category theoretical techniques. Discussed here are the homotopy theory of simplicial sets, and other basic topics such as simplicial groups,Postnikov towers, and bisimplicial sets. The more advanced material in cludes homotopy limits and colimits, localization with respect to a map and with respect to a homology theory, cosimplicial spaces, and homotopy coherence.Interspersed throughout are many results and ideas well-known to experts, but uncollected in the lit erature. Intended for second-year graduate students and beyond, this book introduces many of the basic tools of modern homotopy theory.An extensive background in topology is not assumed. Reviews: a book filling an obvious gap in the literature and the au thors have done an excellent job on it. No monograph or expository paper has been published on this topic inthe last twenty-eight years. - Analele Universitatii din Timisoara is clearly presented and a brief summary preceding every chapter is useful to t he reader. The book should prove enlightening to a broad range of readersincluding prospective students and researchers who want to apply simplicial techniques for whatever reason. - Zentralblatt MATH they succeed. The book is an excellent account of sim plicial homotopy theory from a modern point ofview [] The book is well written. [] The book can be highly recommended to anybody who wants to learn and to apply simplicial techniques Note: Springer eBooks ISBN: 9783034601894 Series: e-books Series: SpringerLink (Online service) Series: Modern Birkhuser Classics Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE  Call number: SPRINGER-2009-9780817646639:ONLINE Show nearby items on shelf Title: Fourier-Mukai and Nahm Transforms in Geometry and Mathematical Physics [electronic resource] Author(s): Claudio Bartocci Ugo Bruzzo Daniel Hernndez Ruiprez Date: 2009 Publisher: Boston : Birkhuser Boston Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: Integral transforms, such as the Laplace and Fourier transforms, have been major tools in mathematics for at least two centuries. In the last three decades the development of a number of novel ideas in algebraic geometry,category theory, gauge theory , and string theory has been closely related to generalizations of integral transforms of a more geometric character. FourierMukai and Nahm Transforms in Geometry and Mathematical Physics examines thealgebro-geometric approach (FourierMukai functors) as w ell as the differential-geometric constructions (Nahm). Also included is a considerable amount of material from existing literature which has not been systematically organizedinto a monograph. Key features: * Basic constructions and definitions are presen ted in preliminary background chapters * Presentation explores applications and suggests several open questions * Extensive bibliography and index Thisself-contained monograph provides an introduction to current research in geometry and mathematical physi cs and is intended for graduate students and researchers just entering this field Note: Springer eBooks Contents: Integral functors Fourier Mukai functors Fourier Mukai on Abelian varieties Fourier Mukai on K3 surfaces Nahm transforms Relative Fourier Mukai functors Fourier Mukai partners and birational geometry Derived and triangulated categories Lattices Miscellaneous results Stability conditions for derived categories ISBN: 9780817646639 Series: e-books Series: SpringerLink (Online service) Series: Progress in Mathematics : v276 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Geometry, algebraic , Differential equations, partial , Global differential geometry , Mathematical physics Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE  Call number: SPRINGER-2008-9783764387426:ONLINE Show nearby items on shelf Title: Modules and Comodules [electronic resource] Author(s): Tomasz Brzeziski Jos Luis Gmez Pardo Ivan Shestakov Patrick F Smith Date: 2008 Publisher: Basel : Birkhuser Basel Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: The 23 articles in this volume encompass the proceedings of the International Conference on Modules and Comodules held in Porto (Portugal) in 2006 and dedicated to Robert Wisbauer on the occasion of his 65th birthday. Thesearticles reflect Professor Wisbauer's wide interests and give an overview of different fields related to module theory, some of which have a long tradition whereas others have emerged in recent years. They include topics in the formaltheory of modules bordering on category theory, in ring theory, in Hopf algebras and quantum groups, and in corings and comodules Note: Springer eBooks Contents: Injective Morita Contexts (Revisited) A Categorical Proof of a Useful Result On Nichols Algebras with Generic Braiding Dual Algebras of Some Semisimple Finite dimensional Hopf Algebras Balanced Bilinear Forms for Corings Ring Hulls of Semiprime Homomorphic Images Notes on Formal Smoothness Certain Chain Conditions in Modules over Dedekind Domains and Related Rings ? Injective Modules A Note on Polynomial Rings over Nil Rings QI modules Corings with Exact Rational Functors and Injective Objects Preradicals of Associative Algebras and their Connections with Pr ISBN: 9783764387426 Series: e-books Series: SpringerLink (Online service) Series: Trends in Mathematics Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Algebra Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE  Call number: SPRINGER-2008-9783540719625:ONLINE Show nearby items on shelf Title: Combinatorial Algebraic Topology [electronic resource] Author(s): Dmitry Kozlov Date: 2008 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: Combinatorial algebraic topology is a fascinating and dynamic field at the crossroads of algebraic topology and discrete mathematics. This volume is the first comprehensive treatment of the subject in book form. The first part ofthe book constitutes a swift walk through the main tools of algebraic topology, including Stiefel-Whitney characteristic classes, which are needed for the later parts. Readers - graduate students and working mathematicians alike - willprobably find particularly useful the sec ond part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Our presentation of standard topics is quite different from that of existingtexts. In addition, several new themes, such as spectral sequ ences, are included. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing thetopological structure theory for graph homomorphisms. The main benefit for the read er will be the prospect of fairly quickly getting to the forefront of modern research in this active field Note: Springer eBooks Contents: Concepts of Algebraic Topology Overture Cell Complexes Homology Groups Concepts of Category Theory Exact Sequences Homotopy Cofibrations Principal ? Bundles and StiefelWhitney Characteristic Classes Methods of Combinatorial Algebraic Topology Combinatorial Complexes Melange Acyclic Categories Discrete Morse Theory Lexicographic Shellability Evasiveness and Closure Operators Colimits and Quotients Homotopy Colimits Spectral Sequences Complexes of Graph Homomorphisms Chromatic Numbers and the Kneser Conjecture Structural Theory of Mo ISBN: 9783540719625 Series: e-books Series: SpringerLink (Online service) Series: Algorithms and Computation in Mathematics, 1431-1550 : v21 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Combinatorics , Algebraic topology Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE  Call number: SPRINGER-2008-9780387789019:ONLINE Show nearby items on shelf Title: Lattices and Ordered Sets [electronic resource] Author(s): Steven Roman Date: 2008 Publisher: New York, NY : Springer New York Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: This book is intended to be a thorough introduction to the subject of ordered sets and lattices, with an emphasis on the latter. It can be used for a course at the graduate or advanced undergraduate level or for independent study.Prerequisites are ke pt to a minimum, but an introductory course in abstract algebra is highly recommended, since many of the examples are drawn from this area. The book has an excellent choice of topics, including a chapter on wellordering and ordinal numbers, which is not u sually found in other texts. The approach is user-friendly and the presentation is lucid. There are more than 240 carefully chosen exercises. Topic coverage includes: modular, semimodular anddistributive lattices, boolean algebras, representation of distr ibutive lattices, algebraic lattices, congruence relations on lattices, free lattices, fixed-point theorems, duality theory and more. Steven Roman is the author of manysuccessful textbooks, including Advanced Linear Algebra, 3rd Edition (Springer 2007), F ield Theory, 2nd Edition (Springer 2005), and Introduction to the Mathematics of Finance (2004) Note: Springer eBooks Contents: Preface Partially Ordered Sets Well Ordered Sets Lattices Modular and Distributive Lattices Boolean Algebras The Representation of Distributive Lattices Algebraic Lattices Prime and Maximal Ideals: Separation Theorems Congruence Relations on Lattices Duality for Distributive Lattices: The Priestley Topology Free Lattices Fixed Point Theorems Appendix A: A Bit of Topology Appendix B: A Bit of Category Theory References Index of Symbols Index ISBN: 9780387789019 Series: e-books Series: SpringerLink (Online service) Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Algebra Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE  Call number: SPRINGER-2007-9783764375249:ONLINE Show nearby items on shelf Title: Tool and Object [electronic resource] : A History and Philosophy of Category Theory Author(s): Ralf Krmer Date: 2007 Publisher: Basel : Birkhuser Basel Size: 1 online resource Note: Springer e-book platform Note: Springer 2013 e-book collections Note: The book is first of all a history of category theory from the beginnings to A. Grothendieck and F.W. Lawvere. Category theory was an important conceptual tool in 20th century mathematics whose influence on some mathematicalsubdisciplines (above all algebraic topology and algebraic geometry) is analyzed. Category theory also has an important philosophical aspect: on the one hand its set-theoretical foundation is less obvious than for other mathematicaltheories, and on the other hand it unifies concep tually a large part of modern mathematics and may therefore be considered as somewhat fundamental itself. The role of this philosophical aspect in the historical development is thesecond focus of the book. Relying on the historical analysis, the author de velops a philosophical interpretation of the theory of his own, intending to get closer to how mathematicians conceive the significance of their activity thantraditional schools of philosophy of science. The book is the first monography exclusively devote d to the history of category theory. To a substantial extent it considers aspects never studied before. The author uses (and justifies theuse of) a methodology combining historical and philosophical approaches. The analysis is not confined to general rema rks, but goes into considerable mathematical detail. Hence, the book provides an exceptionally thorough case studycompared with other works on history or philosophy of mathematics. The philosophical position developed here (inspired by Peircean pragmatism and Wittgenstein) is an interesting alternative to traditional approaches in philosophy ofmathematics like platonism, formalism and intuitionism Note: Springer eBooks Contents: Prelude: Poincar, Wittgenstein, Peirce, and the use of concepts Category theory in Algebraic Topology Category theory in Homological Algebra Category theory in Algebraic Geometry From tool to object: full fledged category theory Categories as sets: problems and solutions Categorial foundations Pragmatism and category theory ISBN: 9783764375249 Series: e-books Series: SpringerLink (Online service) Series: Science Networks. Historical Studies : v32 Series: Mathematics and Statistics (Springer-11649) Keywords: Mathematics , Algebra , Mathematics_$xHistory Availability: Click here to see Library holdings or inquire at Circ Desk (x3401) Click to reserve this book Be sure to include your ID please. More info: Amazon.com More info: Barnes and Noble Full Text: Click here Location: ONLINE