Search Results: strong-shape-and-homology-springer-monographs-in-mathematics

Strong Shape and Homology

Author: Sibe Mardesic

Publisher: Springer Science & Business Media

ISBN: 3662130645

Category: Mathematics

Page: 489

View: 2586

Shape theory, an extension of homotopy theory from the realm of CW-complexes to arbitrary spaces, was introduced by Borsuk 30 years ago and Mardesic contributed greatly to it. One expert says: "If we need a book in the field, this is it! It is thorough, careful and complete."

Handbook of the History of General Topology

Author: C.E. Aull,R. Lowen

Publisher: Springer Science & Business Media

ISBN: 9401704708

Category: Mathematics

Page: 1223

View: 5732

Proceedings of the International Congress of Mathematicians 2010 (ICM 2010)

Author: N.A

Publisher: N.A

ISBN: 9814462934

Category:

Page: N.A

View: 8246

Encyclopedia of General Topology

Author: K.P. Hart,Jun-iti Nagata,J.E. Vaughan

Publisher: Elsevier

ISBN: 9780080530864

Category: Mathematics

Page: 536

View: 2737

This book is designed for the reader who wants to get a general view of the terminology of General Topology with minimal time and effort. The reader, whom we assume to have only a rudimentary knowledge of set theory, algebra and analysis, will be able to find what they want if they will properly use the index. However, this book contains very few proofs and the reader who wants to study more systematically will find sufficiently many references in the book. Key features: • More terms from General Topology than any other book ever published • Short and informative articles • Authors include the majority of top researchers in the field • Extensive indexing of terms

Glasnik Matematički

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 322

Newsletter

Author: New Zealand Mathematical Society

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 3321

Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 7609

Trees

Author: Jean-Pierre Serre

Publisher: Springer Science & Business Media

ISBN: 3642618561

Category: Mathematics

Page: 142

View: 1761

The seminal ideas of this book played a key role in the development of group theory since the 70s. Several generations of mathematicians learned geometric ideas in group theory from this book. In it, the author proves the fundamental theorem for the special cases of free groups and tree products before dealing with the proof of the general case. This new edition is ideal for graduate students and researchers in algebra, geometry and topology.

Classical Topology and Combinatorial Group Theory

Author: John Stillwell

Publisher: Springer Science & Business Media

ISBN: 1461243726

Category: Mathematics

Page: 336

View: 5228

In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler's polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses. What a disappointment "undergraduate topology" proves to be! In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams. Pictures are kept to a minimum, and at the end the student still does nr~ understand the simplest topological facts, such as the rcason why knots exist. In my opinion, a well-balanced introduction to topology should stress its intuitive geometric aspect, while admitting the legitimate interest that analysts and algebraists have in the subject. At any rate, this is the aim of the present book. In support of this view, I have followed the historical development where practicable, since it clearly shows the influence of geometric thought at all stages. This is not to claim that topology received its main impetus from geometric recreations like the seven bridges; rather, it resulted from the l'isualization of problems from other parts of mathematics-complex analysis (Riemann), mechanics (Poincare), and group theory (Dehn). It is these connec tions to other parts of mathematics which make topology an important as well as a beautiful subject.

Recent Progress in Homotopy Theory

Proceedings of a Conference on Recent Progress in Homotopy Theory, March 17-27, 2000, Johns Hopkins University, Baltimore, MD

Author: Donald M. Davis

Publisher: American Mathematical Soc.

ISBN: 0821828010

Category: Mathematics

Page: 409

View: 842

This volume presents the proceedings from the month-long program held at Johns Hopkins University (Baltimore, MD) on homotopy theory, sponsored by the Japan-U.S. Mathematics Institute (JAMI). The book centers on the following: 1. classical and nonclassical theory of $H$-spaces, compact groups, and finite groups, 2. classical and chromatic homotopy theory and localization, 3. classical and topological Hochschild cohomology, 4. elliptic cohomology and its relation to Moonshine and topological modular forms, and 5. motivic cohomology and Chow rings. It surveys the current state of research in homotopy theory and suggests a framework for future developments. The book begins with two historical accounts, of the work of Professors Peter Landweber and Stewart Priddy, in honor of their sixtieth birthdays.

Galois Theory of p-Extensions

Author: Helmut Koch

Publisher: Springer Science & Business Media

ISBN: 3662049678

Category: Mathematics

Page: 191

View: 4843

Helmut Koch's classic is now available in English. Competently translated by Franz Lemmermeyer, it introduces the theory of pro-p groups and their cohomology. The book contains a postscript on the recent development of the field written by H. Koch and F. Lemmermeyer, along with many additional recent references.

Introduction to Singularities and Deformations

Author: Gert-Martin Greuel,Christoph Lossen,Eugenii I. Shustin

Publisher: Springer Science & Business Media

ISBN: 3540284192

Category: Mathematics

Page: 472

View: 4885

Singularity theory is a young, rapidly-growing topic with connections to algebraic geometry, complex analysis, commutative algebra, representations theory, Lie groups theory and topology, and many applications in the natural and technical sciences. This book presents the basic singularity theory of analytic spaces, including local deformation theory and the theory of plane curve singularities. It includes complete proofs.

Combinatorial Algebraic Topology

Author: Dimitry Kozlov

Publisher: Springer Science & Business Media

ISBN: 3540719628

Category: Mathematics

Page: 390

View: 2720

This volume is the first comprehensive treatment of combinatorial algebraic topology in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms.

BPR

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 5033

Boolean Representations of Simplicial Complexes and Matroids

Author: John Rhodes,Pedro V. Silva

Publisher: Springer

ISBN: 3319151142

Category: Mathematics

Page: 173

View: 8518

This self-contained monograph explores a new theory centered around boolean representations of simplicial complexes leading to a new class of complexes featuring matroids as central to the theory. The book illustrates these new tools to study the classical theory of matroids as well as their important geometric connections. Moreover, many geometric and topological features of the theory of matroids find their counterparts in this extended context. Graduate students and researchers working in the areas of combinatorics, geometry, topology, algebra and lattice theory will find this monograph appealing due to the wide range of new problems raised by the theory. Combinatorialists will find this extension of the theory of matroids useful as it opens new lines of research within and beyond matroids. The geometric features and geometric/topological applications will appeal to geometers. Topologists who desire to perform algebraic topology computations will appreciate the algorithmic potential of boolean representable complexes.

Modular Forms and Fermat’s Last Theorem

Author: Gary Cornell,Joseph H. Silverman,Glenn Stevens

Publisher: Springer Science & Business Media

ISBN: 1461219744

Category: Mathematics

Page: 582

View: 4172

This volume contains the expanded lectures given at a conference on number theory and arithmetic geometry held at Boston University. It introduces and explains the many ideas and techniques used by Wiles, and to explain how his result can be combined with Ribets theorem and ideas of Frey and Serre to prove Fermats Last Theorem. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions and curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of the proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serres conjectures, Galois deformations, universal deformation rings, Hecke algebras, and complete intersections. The book concludes by looking both forward and backward, reflecting on the history of the problem, while placing Wiles'theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this an indispensable resource.

Cohomology of Infinite-Dimensional Lie Algebras

Author: D.B. Fuks

Publisher: Springer Science & Business Media

ISBN: 1468487655

Category: Mathematics

Page: 352

View: 506

There is no question that the cohomology of infinite dimensional Lie algebras deserves a brief and separate mono graph. This subject is not cover~d by any of the tradition al branches of mathematics and is characterized by relative ly elementary proofs and varied application. Moreover, the subject matter is widely scattered in various research papers or exists only in verbal form. The theory of infinite-dimensional Lie algebras differs markedly from the theory of finite-dimensional Lie algebras in that the latter possesses powerful classification theo rems, which usually allow one to "recognize" any finite dimensional Lie algebra (over the field of complex or real numbers), i.e., find it in some list. There are classifica tion theorems in the theory of infinite-dimensional Lie al gebras as well, but they are encumbered by strong restric tions of a technical character. These theorems are useful mainly because they yield a considerable supply of interest ing examples. We begin with a list of such examples, and further direct our main efforts to their study.

Algebraic Curves and Riemann Surfaces

Author: Rick Miranda

Publisher: American Mathematical Soc.

ISBN: 0821802682

Category: Mathematics

Page: 390

View: 2949

The book was easy to understand, with many examples. The exercises were well chosen, and served to give further examples and developments of the theory. --William Goldman, University of Maryland In this book, Miranda takes the approach that algebraic curves are best encountered for the first time over the complex numbers, where the reader's classical intuition about surfaces, integration, and other concepts can be brought into play. Therefore, many examples of algebraic curves are presented in the first chapters. In this way, the book begins as a primer on Riemann surfaces, with complex charts and meromorphic functions taking center stage. But the main examples come from projective curves, and slowly but surely the text moves toward the algebraic category. Proofs of the Riemann-Roch and Serre Duality Theorems are presented in an algebraic manner, via an adaptation of the adelic proof, expressed completely in terms of solving a Mittag-Leffler problem. Sheaves and cohomology are introduced as a unifying device in the latter chapters, so that their utility and naturalness are immediately obvious. Requiring a background of one semester of complex variable theory and a year of abstract algebra, this is an excellent graduate textbook for a second-semester course in complex variables or a year-long course in algebraic geometry.

On Thom Spectra, Orientability, and Cobordism

Author: Yu. B. Rudyak

Publisher: Springer Science & Business Media

ISBN: 3540777512

Category: Mathematics

Page: 590

View: 4621

Rudyak’s groundbreaking monograph is the first guide on the subject of cobordism since Stong's influential notes of a generation ago. It concentrates on Thom spaces (spectra), orientability theory and (co)bordism theory (including (co)bordism with singularities and, in particular, Morava K-theories). These are all framed by (co)homology theories and spectra. The author has also performed a service to the history of science in this book, giving detailed attributions.

Interdisciplinary Mathematics Education

A State of the Art

Author: Julian Williams,Wolff-Michael Roth,David Swanson,Brian Doig,Susie Groves,Michael Omuvwie,Rita Borromeo Ferri,Nicholas Mousoulides

Publisher: Springer

ISBN: 3319422677

Category: Education

Page: 36

View: 5300

This book provides an essential introduction to the state-of the-art in interdisciplinary Mathematics Education. First, it begins with an outline of the field’s relevant historical, conceptual and theoretical backgrounds, what “discipline” means and how inter-, trans-, and meta-disciplinary activities can be understood. Relevant theoretical perspectives from Marx, Foucault and Vygotsky are explained, along with key ideas in theory, e.g. boundaries, discourses, identity, and the division of labour in practice. Second, the book reviews research findings of mainly empirical studies on interdisciplinary work involving mathematics in education, in all stages of education that have become disciplined. For example, it reports that a common theme in studies in middle and high schools is assessing the motivational benefits for the learner of subsuming disciplinary motives and even practices to extra-academic problem-solving activities; this is counter-balanced by the effort needed to overcome the disciplinary boundaries in academic institutions, and in professional identities. These disciplinary boundaries are less obviously limitations in middle and primary schools, and in some vocational courses. Third and finally, it explores selected case studies that illustrate these concepts and findings, both in terms of the motivational benefits for learners and the institutional and other boundaries involved.

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