Elementary Topology

A Combinatorial and Algebraic Approach
Author: Donald W. Blackett
Publisher: Academic Press
ISBN: 1483262537
Category: Mathematics
Page: 236
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Elementary Topology: A Combinatorial and Algebraic Approach focuses on the application of algebraic methods to topological concepts and theorems. The publication first elaborates on some examples of surfaces and their classifications. Discussions focus on combinatorial invariants of a surface, combinatorial equivalence, surfaces and their equations, topological surfaces, coordinates on a sphere and torus, and properties of the sphere and torus. The text then examines complex conics and covering surfaces and mappings into the sphere, including applications of the winding number in complex analysis, mappings into the plane, winding number of a plane curve, covering surfaces, and complex conies. The book examines vector fields, network topology, and three-dimensional topology. Topics include topological products and fiber bundles, manifolds of configurations, paths, circuits, and trees, vector fields and hydrodynamics, vector fields on a sphere, and vector fields and differential equations. The publication is highly recommended for sophomores, juniors, and seniors who have completed a year of calculus.

A Combinatorial Introduction to Topology


Author: Michael Henle
Publisher: Courier Corporation
ISBN: 9780486679662
Category: Mathematics
Page: 310
View: 911
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Excellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more. Problems and exercises. Some knowledge of differential equations and multivariate calculus required.Bibliography. 1979 edition.

A Basic Course in Algebraic Topology


Author: W.S. Massey
Publisher: Springer Science & Business Media
ISBN: 9780387974309
Category: Mathematics
Page: 428
View: 5441
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This book provides a systematic treatment of the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. It avoids all unnecessary definitions, terminology, and technical machinery. Wherever possible, the book emphasizes the geometric motivation behind the various concepts.

Explorations in Topology

Map Coloring, Surfaces and Knots
Author: David Gay
Publisher: Elsevier
ISBN: 9780080492667
Category: Mathematics
Page: 352
View: 7415
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Explorations in Topology gives students a rich experience with low-dimensional topology, enhances their geometrical and topological intuition, empowers them with new approaches to solving problems, and provides them with experiences that would help them make sense of a future, more formal topology course. The innovative story-line style of the text models the problems-solving process, presents the development of concepts in a natural way, and through its informality seduces the reader into engagement with the material. The end-of-chapter Investigations give the reader opportunities to work on a variety of open-ended, non-routine problems, and, through a modified "Moore method", to make conjectures from which theorems emerge. The students themselves emerge from these experiences owning concepts and results. The end-of-chapter Notes provide historical background to the chapter’s ideas, introduce standard terminology, and make connections with mainstream mathematics. The final chapter of projects provides opportunities for continued involvement in "research" beyond the topics of the book. * Students begin to solve substantial problems right from the start * Ideas unfold through the context of a storyline, and students become actively involved * The text models the problem-solving process, presents the development of concepts in a natural way, and helps the reader engage with the material

General Topology


Author: Stephen Willard
Publisher: Courier Corporation
ISBN: 9780486434797
Category: Mathematics
Page: 369
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Among the best available reference introductions to general topology, this volume is appropriate for advanced undergraduate and beginning graduate students. Includes historical notes and over 340 detailed exercises. 1970 edition. Includes 27 figures.

New Technical Books


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Engineering
Page: N.A
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Library recommendations for undergraduate mathematics


Author: Lynn Arthur Steen,Mathematical Association of America
Publisher: Mathematical Assn of Amer
ISBN: N.A
Category: Mathematics
Page: 194
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Notices of the American Mathematical Society


Author: American Mathematical Society
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
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Magill's Survey of Science: The standard model-X-ray determination of molecular structure


Author: Frank Northen Magill
Publisher: N.A
ISBN: 9780893566494
Category: Computer science
Page: 2796
View: 9094
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Combinatorial Methods in Topology and Algebraic Geometry


Author: John R. Harper,Richard Mandelbaum
Publisher: American Mathematical Soc.
ISBN: 9780821850398
Category: Mathematics
Page: 349
View: 6894
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This collection marks the recent resurgence of interest in combinatorial methods, resulting from their deep and diverse applications both in topology and algebraic geometry. Nearly thirty mathematicians met at the University of Rochester in 1982 to survey several of the areas where combinatorial methods are proving especially fruitful: topology and combinatorial group theory, knot theory, 3-manifolds, homotopy theory and infinite dimensional topology, and four manifolds and algebraic surfaces. This material is accessible to advanced graduate students with a general course in algebraic topology along with some work in combinatorial group theory and geometric topology, as well as to established mathematicians with interests in these areas.For both student and professional mathematicians, the book provides practical suggestions for research directions still to be explored, as well as the aesthetic pleasures of seeing the interplay between algebra and topology which is characteristic of this field. In several areas the book contains the first general exposition published on the subject. In topology, for example, the editors have included M. Cohen, W. Metzler and K. Sauerman's article on 'Collapses of $K\times I$ and group presentations' and Metzler's 'On the Andrews-Curtis-Conjecture and related problems'. In addition, J. M. Montesino has provided summary articles on both 3 and 4-manifolds.

Science Books


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Publisher: N.A
ISBN: N.A
Category: Science
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The Publishers' Trade List Annual


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Publisher: R. R. Bowker
ISBN: N.A
Category: United States
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Publisher: N.A
ISBN: 9780835221092
Category: Monographic series
Page: 1756
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Publisher: N.A
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Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.

Using the Borsuk-Ulam Theorem

Lectures on Topological Methods in Combinatorics and Geometry
Author: Jiri Matousek
Publisher: Springer Science & Business Media
ISBN: 3540766499
Category: Mathematics
Page: 214
View: 9526
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To the uninitiated, algebraic topology might seem fiendishly complex, but its utility is beyond doubt. This brilliant exposition goes back to basics to explain how the subject has been used to further our understanding in some key areas. A number of important results in combinatorics, discrete geometry, and theoretical computer science have been proved using algebraic topology. While the results are quite famous, their proofs are not so widely understood. This book is the first textbook treatment of a significant part of these results. It focuses on so-called equivariant methods, based on the Borsuk-Ulam theorem and its generalizations. The topological tools are intentionally kept on a very elementary level. No prior knowledge of algebraic topology is assumed, only a background in undergraduate mathematics, and the required topological notions and results are gradually explained.

Combinatorial Group Theory

A Topological Approach
Author: Daniel E. Cohen
Publisher: CUP Archive
ISBN: 9780521349369
Category: Mathematics
Page: 310
View: 1490
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In this book the author aims to show the value of using topological methods in combinatorial group theory.

Combinatorial Algebraic Topology


Author: Dimitry Kozlov
Publisher: Springer Science & Business Media
ISBN: 354071961X
Category: Mathematics
Page: 390
View: 4147
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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.

Classical Topology and Combinatorial Group Theory


Author: John Stillwell
Publisher: Springer Science & Business Media
ISBN: 1461243726
Category: Mathematics
Page: 336
View: 4540
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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.

Applications of Algebraic Topology

Graphs and Networks. The Picard-Lefschetz Theory and Feynman Integrals
Author: S. Lefschetz
Publisher: Springer Science & Business Media
ISBN: 1468493671
Category: Mathematics
Page: 191
View: 4390
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This monograph is based, in part, upon lectures given in the Princeton School of Engineering and Applied Science. It presupposes mainly an elementary knowledge of linear algebra and of topology. In topology the limit is dimension two mainly in the latter chapters and questions of topological invariance are carefully avoided. From the technical viewpoint graphs is our only requirement. However, later, questions notably related to Kuratowski's classical theorem have demanded an easily provided treatment of 2-complexes and surfaces. January 1972 Solomon Lefschetz 4 INTRODUCTION The study of electrical networks rests upon preliminary theory of graphs. In the literature this theory has always been dealt with by special ad hoc methods. My purpose here is to show that actually this theory is nothing else than the first chapter of classical algebraic topology and may be very advantageously treated as such by the well known methods of that science. Part I of this volume covers the following ground: The first two chapters present, mainly in outline, the needed basic elements of linear algebra. In this part duality is dealt with somewhat more extensively. In Chapter III the merest elements of general topology are discussed. Graph theory proper is covered in Chapters IV and v, first structurally and then as algebra. Chapter VI discusses the applications to networks. In Chapters VII and VIII the elements of the theory of 2-dimensional complexes and surfaces are presented.