A Taste Of Topology

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A Taste of Topology

Volker Runde
A Taste of Topology Book PDF

Author : Volker Runde
Publisher : Springer Science & Business Media
Page : 196 pages
File Size : 44,8 Mb
Release : 2007-12-07
Category : Mathematics
ISBN : 038725790X

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A Taste of Topology by Volker Runde Pdf

This should be a revelation for mathematics undergraduates. Having evolved from Runde’s notes for an introductory topology course at the University of Alberta, this essential text provides a concise introduction to set-theoretic topology, as well as some algebraic topology. It is accessible to undergraduates from the second year on, and even beginning graduate students can benefit from some sections. The well-chosen selection of examples is accessible to students who have a background in calculus and elementary algebra, but not necessarily in real or complex analysis. In places, Runde’s text treats its material differently to other books on the subject, providing a fresh perspective.

Experiments in Topology

Stephen Barr
Experiments in Topology Book PDF

Author : Stephen Barr
Publisher : Courier Corporation
Page : 244 pages
File Size : 51,5 Mb
Release : 2012-12-04
Category : Mathematics
ISBN : 9780486152745

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Experiments in Topology by Stephen Barr Pdf

Classic, lively explanation of one of the byways of mathematics. Klein bottles, Moebius strips, projective planes, map coloring, problem of the Koenigsberg bridges, much more, described with clarity and wit.

Elementary Topology

O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov
Elementary Topology Book PDF

Author : O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov
Publisher : American Mathematical Soc.
Page : 432 pages
File Size : 52,7 Mb
Release : 2024-07-04
Category : Mathematics
ISBN : 0821886258

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Elementary Topology by O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov Pdf

This text contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment. Proofs of theorems are separated from their formulations and are gathered at the end of each chapter, making this book appear like a problem book and also giving it appeal to the expert as a handbook. The book includes about 1,000 exercises.

A Topological Aperitif

Stephen Huggett,David Jordan
A Topological Aperitif Book PDF

Author : Stephen Huggett,David Jordan
Publisher : Springer Science & Business Media
Page : 172 pages
File Size : 41,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781447136941

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A Topological Aperitif by Stephen Huggett,David Jordan Pdf

This book takes a new look at the subject, choosing a geometric approach rather than the usual algebraic or combinatorial approach. It starts with a wealth of examples of how to be mathematically certain whether two objects are the same from the point of view of topology. After introducing surfaces, the book explores the properties of polyhedra drawn on these surfaces. More refined tools are developed in a chapter on winding number.

Topology from the Differentiable Viewpoint

John Willard Milnor,David W. Weaver
Topology from the Differentiable Viewpoint Book PDF

Author : John Willard Milnor,David W. Weaver
Publisher : Princeton University Press
Page : 80 pages
File Size : 54,5 Mb
Release : 1997-12-14
Category : Mathematics
ISBN : 0691048339

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Topology from the Differentiable Viewpoint by John Willard Milnor,David W. Weaver Pdf

This elegant book by distinguished mathematician John Milnor, provides a clear and succinct introduction to one of the most important subjects in modern mathematics. Beginning with basic concepts such as diffeomorphisms and smooth manifolds, he goes on to examine tangent spaces, oriented manifolds, and vector fields. Key concepts such as homotopy, the index number of a map, and the Pontryagin construction are discussed. The author presents proofs of Sard's theorem and the Hopf theorem.

Real Mathematical Analysis

Charles Chapman Pugh
Real Mathematical Analysis Book PDF

Author : Charles Chapman Pugh
Publisher : Springer Science & Business Media
Page : 445 pages
File Size : 53,9 Mb
Release : 2013-03-19
Category : Mathematics
ISBN : 9780387216843

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Real Mathematical Analysis by Charles Chapman Pugh Pdf

Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.

Virtual Topology and Functor Geometry

Fred Van Oystaeyen
Virtual Topology and Functor Geometry Book PDF

Author : Fred Van Oystaeyen
Publisher : CRC Press
Page : 170 pages
File Size : 41,5 Mb
Release : 2007-11-15
Category : Mathematics
ISBN : 9781420060577

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Virtual Topology and Functor Geometry by Fred Van Oystaeyen Pdf

Intrinsically noncommutative spaces today are considered from the perspective of several branches of modern physics, including quantum gravity, string theory, and statistical physics. From this point of view, it is ideal to devise a concept of space and its geometry that is fundamentally noncommutative. Providing a clear introduction to noncommutat

Introduction to Topology

Crump W. Baker
Introduction to Topology Book PDF

Author : Crump W. Baker
Publisher : Unknown
Page : 155 pages
File Size : 54,6 Mb
Release : 1997
Category : Mathematics
ISBN : 1575240084

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Introduction to Topology by Crump W. Baker Pdf

The fundamental concepts of general topology are covered in this text whic can be used by students with only an elementary background in calculus. Chapters cover: sets; functions; topological spaces; subspaces; and homeomorphisms.

A Concise Course in Algebraic Topology

J. P. May
A Concise Course in Algebraic Topology Book PDF

Author : J. P. May
Publisher : University of Chicago Press
Page : 262 pages
File Size : 50,9 Mb
Release : 1999-09
Category : Mathematics
ISBN : 0226511839

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A Concise Course in Algebraic Topology by J. P. May Pdf

Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.

Essential Topology

Martin D. Crossley
Essential Topology Book PDF

Author : Martin D. Crossley
Publisher : Springer Science & Business Media
Page : 244 pages
File Size : 50,6 Mb
Release : 2011-02-11
Category : Mathematics
ISBN : 1852337826

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Essential Topology by Martin D. Crossley Pdf

This book brings the most important aspects of modern topology within reach of a second-year undergraduate student. It successfully unites the most exciting aspects of modern topology with those that are most useful for research, leaving readers prepared and motivated for further study. Written from a thoroughly modern perspective, every topic is introduced with an explanation of why it is being studied, and a huge number of examples provide further motivation. The book is ideal for self-study and assumes only a familiarity with the notion of continuity and basic algebra.

Topology and Geometry

Glen E. Bredon
Topology and Geometry Book PDF

Author : Glen E. Bredon
Publisher : Springer Science & Business Media
Page : 580 pages
File Size : 51,8 Mb
Release : 1993-06-24
Category : Mathematics
ISBN : 9780387979267

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Topology and Geometry by Glen E. Bredon Pdf

This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: "An interesting and original graduate text in topology and geometry...a good lecturer can use this text to create a fine course....A beginning graduate student can use this text to learn a great deal of mathematics."—-MATHEMATICAL REVIEWS

Topological Methods in Group Theory

Ross Geoghegan
Topological Methods in Group Theory Book PDF

Author : Ross Geoghegan
Publisher : Springer Science & Business Media
Page : 473 pages
File Size : 42,7 Mb
Release : 2007-12-17
Category : Mathematics
ISBN : 9780387746111

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Topological Methods in Group Theory by Ross Geoghegan Pdf

This book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail. The central subject of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit.

From Geometry to Topology

H. Graham Flegg
From Geometry to Topology Book PDF

Author : H. Graham Flegg
Publisher : Courier Corporation
Page : 210 pages
File Size : 44,6 Mb
Release : 2012-03-08
Category : Mathematics
ISBN : 9780486138497

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From Geometry to Topology by H. Graham Flegg Pdf

This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become larger, and their common topological properties become intuitively clear. Chapters 4–12 give a largely intuitive presentation of selected topics. In the remaining five chapters, the author moves to a more conventional presentation of continuity, sets, functions, metric spaces, and topological spaces. Exercises and Problems. 101 black-and-white illustrations. 1974 edition.

Categories for the Working Mathematician

Saunders Mac Lane
Categories for the Working Mathematician Book PDF

Author : Saunders Mac Lane
Publisher : Springer Science & Business Media
Page : 320 pages
File Size : 55,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475747218

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Categories for the Working Mathematician by Saunders Mac Lane Pdf

An array of general ideas useful in a wide variety of fields. Starting from the foundations, this book illuminates the concepts of category, functor, natural transformation, and duality. It then turns to adjoint functors, which provide a description of universal constructions, an analysis of the representations of functors by sets of morphisms, and a means of manipulating direct and inverse limits. These categorical concepts are extensively illustrated in the remaining chapters, which include many applications of the basic existence theorem for adjoint functors. The categories of algebraic systems are constructed from certain adjoint-like data and characterised by Beck's theorem. After considering a variety of applications, the book continues with the construction and exploitation of Kan extensions. This second edition includes a number of revisions and additions, including new chapters on topics of active interest: symmetric monoidal categories and braided monoidal categories, and the coherence theorems for them, as well as 2-categories and the higher dimensional categories which have recently come into prominence.

The Road to Reality

Roger Penrose
The Road to Reality Book PDF

Author : Roger Penrose
Publisher : Vintage
Page : 1136 pages
File Size : 40,7 Mb
Release : 2021-06-09
Category : Science
ISBN : 9780593315309

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The Road to Reality by Roger Penrose Pdf

**WINNER OF THE 2020 NOBEL PRIZE IN PHYSICS** The Road to Reality is the most important and ambitious work of science for a generation. It provides nothing less than a comprehensive account of the physical universe and the essentials of its underlying mathematical theory. It assumes no particular specialist knowledge on the part of the reader, so that, for example, the early chapters give us the vital mathematical background to the physical theories explored later in the book. Roger Penrose's purpose is to describe as clearly as possible our present understanding of the universe and to convey a feeling for its deep beauty and philosophical implications, as well as its intricate logical interconnections. The Road to Reality is rarely less than challenging, but the book is leavened by vivid descriptive passages, as well as hundreds of hand-drawn diagrams. In a single work of colossal scope one of the world's greatest scientists has given us a complete and unrivalled guide to the glories of the universe that we all inhabit. 'Roger Penrose is the most important physicist to work in relativity theory except for Einstein. He is one of the very few people I've met in my life who, without reservation, I call a genius' Lee Smolin