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A First Course in Topology

2014-05-21 Mathematics
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Release : 2014-05-21
Genre : Mathematics
Kind : eBook
Book Rating : 015/5 ( reviews)

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Book Synopsis A First Course in Topology by : Robert A Conover

Download or read book A First Course in Topology written by Robert A Conover. This book was released on 2014-05-21. Available in PDF, EPUB and Kindle. Book excerpt: Students must prove all of the theorems in this undergraduate-level text, which features extensive outlines to assist in study and comprehension. Thorough and well-written, the treatment provides sufficient material for a one-year undergraduate course. The logical presentation anticipates students' questions, and complete definitions and expositions of topics relate new concepts to previously discussed subjects. Most of the material focuses on point-set topology with the exception of the last chapter. Topics include sets and functions, infinite sets and transfinite numbers, topological spaces and basic concepts, product spaces, connectivity, and compactness. Additional subjects include separation axioms, complete spaces, and homotopy and the fundamental group. Numerous hints and figures illuminate the text. Dover (2014) republication of the edition originally published by The Williams & Wilkins Company, Baltimore, 1975. See every Dover book in print at www.doverpublications.com

A First Course in Topology

2006 Mathematics
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Release : 2006
Genre : Mathematics
Kind : eBook
Book Rating : 849/5 ( reviews)

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Book Synopsis A First Course in Topology by : John McCleary

Download or read book A First Course in Topology written by John McCleary. This book was released on 2006. Available in PDF, EPUB and Kindle. Book excerpt: How many dimensions does our universe require for a comprehensive physical description? In 1905, Poincare argued philosophically about the necessity of the three familiar dimensions, while recent research is based on 11 dimensions or even 23 dimensions. The notion of dimension itself presented a basic problem to the pioneers of topology. Cantor asked if dimension was a topological feature of Euclidean space. To answer this question, some important topological ideas were introduced by Brouwer, giving shape to a subject whose development dominated the twentieth century. The basic notions in topology are varied and a comprehensive grounding in point-set topology, the definition and use of the fundamental group, and the beginnings of homology theory requires considerable time.The goal of this book is a focused introduction through these classical topics, aiming throughout at the classical result of the Invariance of Dimension. This text is based on the author's course given at Vassar College and is intended for advanced undergraduate students. It is suitable for a semester-long course on topology for students who have studied real analysis and linear algebra. It is also a good choice for a capstone course, senior seminar, or independent study.

A First Course in Geometric Topology and Differential Geometry

2011-06-27 Mathematics
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Release : 2011-06-27
Genre : Mathematics
Kind : eBook
Book Rating : 221/5 ( reviews)

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Book Synopsis A First Course in Geometric Topology and Differential Geometry by : Ethan D. Bloch

Download or read book A First Course in Geometric Topology and Differential Geometry written by Ethan D. Bloch. This book was released on 2011-06-27. Available in PDF, EPUB and Kindle. Book excerpt: The uniqueness of this text in combining geometric topology and differential geometry lies in its unifying thread: the notion of a surface. With numerous illustrations, exercises and examples, the student comes to understand the relationship of the modern abstract approach to geometric intuition. The text is kept at a concrete level, avoiding unnecessary abstractions, yet never sacrificing mathematical rigor. The book includes topics not usually found in a single book at this level.

First Concepts of Topology

1966 Mathematics
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Release : 1966
Genre : Mathematics
Kind : eBook
Book Rating : 182/5 ( reviews)

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Book Synopsis First Concepts of Topology by : William G. Chinn

Download or read book First Concepts of Topology written by William G. Chinn. This book was released on 1966. Available in PDF, EPUB and Kindle. Book excerpt: Over 150 problems and solutions.

A First Course in Algebraic Topology

1980-09-25 Mathematics
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Release : 1980-09-25
Genre : Mathematics
Kind : eBook
Book Rating : 954/5 ( reviews)

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Book Synopsis A First Course in Algebraic Topology by : Czes Kosniowski

Download or read book A First Course in Algebraic Topology written by Czes Kosniowski. This book was released on 1980-09-25. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained introduction to algebraic topology is suitable for a number of topology courses. It consists of about one quarter 'general topology' (without its usual pathologies) and three quarters 'algebraic topology' (centred around the fundamental group, a readily grasped topic which gives a good idea of what algebraic topology is). The book has emerged from courses given at the University of Newcastle-upon-Tyne to senior undergraduates and beginning postgraduates. It has been written at a level which will enable the reader to use it for self-study as well as a course book. The approach is leisurely and a geometric flavour is evident throughout. The many illustrations and over 350 exercises will prove invaluable as a teaching aid. This account will be welcomed by advanced students of pure mathematics at colleges and universities.

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