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Basic Algebraic Topology and its Applications

2016-09-16 Mathematics
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Release : 2016-09-16
Genre : Mathematics
Kind : eBook
Book Rating : 43X/5 ( reviews)

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Book Synopsis Basic Algebraic Topology and its Applications by : Mahima Ranjan Adhikari

Download or read book Basic Algebraic Topology and its Applications written by Mahima Ranjan Adhikari. This book was released on 2016-09-16. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study.

Topology and Its Applications

2013-06-12 Mathematics
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Release : 2013-06-12
Genre : Mathematics
Kind : eBook
Book Rating : 222/5 ( reviews)

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Book Synopsis Topology and Its Applications by : William F. Basener

Download or read book Topology and Its Applications written by William F. Basener. This book was released on 2013-06-12. Available in PDF, EPUB and Kindle. Book excerpt: Discover a unique and modern treatment of topology employing a cross-disciplinary approach Implemented recently to understand diverse topics, such as cell biology, superconductors, and robot motion, topology has been transformed from a theoretical field that highlights mathematical theory to a subject that plays a growing role in nearly all fields of scientific investigation. Moving from the concrete to the abstract, Topology and Its Applications displays both the beauty and utility of topology, first presenting the essentials of topology followed by its emerging role within the new frontiers in research. Filling a gap between the teaching of topology and its modern uses in real-world phenomena, Topology and Its Applications is organized around the mathematical theory of topology, a framework of rigorous theorems, and clear, elegant proofs. This book is the first of its kind to present applications in computer graphics, economics, dynamical systems, condensed matter physics, biology, robotics, chemistry, cosmology, material science, computational topology, and population modeling, as well as other areas of science and engineering. Many of these applications are presented in optional sections, allowing an instructor to customize the presentation. The author presents a diversity of topological areas, including point-set topology, geometric topology, differential topology, and algebraic/combinatorial topology. Topics within these areas include: Open sets Compactness Homotopy Surface classification Index theory on surfaces Manifolds and complexes Topological groups The fundamental group and homology Special "core intuition" segments throughout the book briefly explain the basic intuition essential to understanding several topics. A generous number of figures and examples, many of which come from applications such as liquid crystals, space probe data, and computer graphics, are all available from the publisher's Web site.

Basic Algebraic Topology

2016-02-03 Mathematics
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Release : 2016-02-03
Genre : Mathematics
Kind : eBook
Book Rating : 447/5 ( reviews)

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Book Synopsis Basic Algebraic Topology by : Anant R. Shastri

Download or read book Basic Algebraic Topology written by Anant R. Shastri. This book was released on 2016-02-03. Available in PDF, EPUB and Kindle. Book excerpt: Building on rudimentary knowledge of real analysis, point-set topology, and basic algebra, Basic Algebraic Topology provides plenty of material for a two-semester course in algebraic topology. The book first introduces the necessary fundamental concepts, such as relative homotopy, fibrations and cofibrations, category theory, cell complexes, and si

Applications of Algebraic Topology

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 671/5 ( reviews)

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Book Synopsis Applications of Algebraic Topology by : S. Lefschetz

Download or read book Applications of Algebraic Topology written by S. Lefschetz. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Essentials of Topology with Applications

2009-07-28 Mathematics
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Release : 2009-07-28
Genre : Mathematics
Kind : eBook
Book Rating : 757/5 ( reviews)

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Book Synopsis Essentials of Topology with Applications by : Steven G. Krantz

Download or read book Essentials of Topology with Applications written by Steven G. Krantz. This book was released on 2009-07-28. Available in PDF, EPUB and Kindle. Book excerpt: Brings Readers Up to Speed in This Important and Rapidly Growing AreaSupported by many examples in mathematics, physics, economics, engineering, and other disciplines, Essentials of Topology with Applications provides a clear, insightful, and thorough introduction to the basics of modern topology. It presents the traditional concepts of topological

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