Author: Publisher: Academic Press
ISBN: 9780080874050
Category : Mathematics
Languages : en
Pages : 436
Book Description
Seifert and Threlfall, A Textbook of Topology
Seifert and Threlfall, A Textbook of Topology
Author: Publisher: Academic Press
ISBN: 9780080874050
Category : Mathematics
Languages : en
Pages : 436
Book Description
Seifert and Threlfall, A Textbook of Topology
Topology Through Inquiry
Author: Michael StarbirdPublisher: American Mathematical Soc.
ISBN: 1470462613
Category : Education
Languages : en
Pages : 313
Book Description
Topology Through Inquiry is a comprehensive introduction to point-set, algebraic, and geometric topology, designed to support inquiry-based learning (IBL) courses for upper-division undergraduate or beginning graduate students. The book presents an enormous amount of topology, allowing an instructor to choose which topics to treat. The point-set material contains many interesting topics well beyond the basic core, including continua and metrizability. Geometric and algebraic topology topics include the classification of 2-manifolds, the fundamental group, covering spaces, and homology (simplicial and singular). A unique feature of the introduction to homology is to convey a clear geometric motivation by starting with mod 2 coefficients. The authors are acknowledged masters of IBL-style teaching. This book gives students joy-filled, manageable challenges that incrementally develop their knowledge and skills. The exposition includes insightful framing of fruitful points of view as well as advice on effective thinking and learning. The text presumes only a modest level of mathematical maturity to begin, but students who work their way through this text will grow from mathematics students into mathematicians. Michael Starbird is a University of Texas Distinguished Teaching Professor of Mathematics. Among his works are two other co-authored books in the Mathematical Association of America's (MAA) Textbook series. Francis Su is the Benediktsson-Karwa Professor of Mathematics at Harvey Mudd College and a past president of the MAA. Both authors are award-winning teachers, including each having received the MAA's Haimo Award for distinguished teaching. Starbird and Su are, jointly and individually, on lifelong missions to make learning—of mathematics and beyond—joyful, effective, and available to everyone. This book invites topology students and teachers to join in the adventure.
Introduction to Topology
Author: Theodore W. GamelinPublisher: Courier Corporation
ISBN: 0486320189
Category : Mathematics
Languages : en
Pages : 258
Book Description
This text explains nontrivial applications of metric space topology to analysis. Covers metric space, point-set topology, and algebraic topology. Includes exercises, selected answers, and 51 illustrations. 1983 edition.
Elementary Topology
Author: O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. KharlamovPublisher: American Mathematical Soc.
ISBN: 9780821886250
Category : Mathematics
Languages : en
Pages : 432
Book Description
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.
Topology
Author: Tai-Danae BradleyPublisher: MIT Press
ISBN: 0262359626
Category : Mathematics
Languages : en
Pages : 167
Book Description
A graduate-level textbook that presents basic topology from the perspective of category theory. This graduate-level textbook on topology takes a unique approach: it reintroduces basic, point-set topology from a more modern, categorical perspective. Many graduate students are familiar with the ideas of point-set topology and they are ready to learn something new about them. Teaching the subject using category theory--a contemporary branch of mathematics that provides a way to represent abstract concepts--both deepens students' understanding of elementary topology and lays a solid foundation for future work in advanced topics.
Essentials of Topology with Applications
Author: Steven G. KrantzPublisher: CRC Press
ISBN: 1420089757
Category : Mathematics
Languages : en
Pages : 422
Book Description
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
Topology and Geometry
Author: Glen E. BredonPublisher: Springer Science & Business Media
ISBN: 0387979263
Category : Mathematics
Languages : en
Pages : 580
Book Description
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
Introduction to Topology
Author: V. A. VasilʹevPublisher: American Mathematical Soc.
ISBN: 0821821628
Category : Mathematics
Languages : en
Pages : 165
Book Description
This English translation of a Russian book presents the basic notions of differential and algebraic topology, which are indispensable for specialists and useful for research mathematicians and theoretical physicists. In particular, ideas and results are introduced related to manifolds, cell spaces, coverings and fibrations, homotopy groups, homology and cohomology, intersection index, etc. The author notes, "The lecture note origins of the book left a significant imprint on itsstyle. It contains very few detailed proofs: I tried to give as many illustrations as possible and to show what really occurs in topology, not always explaining why it occurs." He concludes, "As a rule, only those proofs (or sketches of proofs) that are interesting per se and have importantgeneralizations are presented."
Computational Topology
Author: Herbert EdelsbrunnerPublisher: American Mathematical Society
ISBN: 1470467690
Category : Mathematics
Languages : en
Pages : 241
Book Description
Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology. Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. This point of view is critically important in turning a mostly theoretical field of mathematics into one that is relevant to a multitude of disciplines in the sciences and engineering. The main approach is the discovery of topology through algorithms. The book is ideal for teaching a graduate or advanced undergraduate course in computational topology, as it develops all the background of both the mathematical and algorithmic aspects of the subject from first principles. Thus the text could serve equally well in a course taught in a mathematics department or computer science department.
Point Set Topology
Author: Steven A. GaalPublisher: Courier Corporation
ISBN: 0486472221
Category : Mathematics
Languages : en
Pages : 338
Book Description
Suitable for a complete course in topology, this text also functions as a self-contained treatment for independent study. Additional enrichment materials make it equally valuable as a reference. 1964 edition.