Topology Now!
Title | Topology Now! PDF eBook |
Author | Robert Messer |
Publisher | American Mathematical Soc. |
Pages | 240 |
Release | 2018-10-10 |
Genre | |
ISBN | 1470447819 |
Topology is a branch of mathematics packed with intriguing concepts, fascinating geometrical objects, and ingenious methods for studying them. The authors have written this textbook to make the material accessible to undergraduate students without requiring extensive prerequisites in upper-level mathematics. The approach is to cultivate the intuitive ideas of continuity, convergence, and connectedness so students can quickly delve into knot theory, the topology of surfaces and three-dimensional manifolds, fixed points and elementary homotopy theory. The fundamental concepts of point-set topology appear at the end of the book when students can see how this level of abstraction provides a sound logical basis for the geometrical ideas that have come before. This organization exposes students to the exciting world of topology now(!) rather than later. Students using this textbook should have some exposure to the geometry of objects in higher-dimensional Euclidean spaces together with an appreciation of precise mathematical definitions and proofs.
Elementary Concepts of Topology
Title | Elementary Concepts of Topology PDF eBook |
Author | Paul Alexandroff |
Publisher | Courier Corporation |
Pages | 68 |
Release | 2012-08-13 |
Genre | Mathematics |
ISBN | 0486155064 |
Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figures.
Experiments in Topology
Title | Experiments in Topology PDF eBook |
Author | Stephen Barr |
Publisher | Courier Corporation |
Pages | 244 |
Release | 2012-12-04 |
Genre | Mathematics |
ISBN | 048615274X |
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.
Topology Now!
Title | Topology Now! PDF eBook |
Author | Robert Messer |
Publisher | Mathematical Association of America |
Pages | 250 |
Release | 2006-05-11 |
Genre | Mathematics |
ISBN | 9780883857441 |
Topology is a branch of mathematics packed with intriguing concepts, fascinating geometrical objects, and ingenious methods for studying them. The authors have written this textbook to make the material accessible to undergraduate students without requiring extensive prerequisites in upper-level mathematics. The approach is to cultivate the intuitive ideas of continuity, convergence, and connectedness so students can quickly delve into knot theory, the topology of surfaces and three-dimensional manifolds, fixed points and elementary homotopy theory. The fundamental concepts of point-set topology appear at the end of the book when students can see how this level of abstraction provides a sound logical basis for the geometrical ideas that have come before. This organization exposes students to the exciting world of topology now(!) rather than later. Students using this textbook should have some exposure to the geometry of objects in higher-dimensional Euclidean spaces together with an appreciation of precise mathematical definitions and proofs.
General Topology
Title | General Topology PDF eBook |
Author | Tom Richmond |
Publisher | Walter de Gruyter GmbH & Co KG |
Pages | 397 |
Release | 2020-07-06 |
Genre | Mathematics |
ISBN | 3110686724 |
The first half of the book provides an introduction to general topology, with ample space given to exercises and carefully selected applications. The second half of the text includes topics in asymmetric topology, a field motivated by applications in computer science. Recurring themes include the interactions of topology with order theory and mathematics designed to model loss-of-resolution situations.
Topology
Title | Topology PDF eBook |
Author | Tai-Danae Bradley |
Publisher | MIT Press |
Pages | 167 |
Release | 2020-08-18 |
Genre | Mathematics |
ISBN | 0262359626 |
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.
A Combinatorial Introduction to Topology
Title | A Combinatorial Introduction to Topology PDF eBook |
Author | Michael Henle |
Publisher | Courier Corporation |
Pages | 340 |
Release | 1994-01-01 |
Genre | Mathematics |
ISBN | 9780486679662 |
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.