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Author: Theodore W. Gamelin Publisher: 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.
Author: Theodore W. Gamelin Publisher: 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.
Author: Steve Warner Publisher: ISBN: 9780999811771 Category : Languages : en Pages : 282
Book Description
Topology for Beginners consists of a series of basic to intermediate lessons in topology. In addition, all the proofwriting skills that are essential for advanced study in mathematics are covered and reviewed extensively. Topology for Beginners is perfect for professors teaching an undergraduate course or basic graduate course in topology. high school teachers working with advanced math students. students wishing to see the type of mathematics they would be exposed to as a math major. The material in this pure math book includes: 16 lessons consisting of basic to intermediate topics in set theory and topology. A problem set after each lesson arranged by difficulty level. A complete solution guide is included as a downloadable PDF file. Topology Book Table Of Contents (Selected) Here's a selection from the table of contents: Introduction Lesson 1 - Sets and Subsets Lesson 2 - Operations on Sets Lesson 3 - Relations Lesson 4 - Functions and Equinumerosity Lesson 5 - Number Systems and Induction Lesson 6 - Algebraic Structures and Completeness Lesson 7 - Basic Topology of R and C Lesson 8 - Continuity in R and C Lesson 9 - Topological Spaces Lesson 10 - Separation and Countability Lesson 11 - Metrizable Spaces Lesson 12 - Compactness Lesson 13 - Continuity and Homeomorphisms Lesson 14 - Connectedness Lesson 15 - Function Spaces Lesson 16 - Algebraic Topology
Author: M.A. Armstrong Publisher: Springer Science & Business Media ISBN: 1475717938 Category : Mathematics Languages : en Pages : 260
Book Description
In this broad introduction to topology, the author searches for topological invariants of spaces, together with techniques for their calculating. Students with knowledge of real analysis, elementary group theory, and linear algebra will quickly become familiar with a wide variety of techniques and applications involving point-set, geometric, and algebraic topology. Over 139 illustrations and more than 350 problems of various difficulties help students gain a thorough understanding of the subject.
Author: Bert Mendelson Publisher: Courier Corporation ISBN: 0486135098 Category : Mathematics Languages : en Pages : 226
Book Description
Concise undergraduate introduction to fundamentals of topology — clearly and engagingly written, and filled with stimulating, imaginative exercises. Topics include set theory, metric and topological spaces, connectedness, and compactness. 1975 edition.
Author: Colin Conrad Adams Publisher: Pearson ISBN: Category : Mathematics Languages : en Pages : 520
Book Description
Learn the basics of point-set topology with the understanding of its real-world application to a variety of other subjects including science, economics, engineering, and other areas of mathematics. Introduces topology as an important and fascinating mathematics discipline to retain the readers interest in the subject. Is written in an accessible way for readers to understand the usefulness and importance of the application of topology to other fields. Introduces topology concepts combined with their real-world application to subjects such DNA, heart stimulation, population modeling, cosmology, and computer graphics. Covers topics including knot theory, degree theory, dynamical systems and chaos, graph theory, metric spaces, connectedness, and compactness. A useful reference for readers wanting an intuitive introduction to topology.
Author: John D. Baum Publisher: Courier Corporation ISBN: 0486668266 Category : Mathematics Languages : en Pages : 164
Book Description
Topology continues to be a topic of prime importance in contemporary mathematics, but until the publication of this book there were few if any introductions to topology for undergraduates. This book remedied that need by offering a carefully thought-out, graduated approach to point set topology at the undergraduate level. To make the book as accessible as possible, the author approaches topology from a geometric and axiomatic standpoint; geometric, because most students come to the subject with a good deal of geometry behind them, enabling them to use their geometric intuition; axiomatic, because it parallels the student's experience with modern algebra, and keeps the book in harmony with current trends in mathematics. After a discussion of such preliminary topics as the algebra of sets, Euler-Venn diagrams and infinite sets, the author takes up basic definitions and theorems regarding topological spaces (Chapter 1). The second chapter deals with continuous functions (mappings) and homeomorphisms, followed by two chapters on special types of topological spaces (varieties of compactness and varieties of connectedness). Chapter 5 covers metric spaces. Since basic point set topology serves as a foundation not only for functional analysis but also for more advanced work in point set topology and algebraic topology, the author has included topics aimed at students with interests other than analysis. Moreover, Dr. Baum has supplied quite detailed proofs in the beginning to help students approaching this type of axiomatic mathematics for the first time. Similarly, in the first part of the book problems are elementary, but they become progressively more difficult toward the end of the book. References have been supplied to suggest further reading to the interested student.
Author: Sue E. Goodman Publisher: American Mathematical Soc. ISBN: 0821847961 Category : Mathematics Languages : en Pages : 258
Book Description
Beginning Topology is designed to give undergraduate students a broad notion of the scope of topology in areas of point-set, geometric, combinatorial, differential, and algebraic topology, including an introduction to knot theory. A primary goal is to expose students to some recent research and to get them actively involved in learning. Exercises and open-ended projects are placed throughout the text, making it adaptable to seminar-style classes. The book starts with a chapter introducing the basic concepts of point-set topology, with examples chosen to captivate students' imaginations while illustrating the need for rigor. Most of the material in this and the next two chapters is essential for the remainder of the book. One can then choose from chapters on map coloring, vector fields on surfaces, the fundamental group, and knot theory. A solid foundation in calculus is necessary, with some differential equations and basic group theory helpful in a couple of chapters. Topics are chosen to appeal to a wide variety of students: primarily upper-level math majors, but also a few freshmen and sophomores as well as graduate students from physics, economics, and computer science. All students will benefit from seeing the interaction of topology with other fields of mathematics and science; some will be motivated to continue with a more in-depth, rigorous study of topology.
Author: Steve Warner Publisher: ISBN: 9781951619039 Category : Mathematics Languages : en Pages : 142
Book Description
Topology for Beginners - Solution GuideThis book contains complete solutions to the problems in the 16 Problem Sets in Topology for Beginners. Note that this book references examples and theorems from Topology for Beginners. Therefore, it is strongly suggested that you purchase a copy of that book before purchasing this one.
Author: John M. Lee Publisher: Springer Science & Business Media ISBN: 038722727X Category : Mathematics Languages : en Pages : 395
Book Description
Manifolds play an important role in topology, geometry, complex analysis, algebra, and classical mechanics. Learning manifolds differs from most other introductory mathematics in that the subject matter is often completely unfamiliar. This introduction guides readers by explaining the roles manifolds play in diverse branches of mathematics and physics. The book begins with the basics of general topology and gently moves to manifolds, the fundamental group, and covering spaces.
Author: O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov Publisher: 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.
Author: Theodore W. Gamelin
Author: Theodore W. Gamelin
Author: Steve Warner
Author: M.A. Armstrong
Author: Bert Mendelson
Author: Colin Conrad Adams
Author: John D. Baum
Author: Sue E. Goodman
Author: Steve Warner
Author: John M. Lee
Author: O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov