Title
A Combinatorial Introduction to Topology (Dover Books on Mathematics),New
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The creation of algebraic topology is a major accomplishment of 20thcentury mathematics. The goal of this book is to show how geometric and algebraic ideas met and grew together into an important branch of mathematics in the recent past. The book also conveys the fun and adventure that can be part of a mathematical investigation.Combinatorial topology has a wealth of applications, many of which result from connections with the theory of differential equations. As the author points out, 'Combinatorial topology is uniquely the subject where students of mathematics below graduate level can see the three major divisions of mathematics analysis, geometry, and algebra working together amicably on important problems.'To facilitate understanding, Professor Henle has deliberately restricted the subject matter of this volume, focusing especially on surfaces because the theorems can be easily visualized there, encouraging geometric intuition. In addition, this area presents many interesting applications arising from systems of differential equations. To illuminate the interaction of geometry and algebra, a single important algebraic tool homology is developed in detail.Written for upperlevel undergraduate and graduate students, this book requires no previous acquaintance with topology or algebra. Point set topology and group theory are developed as they are needed. In addition, a supplement surveying point set topology is included for the interested student and for the instructor who wishes to teach a mixture of point set and algebraic topology. A rich selection of problems, some with solutions, are integrated into the text.
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- Q: What is the main focus of 'A Combinatorial Introduction to Topology'? A: The book primarily focuses on the intersection of geometric and algebraic ideas in topology, specifically emphasizing surfaces to enhance geometric intuition.
- Q: Who is the author of this book? A: The author of 'A Combinatorial Introduction to Topology' is Michael Henle.
- Q: What is the target audience for this book? A: This book is intended for upper-level undergraduate and graduate students, requiring no prior knowledge of topology or algebra.
- Q: How many pages does the book contain? A: The book contains 320 pages.
- Q: What is the binding type of the book? A: The book is available in paperback binding.
- Q: When was 'A Combinatorial Introduction to Topology' published? A: The book was published on March 14, 1994.
- Q: Does this book include exercises or problems? A: Yes, the book integrates a rich selection of problems, some of which come with solutions.
- Q: Is there any supplementary material included? A: Yes, a supplement surveying point set topology is included for interested students and instructors.
- Q: What topics are covered in this topology book? A: The book covers combinatorial topology, point set topology, group theory, and applications related to differential equations.
- Q: Is this book suitable for self-study? A: Yes, the book is structured to facilitate self-study for students, particularly those interested in exploring topology without prior exposure.