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Algebraic Topology: A First Course (Graduate Texts in Mathematics, 153),Used
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To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ ential topology, etc.), we concentrate our attention on concrete prob lems in low dimensions, introducing only as much algebraic machin ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol ogistswithout, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel opment of the subject. What would we like a student to know after a first course in to pology (assuming we reject the answer: half of what one would like the student to know after a second course in topology)? Our answers to this have guided the choice of material, which includes: under standing the relation between homology and integration, first on plane domains, later on Riemann surfaces and in higher dimensions; wind ing numbers and degrees of mappings, fixedpoint theorems; appli cations such as the Jordan curve theorem, invariance of domain; in dices of vector fields and Euler characteristics; fundamental groups
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- Q: What is the primary focus of 'Algebraic Topology: A First Course'? A: The book focuses on introducing key concepts of algebraic topology by connecting these ideas with various areas of mathematics, emphasizing concrete problems in low dimensions.
- Q: Who is the intended audience for this book? A: The book is designed for students of mathematics or science who are not necessarily aiming to become professional algebraic topologists, while also being accessible to those interested in the subject.
- Q: What topics are covered in the book? A: Topics include the relationship between homology and integration, winding numbers, fixed-point theorems, and applications such as the Jordan curve theorem and invariance of domain.
- Q: How many pages does the book have? A: The book has a total of 448 pages.
- Q: What is the binding type of this book? A: The book is available in paperback binding.
- Q: When was 'Algebraic Topology: A First Course' published? A: The book was published on July 27, 1995.
- Q: Who is the author of this book? A: The author of the book is William Fulton.
- Q: Is this book suitable for beginners in topology? A: Yes, the book is designed as a beginning text, making it suitable for those new to the subject.
- Q: What edition of the book is available? A: This is the First Edition of the book.
- Q: When was the release date for this book? A: The release date for 'Algebraic Topology: A First Course' was September 5, 1997.