eBook - ePub
Elementary Point-Set Topology
A Transition to Advanced Mathematics
- 256 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
eBook - ePub
Elementary Point-Set Topology
A Transition to Advanced Mathematics
About this book
In addition to serving as an introduction to the basics of point-set topology, this text bridges the gap between the elementary calculus sequence and higher-level mathematics courses. The versatile, original approach focuses on learning to read and write proofs rather than covering advanced topics. Based on lecture notes that were developed over many years at The University of Seattle, the treatment is geared toward undergraduate math majors and suitable for a variety of introductory courses.
Starting with elementary concepts in logic and basic techniques of proof writing, the text defines topological and metric spaces and surveys continuity and homeomorphism. Additional subjects include product spaces, connectedness, and compactness. The final chapter illustrates topology's use in other branches of mathematics with proofs of the fundamental theorem of algebra and of Picard's existence theorem for differential equations.
"This is a back-to-basics introductory text in point-set topology that can double as a transition to proofs course. The writing is very clear, not too concise or too wordy. Each section of the book ends with a large number of exercises. The optional first chapter covers set theory and proof methods; if the students already know this material you can start with Chapter 2 to present a straight topology course, otherwise the book can be used as an introduction to proofs course also." — Mathematical Association of America
Starting with elementary concepts in logic and basic techniques of proof writing, the text defines topological and metric spaces and surveys continuity and homeomorphism. Additional subjects include product spaces, connectedness, and compactness. The final chapter illustrates topology's use in other branches of mathematics with proofs of the fundamental theorem of algebra and of Picard's existence theorem for differential equations.
"This is a back-to-basics introductory text in point-set topology that can double as a transition to proofs course. The writing is very clear, not too concise or too wordy. Each section of the book ends with a large number of exercises. The optional first chapter covers set theory and proof methods; if the students already know this material you can start with Chapter 2 to present a straight topology course, otherwise the book can be used as an introduction to proofs course also." — Mathematical Association of America
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Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Yes, you can access Elementary Point-Set Topology by Andre L. Yandl,Adam Bowers, Adam Bowers in PDF and/or ePUB format, as well as other popular books in Mathematics & Topology. We have over one million books available in our catalogue for you to explore.
Information
Table of contents
- Cover
- Title Page
- Copyright Page
- Contents
- Preface
- List of Figures
- List of Symbols
- 1 Mathematical Proofs and Sets
- 2 Topological Spaces
- 3 Continuous Functions
- 4 Product Spaces
- 5 Connectedness
- 6 Compactness
- 7 Fixed Point Theorems and Applications
- Index