"Mathematics advanced study semesters."
Prelude: Love, Hate, and Exponentials
Paths and Homotopies
The Winding Number
Topology of the Plane
Integrals and the Winding Number
Vector Fields and the Rotation Number
The Winding Number in Functional Analysis
Coverings and the Fundamental Group
Coda: The Bott Periodicity Theorem
Appendix A: Linear Algebra
Appendix B: Metric Spaces
Appendix C: Extension and Approximation Theorems
Appendix D: Measure Zero
Appendix E: Calculus on Normed Spaces
Appendix F: Hilbert Space
Appendix G: Groups and Graphs.
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Winding around : the winding number in topology, geometry, and analysis by John Roe. ISBN 9781470421984. Published by American Mathematical Society in 2015. Publication and catalogue information, links to buy online and reader comments.
