Chapter 1. Prelude: Love, hate, and exponentials Chapter 2. Paths and homotopies Chapter 3. The winding number Chapter 4. Topology of the plane Chapter 5. Integrals and the winding number Chapter 6. Vector fields and the rotation number Chapter 7. The winding number in functional analysis Chapter 8. Coverings and the fundamental group Chapter 9. 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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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2015