Roe, John,  1959- <br/><br/>
Winding around :  the winding number in topology, geometry, and analysis / 
John Roe. 
 - India  American Mathematical Society  2015 
 - xiii, 269 pages :  illustrations ;  22 cm. 
 - Student mathematical library ;  volume 76 .
<br/><br/> "Mathematics advanced study semesters." 
<br/><br/>Includes bibliographical references and index. 
<br/><br/>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. 
<br/><br/><label>ISBN: </label>9781470438463 9781470421984 (alk. paper) 1470421984 (alk. paper) 
<br/><br/><label>LCCN: </label>2015019246 
<br/><br/><label>Subjects--Topical Terms: </label><br/>Mathematical analysis--Foundations.<br/>Associative law (Mathematics)<br/>Symmetric functions.<br/>Commutative law (Mathematics)<br/>Algebraic topology -- Classical topics -- Degree, winding number.<br/>Manifolds and cell complexes -- Low-dimensional topology -- Fundamental group, presentations, free differential calculus.<br/>Operator theory -- General theory of linear operators -- (Semi-) Fredholm operators; index theories.<br/>Global analysis, analysis on manifolds -- General theory of differentiable manifolds -- Differential forms.<br/>Algebraic topology -- Homology and cohomology theories -- $K$-theory.
<br/><br/><label>LC Class. No.: </label>QA299.8  / .R64 2015 
<br/><br/><label>Dewey Class. No.: </label>515 ROE-J