The text is mostly self-contained, requiring only undergraduate analysis and linear algebra. By relying on a unifying idea-transversality-the authors are able to avoid the use of big machinery or ad hoc techniques to establish the main results. In this way, they present intelligent treatments of important theorems, such as the Lefschetz fixed-point theorem, the Poincare-Hopf index theorem, and Stokes theorem.
The book has a wealth of exercises of various types. Some are routine explorations of the main material. In others, the students are guided step-by-step through proofs of fundamental results, such as the Jordan-Brouwer separation theorem. An exercise section in Chapter 4 leads the student through a construction of de Rham cohomology and a proof of its homotopy invariance.
The book is suitable for either an introductory graduate course or an advanced undergraduate course.
- Hardback | 222 pages
- 184.15 x 260.35 x 12.7mm | 612.35g
- 15 Aug 2010
- American Mathematical Society
- Providence, United States
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