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Introductory Topology

Author: Mohammed Hichem Mortad
Publisher: World Scientific Publishing Company
ISBN: 9814583839
Size: 20.94 MB
Format: PDF, ePub
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The book offers a good introduction to topology through solved exercises. It is mainly intended for undergraduate students. Most exercises are given with detailed solutions.

Differential Topology

Author: Victor Guillemin
Publisher: American Mathematical Soc.
ISBN: 0821851934
Size: 55.90 MB
Format: PDF, ePub
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Differential Topology provides an elementary and intuitive introduction to the study of smooth manifolds. In the years since its first publication, Guillemin and Pollack's book has become a standard text on the subject. It is a jewel of mathematical exposition, judiciously picking exactly the right mixture of detail and generality to display the richness within. 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 Poincaré-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.

Principles Of Mathematical Analysis

Author: Walter Rudin
Publisher: McGraw-Hill Publishing Company
ISBN: 9780070856134
Size: 19.75 MB
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The third edition of this well known text continues to provide a solid foundation in mathematical analysis for undergraduate and first-year graduate students. The text begins with a discussion of the real number system as a complete ordered field. (Dedekind's construction is now treated in an appendix to Chapter I.) The topological background needed for the development of convergence, continuity, differentiation and integration is provided in Chapter 2. There is a new section on the gamma function, and many new and interesting exercises are included. This text is part of the Walter Rudin Student Series in Advanced Mathematics.

Introduction To Smooth Manifolds

Author: John M. Lee
Publisher: Springer Science & Business Media
ISBN: 0387217525
Size: 65.81 MB
Format: PDF
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Author has written several excellent Springer books.; This book is a sequel to Introduction to Topological Manifolds; Careful and illuminating explanations, excellent diagrams and exemplary motivation; Includes short preliminary sections before each section explaining what is ahead and why

Introduction To Topology

Author: Theodore W. Gamelin
Publisher: Courier Corporation
ISBN: 0486320189
Size: 79.76 MB
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This text explains nontrivial applications of metric space topology to analysis. Covers metric space, point-set topology, and algebraic topology. Includes exercises, selected answers, and 51 illustrations. 1983 edition.

Principles Of Topology

Author: Fred H. Croom
Publisher: Courier Dover Publications
ISBN: 0486801543
Size: 78.65 MB
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Originally published: Philadelphia: Saunders College Publishing, 1989; slightly corrected.

Introduction To Topology

Author: Bert Mendelson
Publisher: Courier Corporation
ISBN: 0486135098
Size: 28.35 MB
Format: PDF
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Concise undergraduate introduction to fundamentals of topology — clearly and engagingly written, and filled with stimulating, imaginative exercises. Topics include set theory, metric and topological spaces, connectedness, and compactness. 1975 edition.

Exercises In Functional Analysis

Author: Constantin Costara
Publisher: Springer Science & Business Media
ISBN: 9401702233
Size: 80.27 MB
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This book contains almost 450 exercises, all with complete solutions; it provides supplementary examples, counter-examples, and applications for the basic notions usually presented in an introductory course in Functional Analysis. Three comprehensive sections cover the broad topic of functional analysis. A large number of exercises on the weak topologies is included.