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» » Topology and Its Applications (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts)
Topology and Its Applications (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts) e-book

Author:

William F. Basener

Language:

English

Category:

Math

Subcategory:

Mathematics

ePub size:

1904 kb

Other formats:

lrf rtf azw txt

Rating:

4.4

Publisher:

Wiley-Interscience; 1 edition (November 3, 2006)

Pages:

384

ISBN:

0471687553

Topology and Its Applications (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts) e-book

by William F. Basener


CHOICE, August 2007). a celebration of topology and its many applications.

CHOICE, August 2007). I enjoyed reading it and believe that it would be an interesting textbook from which to learn. This book is the first of its kind to present applications in computer graphics, economics, dynamical systems, condensed matter physics, biology, robotics, chemistry, cosmology, material science, computational topology, and population modeling, as well as other areas of science and engineering. Many of these applications are presented in optional sections, allowing an instructor to customize the presentation.

Topology and Its Applications. Download Product Flyer Pure and Applied Mathematics: A Wiley Series of Texts"" Monographs and Tracts. Download Product Flyer. WILLIAM F. BASENER, PhD, is an Assistant Professor in the Department of Mathematics and Statistics at Rochester Institute of Technology in Rochester, New York. He received his PhD in mathematics in 2001 from Boston University. Dr. Basener is the recipient of numerous teaching awards. Pure and Applied Mathematics: A Wiley Series of Texts"" Monographs and Tracts.

Filling a gap between the teaching of topology and its modern uses in real-world phenomena, Topology and Its Applications is organized around the mathematical theory of topology, a framework of rigorous theorems, and clear, elegant proofs.

This is a great analysis book as others have discussed. The print looks like a cheap photocopy of an original manuscript. Or even a copy of a copy. It is outrageous that they can charge so much for such poor quality work.

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Pure and applied mathematics. A Wiley-Interscience Series of Texts, Monograph, and Tracts. Wiley also publishes its books in a variety of electronic formats. A complete list of the titles in this series appears at the end of this volume. Modern algebra with applications. A Wiley Series of Texts, Monographs, and Tracts. Wiley also publishes its books in a variety of electronic formats

Pure and applied mathematics. A complete list of the titles in this series appears at the end ofthis volume. For more information about Wiley products, visit our web site at ww. iley.

Using a variety of theorems to tie these seemingly disparate topics together, the author demonstrates the essential unity of mathematics.

Discover a unique and modern treatment of topology employing across-disciplinary approach

Implemented recently to understand diverse topics, such as cellbiology, superconductors, and robot motion, topology has beentransformed from a theoretical field that highlights mathematicaltheory to a subject that plays a growing role in nearly all fieldsof scientific investigation. Moving from the concrete to theabstract, Topology and Its Applications displays both the beautyand utility of topology, first presenting the essentials oftopology followed by its emerging role within the new frontiers inresearch.

Filling a gap between the teaching of topology and its modernuses in real-world phenomena, Topology and Its Applications isorganized around the mathematical theory of topology, a frameworkof rigorous theorems, and clear, elegant proofs.

This book is the first of its kind to present applications incomputer graphics, economics, dynamical systems, condensed matterphysics, biology, robotics, chemistry, cosmology, material science,computational topology, and population modeling, as well as otherareas of science and engineering. Many of these applications arepresented in optional sections, allowing an instructor to customizethe presentation.

The author presents a diversity of topological areas, includingpoint-set topology, geometric topology, differential topology, andalgebraic/combinatorial topology. Topics within these areasinclude:

Open setsCompactnessHomotopySurface classificationIndex theory on surfacesManifolds and complexesTopological groupsThe fundamental group and homology

Special "core intuition" segments throughout the book brieflyexplain the basic intuition essential to understanding severaltopics. A generous number of figures and examples, many of whichcome from applications such as liquid crystals, space probe data,and computer graphics, are all available from the publisher's Website.


Spilberg
Book arrived on time and in very good disposition.
The book is very good in that it associates some very important applications to topology. However it has several typo's and a few errors.
Cerana
The book is unique in its attempt to visualize Topology.
The Schaum's outline on Topology may be all needed to pass an exam,
But this book has a lot more figures and applications than many topology books.
Colored figures would improve it.
Uttegirazu
On the upside, the author strives and does a good job to convey intuition and visual examples, which I think is important and not enough people do this, so kudos to the author for this.

On the downside, there are many errors in the exposition and proofs. They range from innocuous (pg. 20, Lemma 6 says 'union' when the equation clearly and correctly shows 'intersection') to intermediate (pg 28, Theorem 9, he claims 'f(f^-1(B)) = B' when really the lhs is a subset of the rhs), to ones that threw me off (pg. 24, 'U x V = p_1(U) intersect p_2(V)' should be 'U x V = p_1^-1(U) intersect p_2^-1(V)'; and pg 65, theorem 31, has incorrect / inconsistent variable references, and states without proof that open balls are path connected. That last one isn't an error, but I had to look up, and this author, who is careful with the concepts part, seems like it would be his style to include it).

All in all, I could recommend a future version if the errors are corrected. It gave me insights and had a conversational tone that made it easy to learn from, but I had to stop because the errors threw me off too much to have confidence that I'll catch more subtle problems in more unfamiliar territory. I hope the author does an updated version with corrections.

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