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1 Burnside Mathematics- Topology

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Graduate Texts in Mathematics #0153: Algebraic Topology: A First Course

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Graduate Texts in Mathematics #0153: Algebraic Topology: A First Course Cover

 

Synopses & Reviews

Publisher Comments:

Reformer, rancher, conservationist, hunter, historian, police commissioner, soldier, the youngest man ever to serve as president of the United States--no other American public figure has led as vigorous and varied a life as Theodore Roosevelt. This volume brings together two fascinating autobiographical works. The Rough Riders (1899) is the story of the 1st U.S. Volunteer Cavalry, the regiment Roosevelt led to enduring fame during the Spanish-American War. With his characteristic elan Roosevelt recounts how these grim hunters of the mountains, these wild rough riders of the plains, endured the heat, hunger, rain, mud, and malaria of the Cuban campaign to charge triumphantly up the San Juan Heights during the Battle of Santiago. In An Autobiography (1913), Roosevelt describes his life in politics and the emergence of his progressive ideas. Surveying his career as a state legislator, civil service reformer, New York City police commissioner, assistant secretary of the navy, governor, and president, Roosevelt writes of his battles against corruption, his role in establishing America as a world power, his passionate commitment to conservation, and his growing conviction that only a strong national government and an energetic presidency could protect the public against the rapacious greed of modern corporations.

Synopsis:

This book introduces the important ideas of algebraic topology by emphasizing the relation of these ideas with other areas of mathematics. Rather than choosing one point of view of modern topology (homotropy theory, axiomatic homology, or differential topology, say) the author concentrates on concrete problems in spaces with a few dimensions, introducing only as much algebraic machinery as necessary for the problems encountered. This makes it possible to see a wider variety of important features in the subject than is common in introductory texts; it is also in harmony with the historical development of the subject. The book is aimed at students who do not necessarily intend on specializing in algebraic topology.

Table of Contents


x Introduction
x Part I: Calculus in the Plane
x Path Integrals
x Angles and Deformations
x Part II: Winding Numbers
x The Winding Number
x Applications of Winding Numbers
x Part III: Cohomology and Homology, I
x De Rham Cohomology and the Jordan Curve Theorem
x Homology
x Part IV: Vector Fields
x Indices of Vector Fields
x Vector Fields on Surfaces
x Part V: Cohomology and Homology, II
x Holes and Integrals
x Mayer-Vietoris
x Part VI: Covering Spaces and Fundamental Groups, I
x Covering Spaces
x The Fundamental Group
x Part VII: Covering Spaces and Fundamental Groups, II
x The Fundamental Group and Covering Spaces
x The Van Kampen Theorem
x Part VIII: Cohomology and Homology, III
x Cohomology
x Variations
x Part IX: Topology of Surfaces
x The Topology of Surfaces
x Cohomology of Surfaces
x Part X: Riemann Surfaces
x Riemann Surfaces
x Riemann Surfaces and Algebraic Curves
x The Riemann-Roch Theorem
x Part XI: Higher Dimensions
x Toward Higher Dimensions
x Higher Homology
x Duality
x Appendices:
x A. Point Set Theory
x B. Analysis
x C. Algebra
x D. On Surfaces
x E. Proof of Borsuk's Theorem
x Hints and Answers
x References

Product Details

ISBN:
9780387943275
Author:
Fulton, William
Author:
Halmos, P. R.
Author:
Fulton, W.
Publisher:
Springer
Location:
New York, NY
Subject:
Topology
Subject:
Algebraic topology
Subject:
Topology - General
Subject:
General Mathematics
Subject:
Mathematics - General
Subject:
MATHEMATICS / Topology
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Copyright:
Edition Description:
1995. Corr. 2nd
Series:
Graduate Texts in Mathematics
Series Volume:
0153
Publication Date:
19950727
Binding:
TRADE PAPER
Language:
English
Illustrations:
Y
Pages:
448
Dimensions:
235 x 155 mm 1390 gr

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Related Subjects


Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry
Science and Mathematics » Mathematics » History
Science and Mathematics » Mathematics » Topology

Graduate Texts in Mathematics #0153: Algebraic Topology: A First Course Used Trade Paper
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Product details 448 pages Springer-Verlag - English 9780387943275 Reviews:
"Synopsis" by , This book introduces the important ideas of algebraic topology by emphasizing the relation of these ideas with other areas of mathematics. Rather than choosing one point of view of modern topology (homotropy theory, axiomatic homology, or differential topology, say) the author concentrates on concrete problems in spaces with a few dimensions, introducing only as much algebraic machinery as necessary for the problems encountered. This makes it possible to see a wider variety of important features in the subject than is common in introductory texts; it is also in harmony with the historical development of the subject. The book is aimed at students who do not necessarily intend on specializing in algebraic topology.
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