Synopses & Reviews
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.
Review
"Fulton has done genuine service for the mathematical community by writing a text on algebraic topology which is genuinely different from the existing texts. Each time a text such as this is published we more truly have a real choice when we pick a book for a course or for self-study. The author, who is an expert in algebraic geometry, has given us his own personal idiosyncratic vision of how the subject should be developed."" AMERICAN MATHEMATICAL MONTHLY
Review
An unintimidating introduction by a master expositor. --CHOICE
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.
Synopsis
To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re- lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ- ential topology, etc.), we concentrate our attention on concrete prob- lems in low dimensions, introducing only as much algebraic machin- ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol- ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel- opment of the subject. What would we like a student to know after a first course in to- pology (assuming we reject the answer: half of what one would like the student to know after a second course in topology)? Our answers to this have guided the choice of material, which includes: under- standing the relation between homology and integration, first on plane domains, later on Riemann surfaces and in higher dimensions; wind- ing numbers and degrees of mappings, fixed-point theorems; appli- cations such as the Jordan curve theorem, invariance of domain; in- dices of vector fields and Euler characteristics; fundamental groups
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