Lecture Notes On Elementary Topology And Geometry
Download Lecture Notes On Elementary Topology And Geometry full books in PDF, epub, and Kindle. Read online free Lecture Notes On Elementary Topology And Geometry ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads.
Author |
: I.M. Singer |
Publisher |
: Springer |
Total Pages |
: 240 |
Release |
: 2015-05-28 |
ISBN-10 |
: 9781461573470 |
ISBN-13 |
: 1461573475 |
Rating |
: 4/5 (70 Downloads) |
Synopsis Lecture Notes on Elementary Topology and Geometry by : I.M. Singer
At the present time, the average undergraduate mathematics major finds mathematics heavily compartmentalized. After the calculus, he takes a course in analysis and a course in algebra. Depending upon his interests (or those of his department), he takes courses in special topics. Ifhe is exposed to topology, it is usually straightforward point set topology; if he is exposed to geom etry, it is usually classical differential geometry. The exciting revelations that there is some unity in mathematics, that fields overlap, that techniques of one field have applications in another, are denied the undergraduate. He must wait until he is well into graduate work to see interconnections, presumably because earlier he doesn't know enough. These notes are an attempt to break up this compartmentalization, at least in topology-geometry. What the student has learned in algebra and advanced calculus are used to prove some fairly deep results relating geometry, topol ogy, and group theory. (De Rham's theorem, the Gauss-Bonnet theorem for surfaces, the functorial relation of fundamental group to covering space, and surfaces of constant curvature as homogeneous spaces are the most note worthy examples.) In the first two chapters the bare essentials of elementary point set topology are set forth with some hint ofthe subject's application to functional analysis.
Author |
: Isadore Manuel Singer |
Publisher |
: |
Total Pages |
: 232 |
Release |
: 1987 |
ISBN-10 |
: OCLC:630198646 |
ISBN-13 |
: |
Rating |
: 4/5 (46 Downloads) |
Synopsis Lecture Notes on Elementary Topology and Geometry by : Isadore Manuel Singer
Author |
: Isadore M. Singer |
Publisher |
: |
Total Pages |
: 214 |
Release |
: 1971 |
ISBN-10 |
: OCLC:180538624 |
ISBN-13 |
: |
Rating |
: 4/5 (24 Downloads) |
Synopsis Lecture Notes on Elementary Topology and Geometry by : Isadore M. Singer
Author |
: Singer |
Publisher |
: |
Total Pages |
: 244 |
Release |
: 2004-01-01 |
ISBN-10 |
: 8181282248 |
ISBN-13 |
: 9788181282248 |
Rating |
: 4/5 (48 Downloads) |
Synopsis Lecture Notes On Elementary Topology And Geometry by : Singer
Author |
: I. M. Singer |
Publisher |
: |
Total Pages |
: |
Release |
: 1967 |
ISBN-10 |
: OCLC:771301767 |
ISBN-13 |
: |
Rating |
: 4/5 (67 Downloads) |
Synopsis Lecture Notes on Elementary Topology and Geometry by : I. M. Singer
Author |
: O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 432 |
Release |
: |
ISBN-10 |
: 0821886258 |
ISBN-13 |
: 9780821886250 |
Rating |
: 4/5 (58 Downloads) |
Synopsis Elementary Topology by : O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov
This text contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment. Proofs of theorems are separated from their formulations and are gathered at the end of each chapter, making this book appear like a problem book and also giving it appeal to the expert as a handbook. The book includes about 1,000 exercises.
Author |
: Mario Benedicty |
Publisher |
: |
Total Pages |
: 346 |
Release |
: 1964 |
ISBN-10 |
: OCLC:431417232 |
ISBN-13 |
: |
Rating |
: 4/5 (32 Downloads) |
Synopsis Class Notes in Elementary Topology and Geometry by : Mario Benedicty
Author |
: Ana Cannas da Silva |
Publisher |
: Springer |
Total Pages |
: 240 |
Release |
: 2004-10-27 |
ISBN-10 |
: 9783540453307 |
ISBN-13 |
: 354045330X |
Rating |
: 4/5 (07 Downloads) |
Synopsis Lectures on Symplectic Geometry by : Ana Cannas da Silva
The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.
Author |
: James F. Davis |
Publisher |
: American Mathematical Society |
Total Pages |
: 385 |
Release |
: 2023-05-22 |
ISBN-10 |
: 9781470473686 |
ISBN-13 |
: 1470473682 |
Rating |
: 4/5 (86 Downloads) |
Synopsis Lecture Notes in Algebraic Topology by : James F. Davis
The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic and geometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, some knowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstruction theory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to present proofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the “big picture”, teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, and homological algebra. The exposition in the text is clear; special cases are presented over complex general statements.
Author |
: Robert W. Ghrist |
Publisher |
: Createspace Independent Publishing Platform |
Total Pages |
: 0 |
Release |
: 2014 |
ISBN-10 |
: 1502880857 |
ISBN-13 |
: 9781502880857 |
Rating |
: 4/5 (57 Downloads) |
Synopsis Elementary Applied Topology by : Robert W. Ghrist
This book gives an introduction to the mathematics and applications comprising the new field of applied topology. The elements of this subject are surveyed in the context of applications drawn from the biological, economic, engineering, physical, and statistical sciences.