Elementary Concepts of Topology

Author: Paul Alexandroff

Publisher: Courier Corporation

ISBN: 0486155064

Category: Mathematics

Page: 64

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Concise work presents topological concepts in clear, elementary fashion, from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups. Includes 25 figures.

Intuitive Concepts in Elementary Topology

Author: B.H. Arnold

Publisher: Courier Corporation

ISBN: 0486275760

Category: Mathematics

Page: 192

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Classroom-tested and much-cited, this concise text is designed for undergraduates. It offers a valuable and instructive introduction to the basic concepts of topology, taking an intuitive rather than an axiomatic viewpoint. 1962 edition.

Elementary Concepts of Topology

Author: Paul Alexandroff

Publisher: Courier Corporation

ISBN: 9780486607474

Category: Mathematics

Page: 73

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Alexandroff's beautiful and elegant introduction to topology was originally published in 1932 as an extension of certain aspects of Hilbert's Anschauliche Geometrie. The text has long been recognized as one of the finest presentations of the fundamental concepts, vital for mathematicians who haven't time for extensive study and for beginning investigators. The book is not a substitute for a systematic text, but an unusually useful intuitive approach to the basic concepts. Its aim is to present these concepts in a clear, elementary fashion without sacrificing their profundity or exactness and to give some indication of how they are useful in increasingly more areas of mathematics. The author proceeds from the basics of set-theoretic topology, through those topological theorems and questions which are based upon the concept of the algebraic complex, to the concept of Betti groups which binds together central topological theories in a whole and upon which applications of topology largely rest. Wholly consistent with current investigations, in which a larger and larger part of topology is governed by the concept of homology, the book deals primarily with the concepts of complex, cycle, and homology. It points the way toward a systematic and entirely geometrically oriented theory of the most general structures of space. First English translation, prepared for Dover by Alan E. Farley. Preface by David Hilbert. Author's Foreword. Index. 25 figures.

Elementary Topology

Author: Michael C. Gemignani

Publisher: Courier Corporation

ISBN: 9780486665221

Category: Mathematics

Page: 270

View: 6867

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Topology is one of the most rapidly expanding areas of mathematical thought: while its roots are in geometry and analysis, topology now serves as a powerful tool in almost every sphere of mathematical study. This book is intended as a first text in topology, accessible to readers with at least three semesters of a calculus and analytic geometry sequence. In addition to superb coverage of the fundamentals of metric spaces, topologies, convergence, compactness, connectedness, homotopy theory, and other essentials, Elementary Topology gives added perspective as the author demonstrates how abstract topological notions developed from classical mathematics. For this second edition, numerous exercises have been added as well as a section dealing with paracompactness and complete regularity. The Appendix on infinite products has been extended to include the general Tychonoff theorem; a proof of the Tychonoff theorem which does not depend on the theory of convergence has also been added in Chapter 7.

Introduction to Topology

Third Edition

Author: Bert Mendelson

Publisher: Courier Corporation

ISBN: 0486135098

Category: Mathematics

Page: 224

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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.

Elementary Theory of Numbers

Author: William Judson LeVeque

Publisher: Courier Corporation

ISBN: 9780486663487

Category: Mathematics

Page: 132

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Superb introduction to Euclidean algorithm and its consequences, congruences, continued fractions, powers of an integer modulo m, Gaussian integers, Diophantine equations, more. Problems, with answers. Bibliography.

A First Course in Topology

An Introduction to Mathematical Thinking

Author: Robert A Conover

Publisher: Courier Corporation

ISBN: 0486780015

Category: Mathematics

Page: 272

View: 4139

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Students must prove all of the theorems in this undergraduate-level text, which features extensive outlines to assist in study and comprehension. Thorough and well-written, the treatment provides sufficient material for a one-year undergraduate course. The logical presentation anticipates students' questions, and complete definitions and expositions of topics relate new concepts to previously discussed subjects. Most of the material focuses on point-set topology with the exception of the last chapter. Topics include sets and functions, infinite sets and transfinite numbers, topological spaces and basic concepts, product spaces, connectivity, and compactness. Additional subjects include separation axioms, complete spaces, and homotopy and the fundamental group. Numerous hints and figures illuminate the text. Dover (2014) republication of the edition originally published by The Williams & Wilkins Company, Baltimore, 1975. See every Dover book in print at www.doverpublications.com

Evolution of Mathematical Concepts

An Elementary Study

Author: Raymond L. Wilder

Publisher: Courier Corporation

ISBN: 0486490610

Category: Mathematics

Page: 216

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Accessible to students and relevant to specialists, this remarkable book by a prominent educator offers a unique perspective on the evolutionary development of mathematics. Rather than conducting a survey of the history or philosophy of mathematics, Raymond L. Wilder envisions mathematics as a broad cultural phenomenon. His treatment examines and illustrates how such concepts as number and length were affected by historic and social events. Starting with a brief consideration of preliminary notions, this study explores the early evolution of numbers, the evolution of geometry, and the conquest of the infinite as embodied by real numbers. A detailed look at the processes of evolution concludes with an examination of the evolutionary aspects of modern mathematics.

How to Solve Applied Mathematics Problems

Author: B. L. Moiseiwitsch

Publisher: Courier Corporation

ISBN: 0486285227

Category: Mathematics

Page: 336

View: 3362

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This workbook bridges the gap between lectures and practical applications, offering students of mathematics, engineering, and physics the chance to practice solving problems from a wide variety of fields. 2011 edition.

A Source Book in Mathematics

Author: David Eugene Smith

Publisher: Courier Corporation

ISBN: 0486158292

Category: Mathematics

Page: 736

View: 1971

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The writings of Newton, Leibniz, Pascal, Riemann, Bernoulli, and others in a comprehensive selection of 125 treatises dating from the Renaissance to the late 19th century — most unavailable elsewhere.

Introduction to Topological Groups

Author: Taqdir Husain

Publisher: Courier Dover Publications

ISBN: 0486819191

Category: Mathematics

Page: 240

View: 8592

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Concise treatment covers semitopological groups, locally compact groups, Harr measure, and duality theory and some of its applications. The volume concludes with a chapter that introduces Banach algebras. 1966 edition.

The Concept of a Riemann Surface

Author: Hermann Weyl

Publisher: Courier Corporation

ISBN: 048613167X

Category: Mathematics

Page: 208

View: 2214

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This classic on the general history of functions combines function theory and geometry, forming the basis of the modern approach to analysis, geometry, and topology. 1955 edition.

Topology

An Introduction with Application to Topological Groups

Author: George McCarty

Publisher: Courier Corporation

ISBN: 9780486656335

Category: Mathematics

Page: 270

View: 8834

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Covers sets and functions, groups, metric spaces, topologies, topological groups, compactness and connectedness, function spaces, the fundamental group, the fundamental group of the circle, locally isomorphic groups, more. 1967 edition.

Point Set Topology

Author: Steven A. Gaal

Publisher: Courier Corporation

ISBN: 0486472221

Category: Mathematics

Page: 336

View: 8834

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Suitable for a complete course in topology, this text also functions as a self-contained treatment for independent study. Additional enrichment materials make it equally valuable as a reference. 1964 edition.

Elementary Point-Set Topology

A Transition to Advanced Mathematics

Author: Andre L. Yandl,Adam Bowers

Publisher: Courier Dover Publications

ISBN: 048680349X

Category: Mathematics

Page: 256

View: 1935

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This versatile, original approach, which focuses on learning to read and write proofs, serves as both an introductory treatment and a bridge between elementary calculus and more advanced courses. 2016 edition.

Lehrbuch der Algebra

Mit lebendigen Beispielen, ausführlichen Erläuterungen und zahlreichen Bildern

Author: Gerd Fischer

Publisher: Springer-Verlag

ISBN: 3834894559

Category: Mathematics

Page: 404

View: 3123

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Dieses ausführlich geschriebene Lehrbuch eignet sich als Begleittext zu einer einführenden Vorlesung über Algebra. Die Themenkreise sind Gruppen als Methode zum Studium von Symmetrien verschiedener Art, Ringe mit besonderem Gewicht auf Fragen der Teilbarkeit und schließlich als Schwerpunkt Körpererweiterungen und Galois-Theorie als Grundlage für die Lösung klassischer Probleme zur Berechnung der Nullstellen von Polynomen und zur Möglichkeit geometrischer Konstruktionen.

Das BUCH der Beweise

Author: Martin Aigner,Günter M. Ziegler

Publisher: Springer-Verlag

ISBN: 3662064545

Category: Mathematics

Page: 247

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Die elegantesten mathematischen Beweise, spannend und für jeden Interessierten verständlich. "Der Beweis selbst, seine Ästhetik, seine Pointe geht ins Geschichtsbuch der Königin der Wissenschaften ein. Ihre Anmut offenbart sich in dem gelungenen und geschickt illustrierten Buch." Die Zeit

Fundamental Concepts of Geometry

Author: Bruce E. Meserve

Publisher: Courier Corporation

ISBN: 048615226X

Category: Mathematics

Page: 336

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Demonstrates relationships between different types of geometry. Provides excellent overview of the foundations and historical evolution of geometrical concepts. Exercises (no solutions). Includes 98 illustrations.

Mathematics for Quantum Chemistry

Author: Jay Martin Anderson

Publisher: Courier Corporation

ISBN: 0486151484

Category: Science

Page: 160

View: 5024

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Introduction to problems of molecular structure and motion covers calculus of orthogonal functions, algebra of vector spaces, and Lagrangian and Hamiltonian formulation of classical mechanics. Answers to problems. 1966 edition.