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General Topology
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John L. Kelley
This classic book is a systematic exposition of general topology. It is especially intended as background for modern analysis. Based on lectures given at the University of Chicago, the University of California and Tulane University, this book is intended to be a reference and a text. As a reference work, it offers a reasonably complete coverage of ...
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Topology
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by
James R Munkres
For a senior undergraduate or first year graduate-level course in Introduction to Topology. Appropriate for a one-semester course on both general and algebraic topology or separate courses treating each topic separately. This text is designed to provide instructors with a convenient single text resource for bridging between general and algebraic ...
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Introducing Fractal Geometry
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Nigel Lesmoir-Gordon, William B Rood, Ralph Edney (Illustrator)
Fractal geometry is the geometry of the natural world. It mirrors the uneven but real shapes of nature, the world as we actually experience it, unlike the idealized forms of Euclidean geometry. We see fractals everywhere. Indeed, we "are" fractal! Using computers, fractal geometry can make precise models of physical structures - from ferns, ...
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Fractals Everywhere
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by
Michael F Barnsley
This volume is the second edition of the highly successful "Fractals Everywhere". The Focus of this text is how fractal geometry can be used to model real objects in the physical world. This edition of "Fractals Everywhere" is the most up-to-date fractal textbook available today. "Fractals Everywhere" may be supplemented by Michael F. Barnsley's ...
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Fractals
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by
John Briggs, Ph.D.
Describes how fractals were discovered, explains their unique properties, and discusses the mathematical foundation of fractals.
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Measure Theory
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by
Paul R Halmos
Useful both as a text for students and as a source of reference for the more advanced mathematician, this book presents a unified treatment of that part of measure theory which is most useful for its application in modern analysis. Topics studied include sets and classes, measures and outer measures, measurable functions, integration, general set ...
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Introduction to Topology: Third Edition
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by
Bert Mendelson
An undergraduate introduction to the fundamentals of topology -- engagingly written, filled with helpful insights, complete with many stimulating and imaginative exercises to help students develop a solid grasp of the subject.
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Algebraic Topology
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by
Allen Hatcher
In most mathematics departments at major universities one of the three or four basic first-year graduate courses is in the subject of algebraic topology. This introductory textbook in algebraic topology is suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and ...
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General topology
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by
Stephen Willard
Among the best available reference introductions to general topology, this volume encompasses two broad areas of topology: "continuous topology," represented by sections on convergence, compactness, metrization and complete metric spaces, uniform spaces, and function spaces; and "geometric topology," covered by 9 sections on connectivity ...
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Introduction to Smooth Manifolds
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John M Lee
This book is an introductory graduate-level textbook on the theory of smooth manifolds, for students who already have a solid acquaintance with general topology, the fundamental group, and covering spaces, as well as basic undergraduate linear algebra and real analysis. It is a natural sequel to the author's last book, Introduction to Topological ...
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Lecture Notes on Elementary Topology and Geometry
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by
I M Singer, J a Thorpe
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Introduction to Topology and Modern Analysis
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George F. Simmons
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Differential Forms in Algebraic Topology
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by
Raoul Bott, Loring W Tu
This text, developed from a first-year graduate course in algebraic topology, is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas- de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes-and include some ...
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Fractals: Endlessly Repeated Geometrical Figures
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by
Hans Lauwerier, Sophia Gill-Hoffstadt (Translator)
In this title the author makes fractals--infinite geometric figures--accessible to the lay person. Also included is a series of artwork and computer programs to create your own PC fractals. Programs run in Turbo BASIC.
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Euler's Gem: The Polyhedron Formula and the Birth of Topology
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by
David S Richeson
Leonhard Euler's polyhedron formula describes the structure of many objects - from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon molecules. Yet Euler's formula is so simple it can be explained to a child. "Euler's Gem" tells the illuminating story of this indispensable mathematical idea. From ancient Greek ...
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Topology
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by
John G. Hocking, Gail S. Young
Designed as a text for a one-year first course in topology, this authoritative volume offers an excellent general treatment of the main ideas of topology. It includes a large number and variety of topics from classical topology as well as newer areas of research activity.
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The Geometry of Physics: An Introduction
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by
Theodore Frankel
This book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, ...
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The Four-Color Theorem: History, Topological Foundations, and Idea of Proof
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by
Rudolf Fritsch, Gerda Fritsch, J Peschke (Translator)
This elegant little book discusses a famous problem that helped to define the field now known as topology: What is the minimum number of colors required to print a map such that no two adjoining countries have the same color, no matter how convoluted their boundaries. Many famous mathematicians have worked on the problem, but the proof eluded ...
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The Shape of Space: How to Visualize Surfaces and Three-Dimensional Manifolds
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Jeffrey Weeks
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Beginning Topology
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by
Sue E Goodman
"Beginning Topology" is designed to give undergraduate students a broad notion of the scope of topology in areas of point-set, geometric, combinatorial, differential, and algebraic topology, including an introduction to knot theory. A primary goal is to expose students to some recent research and to get them actively involved in learning. ...
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Fractals for the Classroom: Part Two: Complex Systems and Mandelbrot Set
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by
Heinz-Otto Peitgen, Evan M Maletsky, Dietmar Saupe
Fractals for the Classroom breaks new ground as it brings an exciting branch of mathematics into the classroom. The book is a collection of independent chapters on the major concepts related to the science and mathematics of fractals. Written at the mathematical level of an advanced secondary student, Fractals for the Classroom includes many ...
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The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots
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by
Colin Conrad Adams
Knots are familiar objects. We use them to moor our boats, to wrap our packages, to tie our shoes. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. "The Knot Book" is an introduction to this rich theory, starting with our familiar understanding of knots and a bit of college algebra and finishing with ...
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Introduction to Manifolds
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by
Loring W Tu
Manifolds, the higher-dimensional analogs of smooth curves and surfaces, are fundamental objects in modern mathematics. Combining aspects of algebra, topology, and analysis, manifolds have also been applied to classical mechanics, general relativity, and quantum field theory. In this streamlined introduction to the subject, the theory of manifolds ...
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Introduction to Differentiable Manifolds
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by
Serge Lang
This book gives an introduction to the basic concepts which are used in differential topology, differential geometry, and differential equations. A certain number of concepts are essential for all three of these areas, and are so basic and elementary, that it is worthwhile to collect them together so that more advanced expositions can be given ...
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Topology and geometry
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by
Bredon
This book is intended as a textbook for a first-year graduate course on algebraic topology, with as strong flavoring in smooth manifold theory. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. It covers most of the topics all ...
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