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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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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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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
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by
John Briggs
Fractals are unique patterns left behind by the unpredictable movements -- the chaos -- of the world at work. The branching patterns of trees, the veins in a hand, water twisting out of a running tap -- all of these are fractals. Learn to recognize them and you will never again see things in quite the same way. Fractals permeate our lives, ...
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Schaum's Outline of General Topology
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by
Syemour Lipschultz, Seymour Lipschutz, Ph.D.
With more than 30 million copies sold, Schaum's are the most popular study guide on the planet. Mathematics students around the world turn to this clear and complete guide to general topology for its through introduction to the subject, including easy-to-follow explanations of topology of the line and plane and topological spaces. With 650 fully ...
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Topology from the Differentiable Viewpoint
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John Willard Milnor
This elegant book by distinguished mathematician John Milnor, provides a clear and succinct introduction to one of the most important subjects in modern mathematics. Beginning with basic concepts such as diffeomorphisms and smooth manifolds, he goes on to examine tangent spaces, oriented manifolds, and vector fields. Key concepts such as homotopy, ...
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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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Elements of the Topology of Plane Sets of Points
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M H A Newman
This book provides an elementary introduction to the ideas and methods of topology by the detailed study of certain topics. There are elegant but rigorous proofs of many of the basic theorems, and special attention is given to the results needed in the theory of functions.
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Catastrophe Theory
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Vladimir I Arnol'd
This well-known booklet, now in its third, expanded edition, provides an informal survey of applications of singularity theory in a wide range of areas. Although the first few chapters touch briefly (and critically) on theThom-Zeeman catastrophe theory, most of the book is concerned with more recent and less controversial aspects, covering such ...
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Fractal Geometry: Mathematical Foundations and Applications
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by
K J Falconer
Since its original publication in 1990, Kenneth Falconer's Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. It introduces the general mathematical theory and applications of fractals in a way that is accessible to students from a wide range of disciplines. This new edition has ...
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Algebraic Topology: An Introduction
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by
William S Massey
William S. Massey Professor Massey, born in Illinois in 1920, received his bachelor's degree from the University of Chicago and then served for four years in the U.S. Navy during World War II. After the War he received his Ph.D. from Princeton University and spent two additional years there as a post-doctoral research assistant. He then taught for ...
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Basic Topology
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by
M A Armstrong
In this broad introduction to topology, the author searches for topological invariants of spaces, together with techniques for calculating them. Students with knowledge of real analysis, elementary group theory, and linear algebra will quickly become familiar with a wide variety of techniques and applications involving point-set, geometric, and ...
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Algebraic topology
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Edwin Henry Spanier
Intended for use both as a text and a reference, this book is an exposition of the fundamental ideas of algebraic topology. The first third of the book covers the fundamental group, its definition and its application in the study of covering spaces. The focus then turns to homology theory, including cohomology, cup products, cohomology operations, ...
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Schaum's Easy Outline of Geometry
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by
Barnett Rich
This crash course: includes fully solved exercises for every topic; offers expert tips for mastering geometry; and, presents all you need to know to pass the course. When you don't have the time...you still need the grade! If your life is too busy to spend hours ploughing through weighty textbooks, and you need every study minute to count, this ...
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Introduction to Topology: Second Edition
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Theodore W. Gamelin, Robert Everist Greene
This text explains nontrivial applications of metric space topology to analysis. Covers metric space, point-set topology, and algebraic topology. Includes exercises, selected answers, and 51 illustrations. 1983 edition.
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The Geometry of Physics: An Introduction
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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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Fractals for the Classroom
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Heinz-Otto Peitgen
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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African Fractals: Modern Computing and Indigenous Design
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by
Ron Eglash
This is an introduction to fractal geometry, its expressions in African cultures, and an exploration of the implications of these findings for cultural theory, maths education and African development. It examines the political and social implications of the existence of African fractal geometry.
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The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots
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Colin C Adams
Over a century old, knot theory is today one of the most active areas of modern mathematics. The study of knots has led to important applications in DNA research and the synthesis of new molecules, and has had a significant impact on statistical mechanics and quantum field theory. Colin Adams's "The Knot Book" is the first book to make cutting ...
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The Colours of Infinity: The Beauty, the Power and the Sense of Fractals
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by
Nigel Lesmoir-Gordon (Editor)
The world??'s founders and leaders of Fractal Geometry describe how the science has developed in the ten years since the making of the ground-breaking TV documentary.
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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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On Knots
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by
Louis H Kauffman
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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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Fractals for the Classroom: Part Two: Complex Systems and Mandelbrot Set
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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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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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