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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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General Topology
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by
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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The Poincare Conjecture: In Search of the Shape of the Universe
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by
Donal O'Shea
In telling this vibrant story, O'Shea makes accessible to general readers for the first time the meaning of the conjecture, and brings alive the field of mathematics and the achievements of generations of mathematicians.
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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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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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A Topological Picturebook
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by
George K Francis
This work covers from Bravo to Springer for reissuing this unique and beautiful book! It not only reminds the older generation of the pleasures of doing mathematics by hand, but also shows the new generation what "hands on" really means.
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Fractal Geometry: Mathematical Foundations and Applications
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by
Kenneth 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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Introducing Fractal Geometry
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by
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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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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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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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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Introduction to Smooth Manifolds
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by
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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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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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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Differential Equations: Geometric Theory
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by
Solomon Lefschetz
Geared toward upper-level undergraduates and graduate students, this text investigates nonlinear differential equations of the second order and includes an extensive overview of the classical literature. 1957 edition.
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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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Elements of the Topology of Plane Sets of Points
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by
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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Geometry and Topology
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by
Miles Reid, Balazs Szendroi
Geometry provides a whole range of views on the universe, serving as the inspiration, technical toolkit and ultimate goal for many branches of mathematics and physics. This book introduces the ideas of geometry, and includes a generous supply of simple explanations and examples. The treatment emphasises coordinate systems and the coordinate ...
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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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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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Mathematical Methods: For Students of Physics and Related Fields
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by
Sadri Hassani
Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important ...
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