# measure topology and fractal geometry undergraduate texts in mathematics

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## Measure Topology And Fractal Geometry

**Author :**Gerald Edgar

**ISBN :**9780387747491

**Genre :**Mathematics

**File Size :**47. 96 MB

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Based on a course given to talented high-school students at Ohio University in 1988, this book is essentially an advanced undergraduate textbook about the mathematics of fractal geometry. It nicely bridges the gap between traditional books on topology/analysis and more specialized treatises on fractal geometry. The book treats such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology. It takes into account developments in the subject matter since 1990. Sections are clear and focused. The book contains plenty of examples, exercises, and good illustrations of fractals, including 16 color plates.

## Measure Topology And Fractal Geometry

**Author :**Gerald A. Edgar

**ISBN :**9781475741346

**Genre :**Mathematics

**File Size :**53. 69 MB

**Format :**PDF, ePub

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From the reviews: "In the world of mathematics, the 1980's might well be described as the "decade of the fractal". Starting with Benoit Mandelbrot's remarkable text The Fractal Geometry of Nature, there has been a deluge of books, articles and television programmes about the beautiful mathematical objects, drawn by computers using recursive or iterative algorithms, which Mandelbrot christened fractals. Gerald Edgar's book is a significant addition to this deluge. Based on a course given to talented high- school students at Ohio University in 1988, it is, in fact, an advanced undergraduate textbook about the mathematics of fractal geometry, treating such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology. However, the book also contains many good illustrations of fractals (including 16 color plates), together with Logo programs which were used to generate them. ... Here then, at last, is an answer to the question on the lips of so many: 'What exactly is a fractal?' I do not expect many of this book's readers to achieve a mature understanding of this answer to the question, but anyone interested in finding out about the mathematics of fractal geometry could not choose a better place to start looking." #Mathematics Teaching#1

## Fractal Geometry And Stochastics Ii

**Author :**Christoph Bandt

**ISBN :**9783034883801

**Genre :**Mathematics

**File Size :**28. 3 MB

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A collection of contributions by outstanding mathematicians, highlighting the principal directions of research on the combination of fractal geometry and stochastic methods. Clear expositions introduce the most recent results and problems on these subjects and give an overview of their historical development.

## A Guide To The Classification Theorem For Compact Surfaces

**Author :**Jean Gallier

**ISBN :**9783642343643

**Genre :**Mathematics

**File Size :**76. 37 MB

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This welcome boon for students of algebraic topology cuts a much-needed central path between other texts whose treatment of the classification theorem for compact surfaces is either too formalized and complex for those without detailed background knowledge, or too informal to afford students a comprehensive insight into the subject. Its dedicated, student-centred approach details a near-complete proof of this theorem, widely admired for its efficacy and formal beauty. The authors present the technical tools needed to deploy the method effectively as well as demonstrating their use in a clearly structured, worked example. Ideal for students whose mastery of algebraic topology may be a work-in-progress, the text introduces key notions such as fundamental groups, homology groups, and the Euler-Poincaré characteristic. These prerequisites are the subject of detailed appendices that enable focused, discrete learning where it is required, without interrupting the carefully planned structure of the core exposition. Gently guiding readers through the principles, theory, and applications of the classification theorem, the authors aim to foster genuine confidence in its use and in so doing encourage readers to move on to a deeper exploration of the versatile and valuable techniques available in algebraic topology.

## Calculus Of Several Variables

**Author :**Serge Lang

**ISBN :**9781461210689

**Genre :**Mathematics

**File Size :**77. 19 MB

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This new, revised edition covers all of the basic topics in calculus of several variables, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green’s theorem, multiple integrals, surface integrals, Stokes’ theorem, and the inverse mapping theorem and its consequences. It includes many completely worked-out problems.

## Fractal Geometry And Stochastics

**Author :**Christoph Bandt

**ISBN :**UOM:39015049093290

**Genre :**Fractals

**File Size :**73. 8 MB

**Format :**PDF, Kindle

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## Bulletin Of The American Mathematical Society

**Author :**

**ISBN :**UOM:49015003188621

**Genre :**Mathematics

**File Size :**80. 5 MB

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## Bulletin New Series Of The American Mathematical Society

**Author :**

**ISBN :**UOM:39015053360742

**Genre :**Mathematics

**File Size :**67. 62 MB

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## Journal Of The Mathematical Society Of Japan

**Author :**

**ISBN :**UOM:39015038969617

**Genre :**Mathematics

**File Size :**64. 63 MB

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**Download :**581

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## Computing The Continuous Discretely

**Author :**Matthias Beck

**ISBN :**9780387461120

**Genre :**Mathematics

**File Size :**20. 16 MB

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This textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. The authors have weaved a unifying thread through basic yet deep ideas in discrete geometry, combinatorics, and number theory. We encounter here a friendly invitation to the field of "counting integer points in polytopes", and its various connections to elementary finite Fourier analysis, generating functions, the Frobenius coin-exchange problem, solid angles, magic squares, Dedekind sums, computational geometry, and more. With 250 exercises and open problems, the reader feels like an active participant.