Measure, Topology, and Fractal Geometry
Title | Measure, Topology, and Fractal Geometry PDF eBook |
Author | Gerald A. Edgar |
Publisher | |
Total Pages | 256 |
Release | 2014-01-15 |
Genre | |
ISBN | 9781475741353 |
Measure, Topology, and Fractal Geometry
Title | Measure, Topology, and Fractal Geometry PDF eBook |
Author | Gerald Edgar |
Publisher | Springer Science & Business Media |
Total Pages | 293 |
Release | 2007-10-23 |
Genre | Mathematics |
ISBN | 0387747494 |
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
Title | Measure, Topology, and Fractal Geometry PDF eBook |
Author | Gerald A. Edgar |
Publisher | Springer Science & Business Media |
Total Pages | 252 |
Release | 2013-04-17 |
Genre | Mathematics |
ISBN | 1475741340 |
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
Measure, Topology, and Fractal Geometry
Title | Measure, Topology, and Fractal Geometry PDF eBook |
Author | Gerald Edgar |
Publisher | Springer |
Total Pages | 0 |
Release | 2008-11-01 |
Genre | Mathematics |
ISBN | 9780387521008 |
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.
The Geometry of Fractal Sets
Title | The Geometry of Fractal Sets PDF eBook |
Author | K. J. Falconer |
Publisher | Cambridge University Press |
Total Pages | 184 |
Release | 1985 |
Genre | Mathematics |
ISBN | 9780521337052 |
A mathematical study of the geometrical aspects of sets of both integral and fractional Hausdorff dimension. Considers questions of local density, the existence of tangents of such sets as well as the dimensional properties of their projections in various directions.
Integral, Probability, and Fractal Measures
Title | Integral, Probability, and Fractal Measures PDF eBook |
Author | Gerald A. Edgar |
Publisher | Springer Science & Business Media |
Total Pages | 292 |
Release | 2013-03-14 |
Genre | Mathematics |
ISBN | 1475729588 |
Providing the mathematical background required for the study of fractal topics, this book deals with integration in the modern sense, together with mathematical probability. The emphasis is on the particular results that aid the discussion of fractals, and follows Edgars Measure, Topology, and Fractal Geometry. With exercises throughout, this is and ideal text for beginning graduate students both in the classroom and for self-study.
Fractals in Probability and Analysis
Title | Fractals in Probability and Analysis PDF eBook |
Author | Christopher J. Bishop |
Publisher | Cambridge University Press |
Total Pages | 415 |
Release | 2017 |
Genre | Mathematics |
ISBN | 1107134110 |
A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.