the shape of space chapman hall crc pure and applied mathematics

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The Shape Of Space

Author : Jeffrey R. Weeks
ISBN : 9780824748371
Genre : Mathematics
File Size : 89. 99 MB
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Maintaining the standard of excellence set by the previous edition, this textbook covers the basic geometry of two- and three-dimensional spaces Written by a master expositor, leading researcher in the field, and MacArthur Fellow, it includes experiments to determine the true shape of the universe and contains illustrated examples and engaging exercises that teach mind-expanding ideas in an intuitive and informal way. Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behavior of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe.

The Shape Of Space

Author : Jeffrey R. Weeks
ISBN : 0824707095
Genre : Mathematics
File Size : 67. 49 MB
Format : PDF, Docs
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Maintaining the standard of excellence set by the previous edition, this textbook covers the basic geometry of two- and three-dimensional spaces Written by a master expositor, leading researcher in the field, and MacArthur Fellow, it includes experiments to determine the true shape of the universe and contains illustrated examples and engaging exercises that teach mind-expanding ideas in an intuitive and informal way. Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behavior of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe.

Fundamentals Of Pattern Recognition Second Edition

Author : Monique L. Pavel
ISBN : 0824788834
Genre : Mathematics
File Size : 29. 3 MB
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Revised, updated, and expanded throughout, this edition of Fundamentals of Pattern Recognition addresses the field of PR from a basic mathematical view-point - treating algebraic, topological, and categorical approaches of PR using concepts from homotopy, shape, and fibre spaces theories as well as computational topology.;Maintaining the features of the first edition, this resource: provides a new section on fibrewise topology that formalizes, for the first time, multicoloured, different gray level pictures and other complex signals consisting of base and value spaces and their interconnections; explores new artificial intelligence problems on the possible interplay between recursion theory and fibrewise image topology in connection with effectiveness and decidability problems; develops original techniques and results, such as the study of extremely irregular shapes by means of the mathematical theory of shape, finite topological spaces, and category theory's applications to PR; exhibits new figures of panoramic hierarchical classifications of all mathematical approaches to PR discussed; and presents five appendices that give quick overviews of dominant concepts in PR and related fields.;Containing open research and development problems to reinforce important methodologies, this second edition of Fundamentals of Pattern Recognition is a guide for applied mathematicians; electrical and electronics, systems, and computer engineers; computer scientists; and upper-level undergraduate and graduate students in applied mathematics and computer science courses in pattern recognition theory and artificial intelligence.

Knots And Surfaces

Author : David W. Farmer
ISBN : 9780821804513
Genre : Mathematics
File Size : 48. 34 MB
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In most mathematics textbooks, the most exciting part of mathematics - the process of invention and discovery - is completely hidden from the reader. The aim of ""Knots and Surfaces"" is to change all that. By means of a series of carefully selected tasks, this book leads readers to discover some real mathematics. There are no formulas to memorize; no procedures to follow. The book is a guide: its job is to start you in the right direction and to bring you back if you stray too far. Discovery is left to you. Suitable for a one-semester course at the beginning undergraduate level, there are no prerequisites for understanding the text. Any college student interested in discovering the beauty of mathematics will enjoy a course taught from this book. The book has also been used successfully with non science students who want to fulfill a science requirement. Also available from the AMS by David W. Farmer is ""Groups and Symmetry: A Guide to Discovering Mathematics"".

Intuitive Topology

Author : Viktor Vasilʹevich Prasolov
ISBN : 9780821803561
Genre : Mathematics
File Size : 23. 80 MB
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This book is an introduction to elementary topology presented in an intuitive way, emphasizing the visual aspect. Examples of nontrivial and often unexpected topological phenomena acquaint the reader with the picturesque world of knots, links, vector fields, and two-dimensional surfaces. The book begins with definitions presented in a tangible and perceptible way, on an everyday level, and progressively makes them more precise and rigorous, eventually reaching the level of fairly sophisticated proofs. This allows meaningful problems to be tackled from the outset. Another unusual trait of this book is that it deals mainly with constructions and maps, rather than with proofs that certain maps and constructions do or do not exist. The numerous illustrations are an essential feature. The book is accessible not only to undergraduates but also to high school students and will interest any reader who has some feeling for the visual elegance of geometry and topology.

Low Dimensional Geometry

Author : Francis Bonahon
ISBN : 9780821848166
Genre : Mathematics
File Size : 90. 22 MB
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The study of 3-dimensional spaces brings together elements from several areas of mathematics. The most notable are topology and geometry, but elements of number theory and analysis also make appearances. In the past 30 years, there have been striking developments in the mathematics of 3-dimensional manifolds. This book aims to introduce undergraduate students to some of these important developments. Low-Dimensional Geometry starts at a relatively elementary level, and its early chapters can be used as a brief introduction to hyperbolic geometry. However, the ultimate goal is to describe the very recently completed geometrization program for 3-dimensional manifolds. The journey to reach this goal emphasizes examples and concrete constructions as an introduction to more general statements. This includes the tessellations associated to the process of gluing together the sides of a polygon. Bending some of these tessellations provides a natural introduction to 3-dimensional hyperbolic geometry and to the theory of kleinian groups, and it eventually leads to a discussion of the geometrization theorems for knot complements and 3-dimensional manifolds. This book is illustrated with many pictures, as the author intended to share his own enthusiasm for the beauty of some of the mathematical objects involved. However, it also emphasizes mathematical rigor and, with the exception of the most recent research breakthroughs, its constructions and statements are carefully justified.

The Shape Of Inner Space

Author : Shing-Tung Yau
ISBN : 9780465022663
Genre : Science
File Size : 30. 49 MB
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String theory says we live in a ten-dimensional universe, but that only four are accessible to our everyday senses. According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds. In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe. Time and again, where Yau has gone, physics has followed. Now for the first time, readers will follow Yau’s penetrating thinking on where we’ve been, and where mathematics will take us next. A fascinating exploration of a world we are only just beginning to grasp, The Shape of Inner Space will change the way we consider the universe on both its grandest and smallest scales.

Groups And Symmetry

Author : David W. Farmer
ISBN : 9780821804506
Genre : Mathematics
File Size : 55. 43 MB
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Mathematics is discovered by looking at examples, noticing patterns, making conjectures, and testing those conjectures. Once discovered, the final results get organized and put in textbooks. The details and the excitement of the discovery are lost. This book introduces the reader to the excitement of the original discovery. By means of a wide variety of tasks, readers are led to find interesting examples, notice patterns, devise rules to explain the patterns, and discover mathematics for themselves. The subject studied here is the mathematics behind the idea of symmetry, but the methods and ideas apply to all of mathematics. The only prerequisites are enthusiasm and a knowledge of basic high-school math. The book is only a guide. It will start you off in the right direction and bring you back if you stray too far. The excitement and the discovery are left to you.

Mostly Surfaces

Author : Richard Evan Schwartz
ISBN : 9780821853689
Genre : Mathematics
File Size : 89. 57 MB
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This book presents a number of topics related to surfaces, such as Euclidean, spherical and hyperbolic geometry, the fundamental group, universal covering surfaces, Riemannian manifolds, the Gauss-Bonnet Theorem, and the Riemann mapping theorem. The main idea is to get to some interesting mathematics without too much formality. The book also includes some material only tangentially related to surfaces, such as the Cauchy Rigidity Theorem, the Dehn Dissection Theorem, and the Banach-Tarski Theorem.

The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigourous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis.


Intuitive Concepts In Elementary Topology

Author : B.H. Arnold
ISBN : 9780486275765
Genre : Mathematics
File Size : 53. 59 MB
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Classroom-tested and much-cited, this concise text is designed for undergraduates. It offers a valuable and instructive introduction to the basic concepts of topology, taking an intuitive rather than an axiomatic viewpoint. 1962 edition.

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