The Shape of Space

Author: Jeffrey R. Weeks
Publisher: Marcel Dekker
ISBN: 082477437X
Release Date: 1985-01-01
Genre: Surfaces

The Shape of Space brings topology to the general reader by showing how to visualize manifolds directly...complements existing textbooks, which often deal only in abstractions, by offering a wealth of concrete examples...includes the first elementary exposition of William P. Thurston's revolutionary discoveries...applies topology to cosmology...gives the first simple pictorial exposition of the Gauss-Bonnet formula...builds intuition with more than 140 hands-on exercises, all with complete solutions...and offers over 170 illustrations. An annotated bibliography lists useful references for further study on specific topics.

The Shape of Space

Author: Jeffrey R. Weeks
Publisher: CRC Press
ISBN: 9780824748371
Release Date: 2001-12-12
Genre: Mathematics

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.

God and the Universe

Author: Arthur Gibson
Publisher: Routledge
ISBN: 9781136365720
Release Date: 2013-10-11
Genre: Religion

Ambitious, controversial and absorbing, God and the Universe tackles the highly-charged issue of God's relevance in the light of new scientific thinking on cosmology. Engaging with poststructuralism, ethics, mathematics, and philosophy through the ages, this persuasively argued book reinvigorates religious debate for the new millennium.

Hyperbolic Manifolds

Author: Albert Marden
Publisher: Cambridge University Press
ISBN: 9781316432525
Release Date: 2016-02-01
Genre: Mathematics

Over the past three decades there has been a total revolution in the classic branch of mathematics called 3-dimensional topology, namely the discovery that most solid 3-dimensional shapes are hyperbolic 3-manifolds. This book introduces and explains hyperbolic geometry and hyperbolic 3- and 2-dimensional manifolds in the first two chapters and then goes on to develop the subject. The author discusses the profound discoveries of the astonishing features of these 3-manifolds, helping the reader to understand them without going into long, detailed formal proofs. The book is heavily illustrated with pictures, mostly in color, that help explain the manifold properties described in the text. Each chapter ends with a set of exercises and explorations that both challenge the reader to prove assertions made in the text, and suggest further topics to explore that bring additional insight. There is an extensive index and bibliography.

Proceedings

Author: Patrick J. Bresnahan
Publisher: University of South Carolina
ISBN: 0963353209
Release Date: 1992
Genre: Cartography


So Inclined

Author: Nina Marlane Thyrum Joblon
Publisher:
ISBN: UCAL:C3403956
Release Date: 1997
Genre:


Liebe und Mathematik

Author: Edward Frenkel
Publisher: Springer-Verlag
ISBN: 9783662434215
Release Date: 2014-11-17
Genre: Mathematics


Lehrbuch der Topologie

Author: Herbert Seifert
Publisher: University of Pennsylvania Press
ISBN: 0821835955
Release Date: 2004-01-20
Genre: Mathematics

The 1930s were important years in the development of modern topology, pushed forward by the appearance of a few pivotal books, of which this is one. The focus is on combinatorial and algebraic topology, with as much point-set topology as needed for the main topics. One sees from the modern point of view that the authors are working in a category of spaces that includes locally finite simplicial complexes. (Their definition of manifold is more properly known today as a ""triangulizable homology manifold"".)Amazingly, they manage to accomplish a lot without the convenient tools of homological algebra, such as exact sequences and commutative diagrams, that were developed later. The main topics covered are: simplicial homology (coefficients in $\mathbb{Z}$ or $\mathbb{Z}_2$), local homology, surface topology, the fundamental group and covering spaces, three-manifolds, Poincare duality, and the Lefschetz fixed point theorem. Few prerequisites are necessary. A final section reviews the lemmas and theorems from group theory that are needed in the text. As stated in the introduction to the important book by Alexandroff and Hopf (which appeared a year after ""Seifert and Threlfall""): 'Its lively and instructive presentation makes this book particularly suitable as an introduction or as a textbook.'