We strive to deliver the best value to our customers and ensure complete satisfaction for all our textbook rentals.
You can return your online books for any reason within our refund period – no questions asked.
Every order is available for express shipping, and return shipping is always free.
You'll be happy with the quality of your books (or we'll ship you another one on our dime).
You can extend your rental up to 14 days – at the same cheap daily rental rate.
If you decide to keep the book it will never cost more than the purchase price.
As always, you have access to over 5 million titles. Plus, you can choose from 5 rental periods, so you only pay for what you’ll use. And if you ever run into trouble, our top-notch U.S. based Customer Service team is ready to help by email, chat or phone.
Supplemental materials are not guaranteed for used textbooks or rentals (access codes, DVDs, workbooks).
Topological Crystallography: With a View Towards Discrete Geometric Analysis (Surveys and Tutorials in the Applied Mathematical Sciences)
Geometry in ancient Greece is said to have originated in the curiosity of mathematicians about the shapes of crystals, with that curiosity culminating in the classification of regular convex polyhedra addressed in the final volume of Euclid’s Elements. Since then, geometry has taken its own path and the study of crystals has not been a central theme in...
Geometry in ancient Greece is said to have originated in the curiosity of mathematicians about the shapes of crystals, with that curiosity culminating in the classification of regular convex polyhedra addressed in the final volume of Euclid’s Elements. Since then, geometry has taken its own path and the study of crystals has not been a central theme in mathematics, with the exception of Kepler’s work on snowflakes. Only in the nineteenth century did mathematics begin to play a role in crystallography as group theory came to be applied to the morphology of crystals. This monograph follows the Greek tradition in seeking beautiful shapes such as regular convex polyhedra. The primary aim is to convey to the reader how algebraic topology is effectively used to explore the rich world of crystal structures. Graph theory, homology theory, and the theory of covering maps are employed to introduce the notion of the topological crystal which retains, in the abstract, all the information on the connectivity of atoms in the crystal. For that reason the title Topological Crystallography has been chosen.Topological crystals can be described as “living in the logical world, not in space,” leading to the question of how to place or realize them “canonically” in space. Proposed here is the notion of standard realizations of topological crystals in space, including as typical examples the crystal structures of diamond and lonsdaleite. A mathematical view of the standard realizations is also provided by relating them to asymptotic behaviors of random walks and harmonic maps. Furthermore, it can be seen that a discrete analogue of algebraic geometry is linked to the standard realizations.Applications of the discussions in this volume include not only a systematic enumeration of crystal structures, an area of considerable scientific interest for many years, but also the architectural design of lightweight rigid structures. The reader therefore can see the agreement of theory and practice.
WHAT'S BONUS TIME?
Normally, new semester rental orders are exactly 125 days.
With “Bonus Time” you can order early and get a FREE extension until 12/19*.
It’s our little way of rewarding you early renters for planning ahead.
But do hurry. The “Bonus Time” offer runs out on 8/8 (11PM PST).
* It can take up to 24 hours for the extension to appear in your account after you receive your textbooks.
Since launching the first textbook rental site in 2006, BookRenter has never wavered from our mission to make education more affordable for all students. Every day, we focus on delivering students the best prices, the most flexible options, and the best service on earth. On March 13, 2012 BookRenter.com, Inc. formally changed its name to Rafter, Inc. We are still the same company and the same people, only our corporate name has changed.