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Popular Mechanics
Popular Mechanics inspires, instructs and influences readers to help them master the modern world. Whether it’s practical DIY home-improvement tips, gadgets and digital technology, information on the newest cars or the latest breakthroughs in science -- PM is the ultimate guide to our high-tech lifestyle.
Flying Magazine
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Dynamical Systems
Several distinctive aspects make Dynamical Systems unique, including: treating the subject from a mathematical perspective with the proofs of most of the results included providing a careful review of background materials introducing ideas through examples and at a level accessible to a beginning graduate student
Flying Magazine
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A First Course in Discrete Dynamical Systems
Given the ease with which computers can do iteration it is now possible for almost anyone to generate beautiful images whose roots lie in discrete dynamical systems. Images of Mandelbrot and Julia sets abound in publications both mathematical and not. The mathematics behind the pictures are beautiful in their own right and are the subject of this text. Mathematica programs that illustrate the dynamics are included in an appendix.
FCC Record
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$G$-Categories
A [italic]G-category is a category on which a group [italic]G acts. This work studies the 2-category [italic]G-cat of [italic]G-categories, [italic]G-functors (functors which commute with the action of [italic]G) and [italic]G-natural transformations (natural transformations which commute with the [italic]G-action). There is a particular emphasis on the relationship between a [italic]G-category and its stable subcategory, the largest sub-[italic]G-category on which [italic]G operates trivially. Also contained here are some very general applications of the theory to various additive [italic]G-categories and to [italic]G-topoi.
Semistability of Amalgamated Products and HNN-Extensions
In this work, the authors show that amalgamated products and HNN-extensions of finitely presented semistable at infinity groups are also semistable at infinity. A major step toward determining whether all finitely presented groups are semistable at infinity, this result easily generalizes to finite graphs of groups. The theory of group actions on trees and techniques derived from the proof of Dunwoody's accessibility theorem are key ingredients in this work.
Phantom Homology
This book uses a powerful new technique, tight closure, to provide insight into many different problems that were previously not recognized as related. The authors develop the notion of weakly Cohen-Macaulay rings or modules and prove some very general acyclicity theorems. These theorems are applied to the new theory of phantom homology, which uses tight closure techniques to show that certain elements in the homology of complexes must vanish when mapped to well-behaved rings. These ideas are used to strengthen various local homological conjectures. Initially, the authors develop the theory in positive characteristic, but it can be extended to characteristic 0 by the method of reduction to characteristic $p$. The book would be suitable for use in an advanced graduate course in commutative algebra.
