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This study in combinatorial group theory introduces the concept of automatic groups. It contains a succinct introduction to the theory of regular languages, a discussion of related topics in combinatorial group theory, and the connections between automatic groups and geometry which motivated the development of this new theory. It is of interest to
Writing in the digital age has been as messy as the inky rags in Gutenberg’s shop or the molten lead of a Linotype machine. Matthew Kirschenbaum examines how creative authorship came to coexist with the computer revolution. Who were the early adopters, and what made others anxious? Was word processing just a better typewriter, or something more?
Research in computational group theory, an active subfield of computational algebra, has emphasised three areas: finite permutation groups, finite solvable groups, and finitely presented groups. This book deals with the third of these areas. The author emphasises the connections with fundamental algorithms from theoretical computer science, particularly the theory of automata and formal languages, computational number theory, and computational commutative algebra. The LLL lattice reduction algorithm and various algorithms for Hermite and Smith normal forms from computational number theory are used to study the abelian quotients of a finitely presented group. The work of Baumslag, Cannonito and Miller on computing nonabelian polycyclic quotients is described as a generalisation of Buchberger's Gröbner basis methods to right ideals in the integral group ring of a polycyclic group. Researchers in computational group theory, mathematicians interested in finitely presented groups and theoretical computer scientists will find this book useful.
A clear exposition, with exercises, of the basic ideas of algebraic topology. Suitable for a two-semester course at the beginning graduate level, it assumes a knowledge of point set topology and basic algebra. Although categories and functors are introduced early in the text, excessive generality is avoided, and the author explains the geometric or analytic origins of abstract concepts as they are introduced.
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Here is a clear, well-organized coverage of the most standard theorems, including isomorphism theorems, transformations and subgroups, direct sums, abelian groups, and more. This undergraduate-level text features more than 500 exercises.
A REESE’S BOOK CLUB PICK * NEW YORK TIMES BESTSELLER The refreshingly original and “startlingly hopeful” (Lisa Taddeo) debut memoir of an over-achieving young lawyer who reluctantly agrees to group therapy and gets psychologically and emotionally naked in a room of six complete strangers—and finds human connection, and herself. Christie Tate had just been named the top student in her law school class and finally had her eating disorder under control. Why then was she driving through Chicago fantasizing about her own death? Why was she envisioning putting an end to the isolation and sadness that still plagued her despite her achievements? Enter Dr. Rosen, a therapist who calmly assures her that if she joins one of his psychotherapy groups, he can transform her life. All she has to do is show up and be honest. About everything—her eating habits, childhood, sexual history, etc. Christie is skeptical, insisting that that she is defective, beyond cure. But Dr. Rosen issues a nine-word prescription that will change everything: “You don’t need a cure. You need a witness.” So begins her entry into the strange, terrifying, and ultimately life-changing world of group therapy. Christie is initially put off by Dr. Rosen’s outlandish directives, but as her defenses break down and she comes to trust Dr. Rosen and to depend on the sessions and the prescribed nightly phone calls with various group members, she begins to understand what it means to connect. “Often hilarious, and ultimately very touching” (People), Group is “a wild ride” (The Boston Globe), and with Christie as our guide, we are given a front row seat to the daring, exhilarating, painful, and hilarious journey that is group therapy—an under-explored process that breaks you down, and then reassembles you so that all the pieces finally fit.
This volume grew out of two AMS conferences held at Columbia University (New York, NY) and the Stevens Institute of Technology (Hoboken, NJ) and presents articles on a wide variety of topics in group theory. Readers will find a variety of contributions, including a collection of over 170 open problems in combinatorial group theory, three excellent survey papers (on boundaries of hyperbolic groups, on fixed points of free group automorphisms, and on groups of automorphisms of compactRiemann surfaces), and several original research papers that represent the diversity of current trends in combinatorial and geometric group theory. The book is an excellent reference source for graduate students and research mathematicians interested in various aspects of group theory.
William Thurston's work has had a profound influence on mathematics. He connected whole mathematical subjects in entirely new ways and changed the way mathematicians think about geometry, topology, foliations, group theory, dynamical systems, and the way these areas interact. His emphasis on understanding and imagination in mathematical learning and thinking are integral elements of his distinctive legacy. This four-part collection brings together in one place Thurston's major writings, many of which are appearing in publication for the first time. Volumes I–III contain commentaries by the Editors. Volume IV includes a preface by Steven P. Kerckhoff. Volume II contains William Thurston's papers on the geometry and topology of 3-manifolds, on complexity, constructions and computers, and on geometric group theory.