In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K-Theory, differential geometry, non-commutative geometry and spectral theory. The book, written in an accessible manner, presents a comprehensive introduction to this area of research, as well as its most recent results and developments.

In this book, children learn the story of Pocahontas. Famous for helping maintain peace between the English colonists and Native Americans, this brave Indian woman befriended the settlers at Jamestown, saving the life of their leader, Captain John Smith, whom she later married.

This book introduces the reader to the most important concepts and problems in the field of l2-invariants. After some foundational material on group von Neumann algebras, l2-Betti numbers are defined and their use is illustrated by several examples. The text continues with Atiyah's question on possible values of l2-Betti numbers and the relation to Kaplansky's zero divisor conjecture. The general definition of l2-Betti numbers allows for applications in group theory. A whole chapter is dedicated to Lück's approximation theorem and its generalizations. The final chapter deals with l2-torsion, twisted variants and the conjectures relating them to torsion growth in homology. The text provides a self-contained treatment that constructs the required specialized concepts from scratch. It comes with numerous exercises and examples, so that both graduate students and researchers will find it useful for self-study or as a basis for an advanced lecture course.

One L, Scott Turow's journal of his first year at law school and a best-seller when it was first published in 1977, has gone on to become a virtual bible for prospective law students. Not only does it introduce with remarkable clarity the ideas and issues that are the stuff of legal education; it brings alive the anxiety and competiveness--with others and, even more, with oneself--that set the tone in this crucible of character building. Each September, a new crop of students enter Harvard Law School to begin an intense, often grueling, sometimes harrowing year of introduction to the law. Turow's group of One Ls are fresh, bright, ambitious, and more than a little daunting. Even more impressive are the faculty. Will the One Ls survive? Will they excel? Will they make the Law Review, the outward and visible sign of success in this ultra-conservative microcosm? With remarkable insight into both his fellows and himself, Turow leads us through the ups and downs, the small triumphs and tragedies of the year, in an absorbing and thought-provoking narrative that teaches the reader not only about law school and the law but about the human beings who make them what they are. In the new afterword for this edition of One L, the author looks back on law school from the perspective of ten years' work as a lawyer and offers some suggestions for reforming legal education.

This theory-to-practice text presents pedagogical approaches to teaching L2 composition in the framework of current theoretical perspectives on L2 writing processes, practices, and writers and provides an array of hands-on, practical examples, materials, and tasks.

Effective Curriculum for Teaching L2 Writing sets out a clear big picture for curricular thinking about L2 writing pedagogy and offers a step-by-step guide to curriculum design with practical examples and illustrations. Its main purpose is to help pre-service and practicing teachers design courses for teaching academic writing and to do this as efficiently and effectively as possible. Bringing together the what and the how-to with research-based principles, what sets this book apart is its overarching focus on language pedagogy and language building. Part 1 examines curricular foundations in general and focuses on what is socially valued in L2 writing and pedagogy at school and at the college and university level. Part 2 is concerned with the nitty-gritty̶—the daily realities of curricular design and classroom instruction. Part 3 takes a close look at the key pedagogical ingredients of teaching academic L2 writing: vocabulary and collocations, grammar for academic writing, and down-to-earth techniques for helping L2 writers to organize discourse and ideas. The Appendix provides an extensive checklist for developing curricula for a course or several courses in language teaching.

The noncommutative versions of fundamental classical results on the almost sure convergence in L2-spaces are discussed: individual ergodic theorems, strong laws of large numbers, theorems on convergence of orthogonal series, of martingales of powers of contractions etc. The proofs introduce new techniques in von Neumann algebras. The reader is assumed to master the fundamentals of functional analysis and probability. The book is written mainly for mathematicians and physicists familiar with probability theory and interested in applications of operator algebras to quantum statistical mechanics.