The winding number is one of the most basic invariants in topology. It measures the number of times a moving point P goes around a fixed point Q, provided that P travels on a path that never goes through Q and that the final position of P is the same as its starting position. This simple idea has far-reaching applications. The reader of this book will learn how the winding number can help us show that every polynomial equation has a root (the fundamental theorem of algebra),guarantee a fair division of three objects in space by a single planar cut (the ham sandwich theorem),explain why every simple closed curve has an inside and an outside (the Jordan curve theorem),relate calculus to curvature and the singularities of vector fields (the Hopf index theorem),allow one to subtract infinity from infinity and get a finite answer (Toeplitz operators),generalize to give a fundamental and beautiful insight into the topology of matrix groups (the Bott periodicity theorem). All these subjects and more are developed starting only from mathematics that is common in final-year undergraduate courses.

Substantially expanded and updated, the new edition of this classic provides unrivaled coverage of the fundamentals of power electronics. Unique in its breadth and depth, this is the definitive guide to power electronics for senior undergraduate and graduate students, and practicing electrical engineers.

This is a compact and user-friendly Vietnamese dictionary. The Tuttle Compact Vietnamese Dictionary is the most up-to-date and complete Vietnamese dictionary yet published. An essential tool to learn Vietnamese, it is written for English speakers and other non-native users who need to look up Vietnamese terms, and can also be used by Vietnamese speakers who are learning English. This dictionary has 25,000 entries covering all contemporary terms likely to be used in educational or business settings. The layout is user-friendly and attractive. Headwords are displayed in blue--this helps the reader to locate words quickly. Information on parts of speech, idiomatic expressions and sample sentences showing the use of the words in context are given for each entry. English pronunciations are given in the English to Vietnamese language section. A comprehensive pronunciation guide and detailed notes on Japanese grammar are also included. Completely comprehensive and up-to-date with over 25,000 entries. Contains English-Vietnamese and Vietnamese-English Clear, user--friendly layout with idioms, and sample sentences given. The ideal dictionary for students, teachers and business people.

A state-of-the-art survey that reports on the progress made in selected areas of this important and growing field, aiding the analysis of existing networks and the design of new and more efficient algorithms for solving various problems on these networks.