One of the famous 23 mathematics problems Hilbert formulated in 1900, the problem asks for a topological description of Lie groups without any direct reference to smooth structure. In notes from a graduate course he taught in 2011 with some extra material from his blog, Tao develops the machinery needed to solve Hilbert's fifth problem, and then uses it to classify approximate groups and finally to develop applications such as Gromov's celebrated theorem. The first part of the book can be used in a one-quarter or one-semester advanced graduate course. It assumes familiarity with basic graduate real analysis and linear algebra. The second part contains additional material that may be but need not be used for the course. Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)
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Terence Tao was the winner of the 2014 Breakthrough Prize in Mathematics. He is the James and Carol Collins Chair of mathematics at UCLA and the youngest person ever to be promoted to full professor at the age of 24. In 2006 Tao became the youngest ever mathematician to win the Fields Medal. His other honours include the George Polya Prize from the Society for Industrial and Applied Mathematics (2010), the Alan T Waterman Award from the National Science Foundation (2008), the SASTRA Ramanujan Prize (2006), the Clay Research Award from the Clay Mathematical Institute (2003), the Bocher Memorial Prize from the American Mathematical Society (2002) and the Salem Prize (2000).
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