02901nam a22004815i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001200172050001000184072001600194072002300210072002300233082001500256082001600271100003000287245006600317264004600383300003300429336002600462337002600488338003600514347002400550490005100574505023000625520115500855650001702010650002402027650001602051650001702067650003602084710003402120773002002154776003602174830005102210856004802261912001402309999001902323952007702342978-0-387-78215-7DE-He21320180115171423.0cr nn 008mamaa100301s2008 xxu| s |||| 0|eng d a97803877821579978-0-387-78215-77 a10.1007/978-0-387-78214-02doi 4aQA252.3 4aQA387 7aPBG2bicssc 7aMAT0140002bisacsh 7aMAT0380002bisacsh04a512.5522304a512.4822231 aStillwell, John.eauthor.10aNaive Lie Theoryh[electronic resource] /cby John Stillwell. 1aNew York, NY :bSpringer New York,c2008. aXV, 217 p.bonline resource. atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda1 aUndergraduate Texts in Mathematics,x0172-60560 aGeometry of complex numbers and quaternions -- Groups -- Generalized rotation groups -- The exponential map -- The tangent space -- Structure of Lie algebras -- The matrix logarithm -- Topology -- Simply connected Lie groups. aIn this new textbook, acclaimed author John Stillwell presents a lucid introduction to Lie theory suitable for junior and senior level undergraduates. In order to achieve this, he focuses on the so-called "classical groups'' that capture the symmetries of real, complex, and quaternion spaces. These symmetry groups may be represented by matrices, which allows them to be studied by elementary methods from calculus and linear algebra. This naive approach to Lie theory is originally due to von Neumann, and it is now possible to streamline it by using standard results of undergraduate mathematics. To compensate for the limitations of the naive approach, end of chapter discussions introduce important results beyond those proved in the book, as part of an informal sketch of Lie theory and its history. John Stillwell is Professor of Mathematics at the University of San Francisco. He is the author of several highly regarded books published by Springer, including The Four Pillars of Geometry (2005), Elements of Number Theory (2003), Mathematics and Its History (Second Edition, 2002), Numbers and Geometry (1998) and Elements of Algebra (1994). 0aMathematics. 0aTopological groups. 0aLie groups.14aMathematics.24aTopological Groups, Lie Groups.2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z9780387782140 0aUndergraduate Texts in Mathematics,x0172-605640uhttp://dx.doi.org/10.1007/978-0-387-78214-0 aZDB-2-SMA c369747d369747 001040708EBookaelibbelibd2018-01-15r2018-01-15w2018-01-15yEBOOK