000 03378nam a22004575i 4500
001 978-0-8176-8406-8
003 DE-He213
005 20140220082759.0
007 cr nn 008mamaa
008 130107s2013 xxu| s |||| 0|eng d
020 _a9780817684068
_9978-0-8176-8406-8
024 7 _a10.1007/978-0-8176-8406-8
_2doi
050 4 _aQA150-272
072 7 _aPBF
_2bicssc
072 7 _aMAT002000
_2bisacsh
082 0 4 _a512
_223
100 1 _aRoytvarf, Alexander A.
_eauthor.
245 1 0 _aThinking in Problems
_h[electronic resource] :
_bHow Mathematicians Find Creative Solutions /
_cby Alexander A. Roytvarf.
264 1 _aBoston :
_bBirkhäuser Boston :
_bImprint: Birkhäuser,
_c2013.
300 _aXXXVII, 405 p. 14 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aPreface -- Using the Stars on Problems -- Understanding the Advanced Skill Requirements -- Acknowledgements -- Jacobi Identities and Related Combinatorial Formulas -- A Property of Recursive Sequences -- A Combinatorial Algorithm in Multiexponential Analysis -- A Frequently Encountered Determinant.- A Dynamical System with a Strange Attractor -- Polar and Singular Value Decomposition Theorems -- 2x2 Matrices Which Are Roots of Unity -- A Property of Orthogonal Matrices -- Convexity and Related Classical Inequalities -- One-Parameter Groups of Linear Transformations.- Some Problems in Combinatorics and Analysis that can be Explored using Generating Functions -- Least Squares and Chebyshev Systems -- References -- Index of Terms.
520 _aThis concise, self-contained textbook gives an in-depth look at problem-solving from a mathematician’s point-of-view. Each chapter builds off the previous one, while introducing a variety of methods that could be used when approaching any given problem. Creative thinking is the key to solving mathematical problems, and this book outlines the tools necessary to improve the reader’s technique. The text is divided into twelve chapters, each providing corresponding hints, explanations, and finalization of solutions for the problems in the given chapter. For the reader’s convenience, each exercise is marked with the required background level. This book implements a variety of strategies that can be used to solve mathematical problems in fields such as analysis, calculus, linear and multilinear algebra and combinatorics. It includes applications to mathematical physics, geometry, and other branches of mathematics. Also provided within the text are real-life problems in engineering and technology. Thinking in Problems is intended for advanced undergraduate and graduate students in the classroom or as a self-study guide. Prerequisites include linear algebra and analysis.
650 0 _aMathematics.
650 0 _aAlgebra.
650 0 _aGlobal analysis (Mathematics).
650 0 _aCombinatorics.
650 1 4 _aMathematics.
650 2 4 _aAlgebra.
650 2 4 _aAnalysis.
650 2 4 _aCombinatorics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780817684051
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-8176-8406-8
912 _aZDB-2-SMA
999 _c94224
_d94224