000 04122nam a22005055i 4500
001 978-3-0346-0050-7
003 DE-He213
005 20181204133148.0
007 cr nn 008mamaa
008 100301s2009 sz | s |||| 0|eng d
020 _a9783034600507
_9978-3-0346-0050-7
024 7 _a10.1007/978-3-0346-0050-7
_2doi
040 _aISI Library, Kolkata
050 4 _aQA150-272
072 7 _aPBF
_2bicssc
072 7 _aMAT002000
_2bisacsh
072 7 _aPBF
_2thema
082 0 4 _a512
_223
100 1 _aManfrino, Radmila Bulajich.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aInequalities
_h[electronic resource] :
_bA Mathematical Olympiad Approach /
_cby Radmila Bulajich Manfrino, José Antonio Gómez Ortega, Rogelio Valdez Delgado.
264 1 _aBasel :
_bBirkhäuser Basel,
_c2009.
300 _a220 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aIntroduction -- 1 Numerical Inequalities -- 1.1 Order in the real numbers -- 1.2 The quadratic function ax2 + 2bx + c -- 1.3 A fundamental inequality, arithmetic mean-geometric mean -- 1.4. A wonderful inequality: the rearrangement inequality -- 1.5 Convex functions -- 1.6 A helpful inequality -- 1.7 The substitutions strategy -- 1.8 Muirhead's theorem -- 2 Geometric Inequalities -- 2.1 Two basic inequalities -- 2.2 Inequalities between the sides of a triangle -- 2.3 The use of inequalities in the geometry of the triangle -- 2.4 Euler's inequality and some applications -- 2.5 Symmetric functions of a, b and c -- 2.6 Inequalities with areas and perimeters. 2.7 Erdös-Mordell theorem -- 2.8 Optimization problems -- 3 Recent Inequality Problems -- 4 Solutions to Exercises and Problems -- Bibliography -- Index.
520 _aThis book is intended for the Mathematical Olympiad students who wish to prepare for the study of inequalities, a topic now of frequent use at various levels of mathematical competitions. In this volume we present both classic inequalities and the more useful inequalities for confronting and solving optimization problems. An important part of this book deals with geometric inequalities and this fact makes a big difference with respect to most of the books that deal with this topic in the mathematical olympiad. The book has been organized in four chapters which have each of them a different character. Chapter 1 is dedicated to present basic inequalities. Most of them are numerical inequalities generally lacking any geometric meaning. However, where it is possible to provide a geometric interpretation, we include it as we go along. We emphasize the importance of some of these inequalities, such as the inequality between the arithmetic mean and the geometric mean, the Cauchy-Schwarz inequality, the rearrangementinequality, the Jensen inequality, the Muirhead theorem, among others. For all these, besides giving the proof, we present several examples that show how to use them in mathematical olympiad problems. We also emphasize how the substitution strategy is used to deduce several inequalities.
650 0 _aAlgebra.
650 0 _aMathematics.
650 0 _aGlobal analysis (Mathematics).
650 1 4 _aAlgebra.
_0http://scigraph.springernature.com/things/product-market-codes/M11000
650 2 4 _aMathematics, general.
_0http://scigraph.springernature.com/things/product-market-codes/M00009
650 2 4 _aAnalysis.
_0http://scigraph.springernature.com/things/product-market-codes/M12007
700 1 _aGómez Ortega, José Antonio.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aDelgado, Rogelio Valdez.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783034600514
776 0 8 _iPrinted edition:
_z9783034600491
856 4 0 _uhttps://doi.org/10.1007/978-3-0346-0050-7
912 _aZDB-2-SMA
942 _cEB
950 _aMathematics and Statistics (Springer-11649)
999 _c426286
_d426286