LEADER 03426nam 22005055 450 001 9910254287603321 005 20200706163204.0 010 $a0-8176-4629-9 024 7 $a10.1007/978-0-8176-4629-5 035 $a(CKB)3710000001079869 035 $a(DE-He213)978-0-8176-4629-5 035 $a(MiAaPQ)EBC6312969 035 $a(MiAaPQ)EBC5575080 035 $a(Au-PeEL)EBL5575080 035 $a(OCoLC)1066188254 035 $a(PPN)19886616X 035 $a(EXLCZ)993710000001079869 100 $a20170220d2017 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMathematical Bridges /$fby Titu Andreescu, Cristinel Mortici, Marian Tetiva 205 $a1st ed. 2017. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Birkhäuser,$d2017. 215 $a1 online resource (VIII, 309 p. 3 illus.) 311 $a0-8176-4394-X 327 $aMathematical (and Other) Bridges -- Cardinality -- Polynomial Functions Involving Determinants -- Some Applications of the Hamilton-Cayley Theorem -- A Decomposition Theorem Related to the Rank of a Matrix -- Equivalence Relations on Groups and Factor Groups -- Density -- The Nested Intervals Theorem -- The Splitting Method and Double Sequences -- The Number e -- The Intermediate Value Theorem -- The Extreme Value Theorem -- Uniform Continuity -- Derivatives and Functions' Variation -- Riemann and Darboux Sums -- Antiderivatives. 330 $aBuilding bridges between classical results and contemporary nonstandard problems, Mathematical Bridges embraces important topics in analysis and algebra from a problem-solving perspective. Blending old and new techniques, tactics and strategies used in solving challenging mathematical problems, readers will discover numerous genuine mathematical gems throughout that will heighten their appreciation of the inherent beauty of mathematics. Most of the problems are original to the authors and are intertwined in a well-motivated exposition driven by representative examples. The book is structured to assist the reader in formulating and proving conjectures, as well as devising solutions to important mathematical problems by making connections between various concepts and ideas from different areas of mathematics. Instructors and educators teaching problem-solving courses or organizing mathematics clubs, as well as motivated mathematics students from high school juniors to college seniors, will find Mathematical Bridges a useful resource in calculus, linear and abstract algebra, analysis and differential equations. Students desiring to hone and develop their mathematical skills or with an interest in mathematics competitions must have this book in their personal libraries. 606 $aAlgebra 606 $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000 615 0$aAlgebra. 615 14$aAlgebra. 676 $a510 700 $aAndreescu$b Titu$4aut$4http://id.loc.gov/vocabulary/relators/aut$0285837 702 $aMortici$b Cristinel$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aTetiva$b Marian$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254287603321 996 $aMathematical Bridges$92283991 997 $aUNINA