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101 0 $aeng
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200 13$aAn Excursion through Elementary Mathematics, Volume I $eReal Numbers and Functions /$fby Antonio Caminha Muniz Neto
205   $a1st ed. 2017.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017.
215   $a1 online resource (XIII, 652 p. 73 illus.) 
225 1 $aProblem Books in Mathematics,$x0941-3502
311   $a3-319-53870-5 
320   $aIncludes bibliographical references and index.
327   $aChapter 1 The Set of Real Numbers -- Chapter 2 Algebraic Identities, Equations and Systems -- Chapter 3 Elementary Sequences -- Chapter 4 Induction and the Binomial Formula -- Chapter 5 Elementary Inequalities -- Chapter 6 The Concept of Function -- Chapter 7 More on Real Numbers -- Chapter 8 Continuous Functions -- Chapter 9 Limits and Derivatives -- Chapter 10 Riemann?s Integral -- Chapter 11 Series of Functions -- Bibliography -- Appendix A Glossary -- Appendix B Hints and Solutions.
330   $aThis book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester undergraduate course. This first volume covers Real Numbers, Functions, Real Analysis, Systems of Equations, Limits and Derivatives, and much more. As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level. The book also explores some of the hardest problems presented at National and International Mathematics Olympiads, as well as many essential theorems related to the content. An extensive Appendix offering hints on or full solutions for all difficult problems rounds out the book.
410  0$aProblem Books in Mathematics,$x0941-3502
606   $aFunctions of real variables
606   $aAlgebra
606   $aMatrix theory
606   $aReal Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12171
606   $aGeneral Algebraic Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/M1106X
606   $aLinear and Multilinear Algebras, Matrix Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11094
615  0$aFunctions of real variables.
615  0$aAlgebra.
615  0$aMatrix theory.
615 14$aReal Functions.
615 24$aGeneral Algebraic Systems.
615 24$aLinear and Multilinear Algebras, Matrix Theory.
676   $a512.786
700   $aCaminha Muniz Neto$b Antonio$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767139
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910254309103321
996   $aAn Excursion through Elementary Mathematics, Volume I$92222456
997   $aUNINA