LEADER 04054nam  22005535  450 
001 9910300105403321
005 20200706205156.0
010   $a3-319-77977-X
024 7 $a10.1007/978-3-319-77977-5
035   $a(CKB)4100000003359569
035   $a(DE-He213)978-3-319-77977-5
035   $a(MiAaPQ)EBC5577942
035   $a(PPN)226696022
035   $a(EXLCZ)994100000003359569
100   $a20180417d2018      u|         0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 13$aAn Excursion through Elementary Mathematics, Volume III $eDiscrete Mathematics and Polynomial Algebra /$fby Antonio Caminha Muniz Neto
205   $a1st ed. 2018.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018.
215   $a1 online resource (XII, 648 p. 24 illus.) 
225 1 $aProblem Books in Mathematics,$x0941-3502
311   $a3-319-77976-1 
320   $aIncludes bibliographical references and index.
327   $aChapter 01- Elementary Counting Techniques -- Chapter 02- More Counting Techniques -- Chapter 03- Generating Functions -- Chapter 04- Existence of Configurations -- Chapter 05- A Glimpse on Graph Theory -- Chapter 06- Divisibility -- Chapter 07- Diophantine Equations -- Chapter 08- Arithmetic Functions -- Chapter 09- Calculus and Number Theory -- Chapter 10- The Relation of Congruence -- Chapter 11- Congruence Classes -- Chapter 12- Primitive Roots and Quadratic Residues -- Chapter 13- Complex Numbers -- Chapter 14- Polynomials. Chapter 15- Roots of Polynomials -- Cahpter 16- Relations Between Roots and Coefficients -- Chapter 17- Polynomials over R -- Chapter 18- Interpolation of Polynomials -- Chapter 19- On the Factorization of Polynomials -- Chapter 20- Algebraic and Transcendental Numbers -- Chapter 21- Linear Recurrence Relations -- Chapter 22- Hints and Solutions.
330   $aThis book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester undergraduate course. This third and last volume covers Counting, Generating Functions, Graph Theory, Number Theory, Complex Numbers, Polynomials, and much more. As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level. The book also explores some of the hardest problems presented at National and International Mathematics Olympiads, as well as many essential theorems related to the content. An extensive Appendix offering hints on or full solutions for all difficult problems rounds out the book.
410  0$aProblem Books in Mathematics,$x0941-3502
606   $aDiscrete mathematics
606   $aAlgebra
606   $aField theory (Physics)
606   $aDiscrete Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29000
606   $aField Theory and Polynomials$3https://scigraph.springernature.com/ontologies/product-market-codes/M11051
615  0$aDiscrete mathematics.
615  0$aAlgebra.
615  0$aField theory (Physics).
615 14$aDiscrete Mathematics.
615 24$aField Theory and Polynomials.
676   $a511.1
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   $a9910300105403321
996   $aAn Excursion through Elementary Mathematics, Volume III$92018994
997   $aUNINA