03398nam a22004695i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001200172072001600184072002300200072001500223100008200238245009600320250001800416264007300434300006400507336002600571337002600597338003600623347002400659490004900683505037800732520136201110650002602472650002102498650002602519650002102545700008202566710003402648773002602682776003602708776003602744830005602780856004602836912001402882912001502896999001702911978-3-031-55384-4DE-He21320251030111821.0cr nn 008mamaa240416s2024    sz |    s    |||| 0|eng d  a97830315538449978-3-031-55384-47 a10.1007/978-3-031-55384-42doi 4aQA297.4 7aPBD2bicssc 7aMAT0080002bisacsh 7aPBD2thema1 aBall, Simeon.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut97526812aA Course in Combinatorics and Graphsh[electronic resource] /cby Simeon Ball, Oriol Serra.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Birkhäuser,c2024.  aXI, 172 p. 86 illus., 10 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aCompact Textbooks in Mathematics,x2296-455X0 aPreface -- Chapter 1 Symbolic Enumeration -- Chapter 2 Labelled enumeration -- Chapter 3 Enumeration with symmetries -- Chapter 4 Finite Geometries and Latin Squares -- Chapter 5 Matchings -- Chapter 6 Connectivity -- Chapter 7 Planarity -- Chapter 8 Graph Colouring -- Chapter 9 Extremal Graph Theory -- Chapter10 Hints and solutions to selected exercises -- Bibliography.  aThis compact textbook consists of lecture notes given as a fourth-year undergraduate course of the mathematics degree at the Universitat Politècnica de Catalunya, including topics in enumerative combinatorics, finite geometry, and graph theory. This text covers a single-semester course and is aimed at advanced undergraduates and masters-level students. Each chapter is intended to be covered in 6-8 hours of classes, which includes time to solve the exercises. The text is also ideally suited for independent study. Some hints are given to help solve the exercises and if the exercise has a numerical solution, then this is given. The material covered allows the reader with a rudimentary knowledge of discrete mathematics to acquire an advanced level on all aspects of combinatorics, from enumeration, through finite geometries to graph theory. The intended audience of this book assumes a mathematical background of third-year students in mathematics, allowing for a swifter use of mathematical tools in analysis, algebra, and other topics, as these tools are routinely incorporated in contemporary combinatorics. Some chapters take on more modern approaches such as Chapters 1, 2, and 9. The authors have also taken particular care in looking for clear concise proofs of well-known results matching the mathematical maturity of the intended audience. 0aDiscrete mathematics. 0aGeometry.96876314aDiscrete Mathematics.24aGeometry.9687631 aSerra, Oriol.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut9752692 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303155383708iPrinted edition:z9783031553851 0aCompact Textbooks in Mathematics,x2296-455X97527040uhttps://doi.org/10.1007/978-3-031-55384-4  aZDB-2-SMA  aZDB-2-SXMS  c59163d59163