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020 _a9783031553844
_9978-3-031-55384-4
024 7 _a10.1007/978-3-031-55384-4
_2doi
050 4 _aQA297.4
072 7 _aPBD
_2bicssc
072 7 _aMAT008000
_2bisacsh
072 7 _aPBD
_2thema
100 1 _aBall, Simeon.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_975268
245 1 2 _aA Course in Combinatorics and Graphs
_h[electronic resource] /
_cby Simeon Ball, Oriol Serra.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Birkhäuser,
_c2024.
300 _aXI, 172 p. 86 illus., 10 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aCompact Textbooks in Mathematics,
_x2296-455X
505 0 _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.
520 _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.
650 0 _aDiscrete mathematics.
650 0 _aGeometry.
_968763
650 1 4 _aDiscrete Mathematics.
650 2 4 _aGeometry.
_968763
700 1 _aSerra, Oriol.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_975269
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031553837
776 0 8 _iPrinted edition:
_z9783031553851
830 0 _aCompact Textbooks in Mathematics,
_x2296-455X
_975270
856 4 0 _uhttps://doi.org/10.1007/978-3-031-55384-4
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c59163
_d59163