03311nam 22005535 450 991085198110332120251113175336.09783031553844303155384510.1007/978-3-031-55384-4(MiAaPQ)EBC31281352(Au-PeEL)EBL31281352(CKB)31517396000041(DE-He213)978-3-031-55384-4(EXLCZ)993151739600004120240416d2024 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierA Course in Combinatorics and Graphs /by Simeon Ball, Oriol Serra1st ed. 2024.Cham :Springer Nature Switzerland :Imprint: Birkhäuser,2024.1 online resource (180 pages)Compact Textbooks in Mathematics,2296-455X9783031553837 3031553837 Preface -- 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.This 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.Compact Textbooks in Mathematics,2296-455XDiscrete mathematicsGeometryDiscrete MathematicsGeometryDiscrete mathematics.Geometry.Discrete Mathematics.Geometry.511.1Ball Simeon978508Serra Oriol1769438MiAaPQMiAaPQMiAaPQBOOK9910851981103321A Course in Combinatorics and Graphs4240112UNINA