A Course in Combinatorics and Graphs / Compact Textbooks in Mathematics (PDF)
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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.
¿Oriol Serra is full professor at the Department of Mathematics of the Universitat Politècnica de Catalunya in Barcelona. His research interestsare in combinatorics, graph theory and combinatorial number theory. He has been particularly interested in isoperimetric problems, Ramsey Theory, extremal and probabilistic combinatorics and additive combinatorics. He has published more than 100 research and divulgation papers, has been invited speaker in key conferences and has been involved in the organization of several of them. He has been involved in teaching Combinatorics and Graph Theory at undergraduate and master levels, particularly in a successful course on the topic jointly with Prof. Simeon Ball. He has served as chair of the department of mathematics, vicedean of research of the School of Mathematics at UPC and member of the Executive Committee of the Barcelona Graduate School of Mathematics among other duties.
- Autoren: Simeon Ball , Oriol Serra
- 2024, 2024, 172 Seiten, Englisch
- Verlag: Springer Nature Switzerland
- ISBN-10: 3031553845
- ISBN-13: 9783031553844
- Erscheinungsdatum: 16.04.2024
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- Größe: 4.84 MB
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