A Course in Combinatorics and Graphs

Ball, Simeon, Serra, Oriol

A Course in Combinatorics and Graphs
  • 出版商: Birkhauser Boston
  • 出版日期: 2024-04-17
  • 售價: $2,380
  • 貴賓價: 9.5 折 $2,261
  • 語言: 英文
  • 頁數: 172
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031553837
  • ISBN-13: 9783031553837

    • 下單後立即進貨 (約1週~2週)

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商品描述

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 useof 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.

商品描述(中文翻譯)

這本緊湊的教科書是根據加泰羅尼亞理工大學數學學位的四年級本科課程講義編寫而成，包括列舉組合學、有限幾何和圖論等主題。本書涵蓋了一個學期的課程，適用於高年級本科生和碩士級學生。每個章節的內容預計需要6-8小時的課堂時間，包括解題時間。本書也非常適合自學使用。書中提供了一些提示來幫助解題，如果題目有數值解，也會給出解答。本書所涵蓋的內容使讀者在具備離散數學基礎知識的基礎上，能夠在列舉、有限幾何和圖論等各個方面達到高級水平。

本書的目標讀者是具備數學背景的三年級數學學生，這樣可以更快地運用分析、代數和其他主題中的數學工具，因為這些工具在當代組合學中經常被使用。一些章節採用了更現代的方法，例如第1、2和9章。作者們還特別注意尋找清晰簡潔的著名結果證明，以符合目標讀者的數學成熟度。

作者簡介

Simeon Ball is senior lecturer at the Department of Mathematics of the Universitat Politècnica de Catalunya in Barcelona. He has been invited speaker at many international conferences, as well as serving on the scientific and organising committee for many conferences. His research interests include classical and quantum error-correcting codes, incidence problems in real and finite geometries, graphs and semifields, and is particularly focused on applying geometrical and algebraic methods to these combinatorial objects. He has published more than 70 research papers and two books and serves on the editorial board of the Journal of Geometry and the Journal of Combinatorial Theory Series A, having previously served on the editorial board of Designs, Codes and Cryptography and Finite Fields and Their Applications.

​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.

作者簡介(中文翻譯)

Simeon Ball是巴塞隆納波利特克尼克大學數學系的高級講師。他曾應邀在許多國際會議上發表演講，並擔任多個會議的科學和組織委員會成員。他的研究興趣包括經典和量子錯誤修正碼、實際和有限幾何中的相交問題、圖形和半域，並特別關注將幾何和代數方法應用於這些組合對象。他發表了70多篇研究論文和兩本書，並擔任《幾何學雜誌》和《組合理論A系列》的編輯委員會成員，之前還曾擔任《設計、編碼和密碼學》和《有限域及其應用》的編輯委員會成員。

Oriol Serra是巴塞隆納波利特克尼克大學數學系的教授。他的研究興趣涉及組合數學、圖論和組合數論。他對等周問題、拉姆齊理論、極值和概率組合學以及加法組合學特別感興趣。他發表了100多篇研究和普及論文，曾應邀在重要會議上發表演講，並參與了多個會議的組織工作。他曾在本科和碩士課程中教授組合數學和圖論，尤其是與Simeon Ball教授合作的一門成功課程。他曾擔任數學系主任、波利特克尼克大學數學學院研究副院長以及巴塞隆納數學研究生院執行委員會成員等職務。

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