組合學(xué)：導(dǎo)論（影印版）

　　組合學(xué)是一門(mén)關(guān)于有限集的計(jì)數(shù)、存在性、構(gòu)造和優(yōu)化問(wèn)題的數(shù)學(xué)學(xué)科。本書(shū)著重于前三類(lèi)問(wèn)題，內(nèi)容包括：基本計(jì)數(shù)和存在性原理、分布、生成函數(shù)、遞推關(guān)系、Pólya理論、組合設(shè)計(jì)、糾錯(cuò)碼、偏序集，以及圖論的一些應(yīng)用（包括樹(shù)的計(jì)數(shù)、色多項(xiàng)式和Ramsey理論入門(mén)）。閱讀本書(shū)只需掌握單變量微積分，并熟悉集合論和基本的證明技巧。本書(shū)著重論述了組合學(xué)的特點(diǎn)：雙射和組合證明、遞歸分析和計(jì)數(shù)問(wèn)題分類(lèi)。本書(shū)適用范圍極廣，可用于組合數(shù)學(xué)的本科課程、離散數(shù)學(xué)的第二學(xué)期課程、應(yīng)用數(shù)學(xué)的研究生入門(mén)課程，同時(shí)適合自學(xué)。本書(shū)之所以稱(chēng)為導(dǎo)引，在于分布在全書(shū)八章中的大約350個(gè)問(wèn)題。這些問(wèn)題可用來(lái)檢查學(xué)習(xí)成果，也讓讀者為每節(jié)后的練習(xí)（共有470多個(gè)）做好準(zhǔn)備。大部分章節(jié)以游記結(jié)尾，通過(guò)趣聞?shì)W事、未解決問(wèn)題、進(jìn)一步閱讀的建議以及與所聞所見(jiàn)有關(guān)的數(shù)學(xué)家傳記的形式，為內(nèi)容增色不少。

　　David R.Mazur，is Associate Professor of Mathematics at Western New England College in Springfield， Massachusetts. He was born on October 23， 1971 in Washington， D.C. He received his undergraduate degree in mathematics from the University of Delaware in 1993， and also won the Department of Mathematical Sciences' William D. Clark prize for unusual ability in the major that year. He then received two fellowships for doctoral study in the Department of Mathematical Sciences （now the Department of Applied Mathematics and Statistics） at The Johns Hopkins University. From there he received his Master's in 1996 and his Ph.D. in 1999 under the direction of Leslie A. Hall， focusing on operations research， integer programming， and polyhedral combinatorics. His dissertation， Integer Programming Approaches to a Multi-Facility Location Problem， won first prize in the 1999 joint United Parcel Service/INFORMS Section on Location Analysis Dissertation Award Competition. The competition occurs once every two years to recognize outstanding dissertations in the field of location analysis.