# 浙江大学《特殊函数：从组合数学到微积分》国际化课程报名通知

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Dan Ciubotaru

 紫金港东1A-507

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（一）中文简介

（二）英文简介

The aim of this course is to use the famous gamma function and other special functions as motivation to teach several important topics in discrete and continuous mathematics. One of the most common functions in combinatorics and number theory is the factorial: n!=1*2*3*...*n; it counts the number of ways in each one can permute n objects. Because it is such a natural object, the factorial appears everywhere in combinatorics and in basic number theory and there are many beautiful identities involving it, that can be understood using only high school mathematics. The gamma function Γ(s), one of the ubiquitous functions in mathematics and statistics, can be regarded as an extension of the factorial, firstly from natural numbers to positive numbers (for example "what is (1/2)!?"), and then to all complex numbers s. We will learn some of the wonderful properties that this function has and how it relates to other parts of mathematics, for example, probability, or modern number theory (Riemann's zeta function). We may even explore remarkable advanced identities involving  Γ(s) such as Γ(s)*Γ(1-s)=π/sin(πs).

（一）授课方式与要求

（二）考试评分与建议

Dan Ciubotaru, From Combinatorics to Calculus (via the Gamma function), lecture notes(pdf).

1.Robert Young, Excursions in Calculus: An interplay of the Continous and the Discrete (Dolciani Mathematical Expositions).

2.Emile Artin, The Gamma Function, (Dover Books on Mathematics).