stirling reading list

Structure and content
The MSc in Media Management has been developed to prepare media managers to meet the challenges posed by unprecedented change and increased competition in the media environment. This full-time academic course is designed to provide media practitioners with a wider analytical perspective on the main issues affecting their work and offers graduates a rigorous foundation for a career in the media industry. The course builds on Communications, Media & Culture's extensive links with the media industry and draws on a range of related disciplines including media studies, economics, marketing and business studies. The MSc consists of two components: a taught course followed by a Dissertation. Based primarily in the Communications, Media & Culture department, the taught component also involves postgraduate modules offered by, or in collaboration with, the School of Management. The taught course takes place within the University's two 15-week semesters and involves lectures, seminars, tutorials and case-study work. Students will take two core modules and two elective modules concurrently in the Autumn Semester, plus two core modules and one elective module concurrently in Spring Semester making a total of seven taught modules across the year.
Delivery and assessment
The course is taught with a combination of lectures, seminars, workshops and tutorials. Formal teaching is augmented by occasional guest speakers, usually experienced practitioners from the media industry who are able to provide a strategic or practical insight into current management issues.
Recommended reading
MMAP12: Mass Media Research Methods This course is organised around the discussion of issues and problems rather than articles or books, but the following reading list is an important first source for the development of your own ideas about research methods. You are expected to incorporate reference to appropriate reading (fully referenced in accordance with the Harvard system of referencing) in your assignments. Guides to Research Methods
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Berger, A. A. (1998) Media Research Techniques (2ndedn). London: Sage.

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Bertrand, I. and P. Hughes (2004) Media Research Methods. London: Palgrave MacMillan.
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Bryman, A. (2004) Social Research Methods (2ndedn). Oxford: Oxford University Press.
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Deacon, D., Pickering, M., Golding, P. and Murdock, G. (2007) Researching Communications: A Practical Guide to Methods in Media and Cultural Analysis. London: Arnold. Second Edition.
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Gill, J., and P. Johnson (2010) Research Methods for Managers. London: Sage. Fourth Edition.
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Hansen, A., Cottle, S., Negrine, R. and Newbold, C. (1998) Mass Communication Research Methods. London: Macmillan.
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Jensen, K. B. and Jankowski, N. W. (eds) (1991) A Handbook of Qualitative Methodologies for Mass Communications Research. London: Routledge (available as e-book through Athens).
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Messenger-Davies, M. and N. Mosdell (2006) Practical Research Methods for Media & Cultural Studies: Making People Count. Edinburgh: EUP.
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Oliver, P. (2004) The Student’s Guide to Research Ethics. Maidenhead: Open University Press.
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Rubin, R. B., Rubin, A. M. and Piele, L. J. (1992) Communication Research Strategies and Sources (3rdedn). Belmont, CA: Thomson Wadsworth.
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Saunders, M., A. Thornhill and P. Lewis (2009) Research Methods for Business Students. London: Prentice Hall. Fifth Edition.
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Seale, C. (2004) Researching Society and Culture (2ndedn). London: Sage. Wimmer, R. D. and Dominick, J. R. (2006) Mass Media Research: an Introduction (8thedn). Belmont CA: Thomson Wadsworth.

MMAP11: Media Economics Highly Recommended books
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Albarran, Alan B. (2010) The Media Economy, London: Routledge. Alexander, Alison, Owers, James, Carveth, Rod, Hollifield, Ann and Greco, Albert (eds.), (2004), Media Economics: Theory and Practice (3rd ed), Mahwah, NJ: Lawrence Erlbaum Associates.
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Doyle, Gillian (2002) Understanding Media Economics, London: Sage Publications.
These books are similar in their content structure, divided into chapters on the economics of specific media industries/sectors. Albarran is a new and potentially very useful introductory text with a global focus. Alexander et al (2004) provides knowledge and insights into the US media industries while Doyle (2004) is more European-centred. Together, they are useful in gaining a thorough understanding of the economic operations of the media in the western world. Recommended books
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Hoskins, Colin, McFadyen, Stuart and Finn, Adam (2004) Media Economics: Applying Economics to New and Traditional Media, Thousand Oaks, Calif: Sage Publications.
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Picard, Robert (2002) The Economics and Financing of Media Companies. New York: Fordham University Press.
Instead of being divided into chapters on different media industries as in Alexander et al (2004) and Doyle (2002), these two texts approach media economics according to key concepts and issues and are important supplementary readings for those who wish to obtain a clear and in-depth understanding of whey they learn from lectures and the other readings.
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Strunk, William and White, E.B. (1999/2008) The Elements of Style, New York: Pearson.

This is a helpful guide on writing clearly and correctly. You can also access writing and language skills help – contact your Programme Director (Dr Richard Haynes) for advice. MMAP14: Media Regulation and Policy Recommended Reading: There is no course text as such. However, students are strongly encouraged to purchase
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Carey P et.al, Media Law, Sweet& Maxwell; 5th edition: London, 2010
BSMP31: Strategic Management CORE TEXTS The core text for the module is:
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Johnson, G, Scholes, K, Whittington, R (2012), Fundamentals of Strategy, 2nd Edition, Prentice Hall, ISBN: 978-0-273-75725-2.
The first edition of the core text is available as an e-book for ￡ 23.99 and can be purchased from the following website. https://www.docsj.com/doc/1610660903.html,/bookshop/detail.asp?item=100000000483235
Module titles
Semester 1:
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and two options of:
Media Economics (MMAP11) Mass Media Research Methods (MMAP12)
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Media Environment (MMAP13) Accounting and Finance (ACCP30) Managing International Organisations (BSMP24) Strategic Public Relations Planning (PREP61)

Semester 2:
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and two options of:
Media Regulation and Policy (MMAP14) Strategic Management (BSMP31)
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Summer:
Marketing Communications (MKTP30) Media Rights (MMAP15) Advertising (PCMCX3)
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Dissertation
Career opportunities
Skills you can develop through this course As you progress through your Media Management degree, you will have the opportunity to develop the following practical skills and attributes that are much sought after by prospective employers: ?Media industry awareness – through case study analysis, guest lectures and site visits to media organisations, you will develop an understanding of what is going on in the media sector and rapid developments in other digitally related industries. ?Written and oral communication – media management involves communication both internally and externally with various stakeholders. The course develops your abilities to communicate through various essays, reports, presentations and online activities. ?Teamworking – groupwork is an essential part of your Media Management degree, both during management and communications modules simulate real-life scenarios in business and marketing communications. ?Research and analysis – critical learning is a key aspect of any Master's course in media and communications and you will be given the opportunity to develop your own research skills to carry out both small-scale and larger research projects including the Master's dissertation. ?Time management – you will learn how to manage your time more effectively through your active involvement in group projects, as well as by successfully juggling your weekly workload in order to meet your (sometimes conflicting) deadlines for coursework ?Self-confidence – the media industry needs confident, self-starters and your active participation in the degree programme and the wider postgraduate community will build your personal confidence and professional prospects. Where are our graduates now?

Our graduates are spread throughout the world. At present we are in contact with graduates in 30 countries around the world. Media Management graduates are currently contributing to the performance of the following organisations:
?BBC Worldwide ?Channel 4 ?China Radio HIT FM ?Vodafone Greece ?Radio One India (A Midday/BBC Joint Venture) ?MTV ?ERT S.A. ?Southerna Africa Development Community ?Skattedirektoratet ?Wyeside Arts Centre ?MTV Networks UK ?Summerhouse Publishing ?Jetlag Advertising ?Motorpress Hellas SA ?Google India Pvt Ltd ?Dagavisen ?Mobistar - Orange Group ?Vodafone Greece ?Ministry of Education & European Commission ?Asia Reach Media ?Tele2 Norway ?ThinkDigital ?Indian Music Industry ?McCann Universal Media ?Cooperative Bank of Chania, Crete ?Adcosp - Simeka TWS Communications ?Corporate Communications, Avon ?Giacometti: Branding e Arquitetura de Negócios ?Vodafone ?BòrdnaGàidhlig
To provide you with an indication as to what you can do with your Media Management degree, graduates entering into employment in the past two years are currently working with: ?Editor-in-Chief

?Reputation Executive ?Social Media Researcher ?Communications Executive ?Lecturer ?Internship in Online Marketing Building on that foundation, alumni of Stirling’s Media Management degree who graduated between five and ten years ago have since advanced into some of the following positions: ?Director, International Marketing ?Researcher ?Business Analyst ?Chief Executive ?General Manager ?Associate Account Director ?Vice President ?Head, Magna Home Video and Magna Films Some of our more established alumni are currently leading and shaping Media Management strategy across many different sectors – here is an example of how a few former Stirling Media Management students have advanced in their careers:
?Marketing Manager ?Vice President of Programming, Creative & Content ?Content & Produce Development ?Manager ?PR Executive ?Project Manager ?Communications Consultant ?Account Executive ?Communication Manager in Public Relations Department ?Creative Partner ?Financial Control/Analysis Manager ?Account Associate ?Managing Director ?Head of Regulatory Affairs ?Head of Customer Base Management ?Project Manager ?Business Development & Operations Director ?Business Development Director ?Director, Global Digital Marketing ?Press Officer

?Marketing Director ?Accounts Director ?Head of Corporate Relations
Graduating with a degree in Media Management does not necessarily mean that you have to progress into a career in that field. A Media Management degree is a solid foundation upon which to base a career in a variety of different fields, as is shown by some of the potentially less obvious roles that our Media Management graduates are currently working as: ?Area Manager ?Regional Sales Director ?In-house Lawyer ?Head of Finance

浅谈Stirling数极其简单应用

摘要 组合数学中的许多问题是数学中的精华，组合数学的应用也涉及到自然科学的许多领域。本文对Stirling数进行了研究。 本文的工作分为三部分：第一部分，介绍了Stirling数的概念和性质；第二部分列举了关于两类Stirling数之间的几个关系式。重点介绍了两类Stirling阵之间的关系，并分别用Stirling阵和Stirling展开式证明了两类Stirling数的反演和互逆关系;第三部分则简单介绍了两类Stirling数的简单应用。 关键词：Stirling数；基本性质；关系；简单应用

Abstract The problems in combination of mathematics is the essence of mathematics.the application of combination of mathematics relates to many fields of natural science. This paper is divided into three parts: the first part,introduces the concept and the characteristics of Stirling number ; the second part lists several relations which is about two Stirling number . It focuses on the relations between the two types of Stirling array, using the Stirling matrix and Stirling expansion to proved the inversion and reciprocal relationship of the two kinds of Stirling numbers; the third part introduces the simple application of the two kinds of the Stirling numbers. Keywords Stirling number; basic characteristics; relations; simple application

Stirling公式

Stirling's Formula An important formula in applied mathematics as well as in probability is the Stirling's formula known as where is used to indicate that the ratio of the two sides goes to 1 as n goes to . In other words, we have or Proof of the Stirling's Formula First take the log of n! to get Since the log function is increasing on the interval , we get for . Add the above inequalities, with , we get Though the first integral is improper, it is easy to show that in fact it is convergent. Using the antiderivative of (being ), we get

Next, set We have Easy algebraic manipulation gives Using the Taylor expansion for -1 < t < 1, we get This implies We recognize a geometric series. Therefore we have From this we get 1. the sequence is decreasing;

Stirling 公式

谈Stirling 公式（转） 彭宇煦 12位粉丝 1楼 甲、一个机率问题 什麽是一个事件(event) 的几率？这是机率论最基本也是争论最多的一个问题。 举最简单的例子来说明：丢一个公正铜板(fair coin)，出现正面(head) 的机率为这是什麽意思呢？常识性的解释大致是，将此铜板独立地丢「很多」次，那麽正面出现的次数「大约」占一半，这是在随机的说不准中很确定的事情。所谓的「平均律」(the law of averages) 或「大数法则」(the law of large numbers) 隐隐约约就是指着这个解释。不过，常识往往是含糊的或自相矛盾的，需要加以精炼。事实上，「数学是精炼的常识」(Mathematics is refined comm on sense)。常识是我们作观念探险之旅的出发点。 问1： 丢2n 次铜板，正面恰好出现n 次的机率有多大？ 根据组合学，丢2n 次铜板，共有22n 种可能结果，假设每一种结果发生的机会均等，那麼2n 次中有n 次为正面的结果共有2nCn 种，故得机率为 我们更有兴趣的问题是，当n 趋近时，p2n 会趋近於多少？上述常识性的解释似乎是说，，这成立吗？这需要对(1)式作精确的估算，於是引出了下面的 问2： 当n 很大时，如何估算？更明确地说：当n 趋近时，n! 的渐近相等式(Asymptotically equal formula) 是什麼？即要找一个「好用」(an) 使得 我们希望找到这样的(an)，然后代入(1)式中计算出极限值，就可以检验上述常识性的机率解释是否正确。 n! 的渐近相等式存在吗？如何找？这就来到了Stirling 公式的大门口。在文献上，有许多文章论述Stirling 公式的简化证明或机率式的证明，不过都只是在已经知道公式后，给出证明而已，并没有说出如何「看出」或「猜出」公式的追寻、探险过程。因此令人有「美中不足」或「未尽妙理」的感觉。本文我们就试著来补上这个缺憾，展示一种推测式的猜想过程。我们不排斥还有其它猜想过程因为登一座山可以有各种不同的路径，路径越多越美妙。 PS：本篇内容较多，等我慢慢贴，为保证阅读流畅性，请暂时不要插楼，谢谢！

斯特林公式Stirling Formular

题目：关于阶乘的近似公式 1.相关历史与进程 历史上对阶乘的估计在数学上有着重要的作用，首先是它在概率论与数理统计中，最早可以追溯到1733年一位法国的数学家de Moivre 的工作，同时也是第一次遇到对整数阶乘的估计问题。在他研究Gauss 分布和中心极限定理时发现了如下公式： !constant n n n e ?? ≈ ? ?? 然后，瑞典数学家Stirling 在试图给出二项分布的一般的近似值时，发现了未知的常数： constant =Stirling 公式： !n n n n e σ? ≈=?? 紧接着他就得到如下的结果，并发表在了Miscellaneis Analyticis Supplementum 中： 221 111ln[(1)!]~ln()ln(2)222(21)k k k B n n n n k k n π-≥? ?---++ ?-??∑ (1) 公式(1)也被称为Stirling 级数，其中的2k B 称为Bernoulli 数，定义如下： 0011,0k j j k B B j =+??== ?? ?∑ 其中1k ≥。将(1)式的前m 项记为 2211exp 2(21)n m k m k k B n e k k x τ-=??? = ? ?-??? ∑ 同时Euler 提出了一个函数，它可以作为整数的阶乘在正实数中的拟合。这函数便是Γ-函数： 10 ()t z z e t dt +∞ -Γ=?，也可以定义为极限的形式： !()lim (1)() z n n n z z z z n →∞Γ=++ 而且显然有(1)!n n Γ+=，而且目前对阶乘的估计也或多或少的用Γ-函数来描述，甚至利用 Γ-函数的性质来发现新的更好的渐进函数。 之后，关于!n 的渐进公式的探索逐渐缓慢下来。直到最近才有了新的突破。 2.第一种有关!n 的渐进形式——含有幂级数的渐进公式 依靠幂级数来求数值解的思想一直是较好的方法。其中在Stirling 所处的时期便已经有了一个幂级数展开，而且拥有着各种相似的形式，如在Abramowitz 和Stegun [1]的书中记载着：

第二类stirling数S(n,n-7)的一个公式1

第二类stirling 数(,7)S n n -的一个公式 李妙珊 （华南师范大学, 数学科学学院, 广东, 广州,510631） 摘 要: 本文运用组合理论对第二类stirling 数展开分析,从而给出当14n ≥时, 第二类stirling 数(,7)S n n -的一个公式. 关键词: 非空子集合; 组合; 第二类stirling 数 1．定义与符号 定义1 从n 个不同事物中取出m 个的组合数,记作m n C . 定义2 把含有n 个元素的一个集合分成恰好有k 个非空子集合的分拆数目就叫 做第二类stirling 数,并记作(,)S n k ,对于0n k ==时,定义(0,0)S =0;当(,)0n k S n k <=时,. 对于集合A,我们用|A|表示A 的基数. 关于第二类stirling 数的性质与计算方法,我们给出以下几个引理. 引理 []11 1112 1 1(,1)1,(,2)21,(,3)(31)2, 2,n n n n n S n S n S n S n S n n S n n ---≥==-=+-当时，（,0)=0,（,-1)=C （,)=1. 引理 []12 1(,)(1,1)(1,).k n S n k S n k kS n k ≤≤=--+-当 时, 为了方便下面定理1的证明，根据引理1和引理2，我们可以算出以下几个 第二类stirling 数： 89 91(9,2)21255;(10,3)(31)29330;(11,4)145750;2 S S S =-== +-==(12,5)1379400.S = 作者简介:李妙珊（l983一）, 女, 广东佛山人,华南师范大学硕士研究生。研究方向:图论与组合最优化。

stirlings formula斯特林(stirling)公式

stirlings formula斯特林(stirling)公式 Stirling's FormulaAn important formula in applied mathematics as well as in probability is the Stirling's formula known as where is used to indicate that the ratio of the two sides goes to 1 as n goes to . In other words, we have or

Proof of the Stirling's Formula First take the log of n! to get Since the log function is increasing on the interval , we get for . Add the above inequalities, with , we get Though the first integral is improper, it is easy to show that in

fact it is convergent. Using the antiderivative of (being ), we get Next, set We have Easy algebraic manipulation gives

Using the Taylor expansion for -1 < t < 1, we get This implies We recognize a geometric series. Therefore we have

用Stirling逼近近似计算阶乘的探讨与应用

用Stirling 逼近近似计算阶乘的探讨与应用 江苏省赣榆高级中学 仲晨 myheimu@https://www.docsj.com/doc/1610660903.html, 【关键词】：Stirling 逼近，阶乘，极限论，微积分，数学实验，计算机算法 “阶乘”（factorial ）在信息学竞赛中具有重要角色，更广泛的说，“阶乘”在数学领域也是占有重要地位。在许多人刚刚学习计算机语言的时候，大多会被要求写一个算阶乘的程序，而在学习高精度算法的时候，也会写一个计算较大数字阶乘的程序。不过，在实际的运用之中，可能遇到更大数字的阶乘计算和不同要求的阶乘结果，例如：TOJ （同济大学ACM 网络题库，https://www.docsj.com/doc/1610660903.html,/problem.php ）的1016题——“求N ！左边第二位的数字”，这就需要一定的精度思考了。 可是我们通常对于较大数字阶乘的要求是求结果位数或前几位数字，这怎么办呢？ 在刘汝佳的《算法艺术与信息学竞赛》一书中，（Page241）介绍了Stirling 公式： 其中的～符号是指“同阶”或“相当”，即两者随n 增加的大致速度相同，在n 较大时， 两者极其相近。 这是一个极限的概念（现行教材高二下学期数学内容），属于微分学内容，准确写法为： () 1 2! lim =+∞ →n n e n n n π 但遗憾的是在《算法艺术与信息学竞赛》书中只提供了这个算式，并无他物！ 本人近日看到一本数学科普读物——《好玩的数学——不可思议的 e 》（陈任政著， 科学出版社），其中5.12节简介了Stirling 逼近近似算阶乘，本人感到好奇，于是对这种算法的具体步骤进行了分析，并研究了它的精确度，故为本文。在2005年8月7日完工之日，笔者上网搜索了一下，找到了一些关于Stirling 逼近的文章，偶然地在臺灣亞洲聚合公司蔡永裕《談Stirling 公式的改良》（刊自台湾《數學傳播》20卷4期，民国85年12月）一文