邹恒甫回答: 数学和对策论的学习
[发布者 daniel (http://danielyoung.blog.sohu.com/)
2007-06-21 21:44
邹老师你的博客似乎不能留言。只有在这里评论里请教一个与上文无关的问题。Mankiw在自己的博客里认为经济学学生应该学习的数学有
Calculus
Linear Algebra
Multivariable Calculus
Real Analysis
Probability Theory
Mathematical Statistics
Game Theory
Differential Equations
您知道我们中国大学生普遍的数学基础是:微积分、线性代数和概率统计。请问您同意Mankiw的推荐吗?数学当然是越多越好。但在考虑到我们仍然有其它很多学习任务,如高级宏观、微观,的前提下您能为中国的经济学硕士研究生的数学学习做出指点吗?能否具体到参考书?谢谢您!]
邹恒甫回答如下:
MANKIW的建议非常好! THOMAS SARGENT的建议更好,要求更高:
http://homepages.nyu.edu/~ts43/
Recommended Math Courses for Economics Graduate Students
Disclaimer: The opinions expressed on this page are my own and do not represent the policy or opinions of the economics department. The recommendations here are based primarily on the success of past students who have taken the path I describe.
Remark: Distinguished Stanford graduates such as David Kreps and Darrell Duffie contributed important new ideas in economics from the beginning of their careers partly because they are creative and partly because they were extraordinarily well equipped in mathematical and statistical tools.
Here is a list of recommended courses:
Math courses for Stanford students
Math Department
Math 103, 104, Linear algebra | |
Math 113, 114 Linear algebra and matrix theory | |
Math 106, Introduction to functions of a complex variable (especially useful for econometrics and time series analysis) | |
Math 124, Introduction to stochastic processes | |
Math 130, Ordinary differential equations | |
Math 131, Partial differential equations | |
Math 175, Functional analysis | |
Math 205A, B, C, Real analysis and functional analysis | |
Math 230A, B, C, Theory of Probability | |
Math 236, Introduction to stochastic differential equations |
Engineering Economic Systems and Operations Research
EESOR 313, Vector Space Optimization. This course is taught from `the Bible' by the author (Luenberger). The book is wonderful and widely cited by economists | |
EESOR 322, Stochastic calculus and control |
Statistics
Stat 215-217, Stochastic processes (Cover) | |
Stat 218, Modern Markov chains (Diaconis) | |
Stat 310 A, B, Theory of probability (Dembo) |
These are very useful courses for applied work in econometrics, macroeconomic theory, and applied industrial organization. They describe the foundations of methods used to specify and estimate dynamic competitive models.
Just as in jogging, I recommend not overdoing it. Rather, find a pace that you can sustain throughout your years here. You will find that taking these courses doesn't really cost time, because of your improved efficiency in doing economics.
There are many other courses that are interesting and useful. The most important thing is just to get started acquiring the tools and habits these courses will convey
Math courses for NYU students
I recommend that graduate students in economics at Stanford and NYU take or audit a stream of math and statistics classes while they are here. If you take one course a quarter from the second year on, you will have at least nine quarters under your belt by the time you graduate. While it may be painful at first, like jogging, after a while the pain will vanish and you will acquire a facility in writing and reading economics. My experience has been that students who pay the price of learning adequate mathematical and statistical tools have much easier times writing their theses and acquiring jobs. This is certainly true in applied fields like macroeconomics.
You are very lucky because at Stanford and NYU there are wonderful courses taught by some of the most distinguished people in the world. Here are some courses I recommend.
请全中国的宏观经济和金融类的学生好好地看一下THOMAS SARGENT在纽约大学(NYU)的个人主页,紧跟他学习:
http://homepages.nyu.edu/~ts43/
另外,请关注THOMAS SARGENT的学生Lars Peter Hansen的个人主页:
http://home.uchicago.edu/~lhansen/
他有`无穷多'的文章和书稿供你们免费地下载.
ROBERT LUCAS, JR 更是不得了.他的个人主页:
http://home.uchicago.edu/~sogrodow/
他的许多新论文:
http://home.uchicago.edu/~sogrodow/homepage/papers.html
对策论(Game Theory):请看NYU的ARIEL RUBINSTEN 的个人主页(他也有`无穷多'的文章和书稿供你们免费地下载!)他会来CEMA 讲课, 你们一定要来参加.否则,我就不高兴了!)RUBINSTEIN最反对剥削学生,所以,他的文章和书都可免费下载!我当然赞成他.但我的文章同他的比起来就是垃圾50篇(http://econ.gsm.pku.edu.cn/Hzou/index.htm)!
http://arielrubinstein.tau.ac.il/
绝对不要看中文的对策论!那是绝对地误入歧途,误人子弟!!!