QS University Ranking 2017 by Math Subject

This ranking has criteria which are quite subjective, eg. Employer reputation (depends on individual country, local employment for Math graduates, job opportunities), also Citations refer predominantly to English publications which are not in favor of non-English speaking countries like China, Japan, France, etc.

If by real substance of Math education for Mathematicians, the 32th Ecole Normale Supérieure (Paris) – the alma mater of Evariste Galois – should be ranked among the Top 3 in the World, having produced 1/3 of the Fields Medals (Nobel Prize equivalent in Math) by a single country and a single university.

Top 5:

  1. MIT
  2. Harvard 
  3. Stanford 
  4. Oxford
  5. Cambridge

18. University of Tokyo

20. Peking University 北京大学

22. Ecole Polytechnique (France)

26. TsingHua University 清华大学

28. Hong Kong University

32. Ecole Normale Supérieure (Paris)


中国数学考研 Graduate Math Exams


考题难, 重视理论基础, 不是技巧。计算量大, 时间(3小时)不够。

国家 “及格” 底线 : 58~ 90分 (总分 : 150 分) – 根据 理工 / 经管系 , 不同重点大学, 底线各异。


[例子] p (x) = a + bx+cx^{2}+dx^{3}

p(x) - tan x \sim x^{3}, \text { when } x \to 0

Find a, b, c, d ?

[Solution] : 

1. Don’t use l’Hôpital Rule for  \displaystyle \lim \frac {f}{g}

2. Apply Taylor expansion :

\tan x = x + \frac {1}{3}x^{3} + o (x^{3})
p (x) - \tan x = a + (b -1)x + (c - \frac {1}{3})x^{3} + o (x^{3})

p(x) - tan x \sim x^{3}, \text { when } x \to 0

\iff \boxed {a=0, b=1, c=\frac {4}{3}}