Math basics for Macro&Micro economics and econometrics I have just been admitted to a graduate school for studies in economics and I major in public administration during my undergraduate time. I have learnt linear algebra, single variable calculus, probability theory and mathematical statistics by myself(Otherwise I will not be admitted). After all I am a amateur in economics, and I have another 5 months to go before register to the graduate school. 

So, I think I'd better to equip myself with solid mathematical knowledge to deal with the courses in the first year, which are showed in the title.

ps. The books I will use in these courses are:


  Microeconomic Theory, Andreu Mas-Colell 
  
  Advanced Macroeconomics, David Romer
  
  And there is no prescribed textbook for econometrics.


Any ides are going to be appreciated, and if I didn't make a clear expression of my question, please tell me to edit my question.
I recommended familiarity with the following topics: 


partial differentiation and optimization of multivariate functions 
study fixed point theorems. Kakutani and Brower are good ideas. 
Set theory is very important 
analysis (especially sequences, sub-sequences, convergence of sequences, etc.) 
Topology (basics is good enough. For example, understanding the open ball for local non-satiation)
Contraction mapping theorem (For Bellman equations in Macro) 
Value functions / Bellman equations 
Envelope Theorem 
Be very comfortable with calculus (so...do some review if you aren't) 
Familiarize yourself with the simplex 
basic ideas of function properties like concavity, convexity, quasi-concavity, quasi-convexity, continuous, differentiable, discontinuity etc. 
Take a look at point-to-set mappings 


Edit: 


I'll add for point to set mapping that upper, lower-hemicontinuity and hemicontinuity are necessary as well
Taylor expansions around a point c for multivariate and log functions
glance over methods of log-linearization 
This isn't too hard but very important: binary relations over finite and infinite sets. To be a bit more specific - completeness, transitivity etc. 
I also recommend being familiar with cyclicity etc. 
The separating and supporting hyperplane theorems 


This may sound silly, but also make sure you are ridiculously comfortable with algebra. Sometimes I feel like the unending onslaught of algebra is the thing that slows me down the most during exams etc. 

Edit: I'd like to recommend a book for math prep that covers almost everything I've listed: The Foundations of Mathematical Economics by Michael Carter 

It's a solid book with good exercises and readily available solutions to confirm your answers.

Alright - I tried to give you some specific things rather than provide the broad strokes. I figure it is easy enough to know that you should study a subject and so I've tried to highlight what I remember being the important little bits of math that we use most often. 

Good luck with graduate school.