<p>Expanding my comments into an answer:  For concreteness I recommend making sure you finish the chapter on Partial Derivatives in your multi-variable Calculus class; a common book is <a href="http://rads.stackoverflow.com/amzn/click/0538497815" rel="nofollow">Stewart's Calculus</a>, here PDs is chapter 14.  </p>

<p>In general I feel good preparation comes from increasing mathematical maturity; from a class such as real analysis is great, but here the common book is <a href="http://rads.stackoverflow.com/amzn/click/1259064786" rel="nofollow">Rudin's Analysis</a> which is more suited for Math majours than economics, so I recommend working through <a href="http://rads.stackoverflow.com/amzn/click/0914098918" rel="nofollow">Spivak's Calculus</a> for a rigorous introduction to proofs and reviewing calculus concepts at the same time, in another's words, "This is no ordinary calculus book!" </p>

<p>Finally I will recommend a book that introduces a wide range of rigorous math intended for Economists <a href="http://rads.stackoverflow.com/amzn/click/0691118671" rel="nofollow">An Introduction to Mathematical Analysis for Economic Theory and Econometrics </a>.  This is what I will be reading this summer :D</p>

CC BY-SA 3.0
2016-04-18T14:43:39.153Z
2016-04-18T14:43:39.153Z
Sunhwa
<p>I recommended familiarity with the following topics: </p>

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

<p>Edit: </p>

<ul>
<li>I'll add for point to set mapping that upper, lower-hemicontinuity and hemicontinuity are necessary as well</li>
<li>Taylor expansions around a point c for multivariate and log functions</li>
<li>glance over methods of log-linearization </li>
<li>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. </li>
<li>The separating and supporting hyperplane theorems </li>
</ul>

<p>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. </p>

<p>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 </p>

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

<p>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. </p>

<p>Good luck with graduate school.</p>

CC BY-SA 3.0
2016-04-22T13:29:07.477Z
Two things I miss in this answer are game theory and statistics/econometrics (maximum likelihood principle, central limit theorem, an array of statistical processes, an array of hypothesis tests, and an array of discrete and continuous distributions). 
          
Depending on the graduate school in question, heterodox economics may also be taught. This takes up the point raised in the answer/comment by user20172. In that case, the basics of evolutionary game theory and of dynamic systems will also be required (up to the point where one is able to understand bifurcations and chaos).
0range
CC BY-SA 3.0
2016-04-18T15:30:53.323Z
2016-04-19T15:21:05.717Z
2016-04-19T15:21:05.717Z
123
<p>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. </p>

<p>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.</p>

<p>ps. The books I will use in these courses are:</p>

<blockquote>
  <p><em>Microeconomic Theory</em>, Andreu Mas-Colell </p>
  
  <p><em>Advanced Macroeconomics</em>, David Romer</p>
  
  <p>And there is no prescribed textbook for econometrics.</p>
</blockquote>

<p>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.</p>

CC BY-SA 3.0
2016-04-18T13:54:24.373Z
I'm just finishing my first semester of Macro using this book, so I can provide insight for half the math used.  You are only really missing Multi-variable Calculus, there are partial differentials you will use in maximizing utility, and look up Lagrangian.  My professor called it a "rather math intensive book."  There are some places where a good understanding of expectation is helpful, so review that too.
Sunhwa
CC BY-SA 3.0
2016-04-18T14:01:29.360Z
@Sunhwa Actually I have attend a multi-variable Calculus class, but I haven't finished it yet. I wonder is that necessary to learn real analysis or go futher in linear algebra. I mean, it's definitely useful to learn as many as possible mathematical knowledge. But the reality is the time I have is limited. So,in your opinion, what's the most diffcult and useful tools in mathematics to deal with economics problems?
Rowan
CC BY-SA 3.0
2016-04-18T14:23:11.467Z
It is not necessary to learn real analysis, but it often increases one's mathematical maturity, which I feel is the best thing you can do to prepare.  There will be very many different kinds of math you will encounter, so preparing for all of it is impossible.  But mathematical maturity has a holistic effect
Sunhwa
CC BY-SA 3.0
2016-04-18T14:39:56.623Z
@Sunhwa OK. I got it. Thanks for your advice ;)
Rowan
CC BY-SA 3.0
2016-04-19T16:23:04.523Z
A good book is Mathematics for Economists by Simon and Blume
DornerA
CC BY-SA 3.0
2016-04-19T18:12:30.457Z
It might also be interesting to read this thread, just as a different view of the overall state of economics: http://www.nakedcapitalism.com/2011/09/economics-debunked-chapter-two-for-sixth-graders.html It won't help you much with preparing for your graduate studies but it's an amusing read.
user20172
<macroeconomics><microeconomics><econometrics><soft-question>
Math basics for Macro&Micro economics and econometrics
Rowan
# Math basics for Macro&Micro economics and econometrics

(Asked by: username_0 on 2016-04-18)

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.

**Tags:** macroeconomics, microeconomics, econometrics, soft-question

> **Comments:**
> **username_1**: I'm just finishing my first semester of Macro using this book, so I can provide insight for half the math used.  You are only really missing Multi-variable Calculus, there are partial differentials you will use in maximizing utility, and look up Lagrangian.  My professor called it a "rather math intensive book."  There are some places where a good understanding of expectation is helpful, so review that too.  
> **username_0**: @username_1 Actually I have attend a multi-variable Calculus class, but I haven't finished it yet. I wonder is that necessary to learn real analysis or go futher in linear algebra. I mean, it's definitely useful to learn as many as possible mathematical knowledge. But the reality is the time I have is limited. So,in your opinion, what's the most diffcult and useful tools in mathematics to deal with economics problems?  
> **username_1**: It is not necessary to learn real analysis, but it often increases one's mathematical maturity, which I feel is the best thing you can do to prepare.  There will be very many different kinds of math you will encounter, so preparing for all of it is impossible.  But mathematical maturity has a holistic effect  
> **username_0**: @username_1 OK. I got it. Thanks for your advice ;)  
> **username_2**: A good book is Mathematics for Economists by Simon and Blume  
> **username_3**: It might also be interesting to read this thread, just as a different view of the overall state of economics: http://www.nakedcapitalism.com/2011/09/economics-debunked-chapter-two-for-sixth-graders.html It won't help you much with preparing for your graduate studies but it's an amusing read.  

---

## 2 answers

### Answer by username_4 on 2016-04-18. Score: 9 | Accepted answer

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.

> **Comments:**
> **username_5**: Two things I miss in this answer are game theory and statistics/econometrics (maximum likelihood principle, central limit theorem, an array of statistical processes, an array of hypothesis tests, and an array of discrete and continuous distributions).             Depending on the graduate school in question, heterodox economics may also be taught. This takes up the point raised in the answer/comment by username_3. In that case, the basics of evolutionary game theory and of dynamic systems will also be required (up to the point where one is able to understand bifurcations and chaos).  

---

### Answer by username_1 on 2016-04-18. Score: 1

Expanding my comments into an answer: For concreteness I recommend making sure you finish the chapter on Partial Derivatives in your multi-variable Calculus class; a common book is [Stewart's Calculus](http://rads.stackoverflow.com/amzn/click/0538497815), here PDs is chapter 14.

In general I feel good preparation comes from increasing mathematical maturity; from a class such as real analysis is great, but here the common book is [Rudin's Analysis](http://rads.stackoverflow.com/amzn/click/1259064786) which is more suited for Math majours than economics, so I recommend working through [Spivak's Calculus](http://rads.stackoverflow.com/amzn/click/0914098918) for a rigorous introduction to proofs and reviewing calculus concepts at the same time, in another's words, "This is no ordinary calculus book!"

Finally I will recommend a book that introduces a wide range of rigorous math intended for Economists [An Introduction to Mathematical Analysis for Economic Theory and Econometrics](http://rads.stackoverflow.com/amzn/click/0691118671) . This is what I will be reading this summer :D


---

