# 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

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'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. Commented Apr 18, 2016 at 13:54
• @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? Commented Apr 18, 2016 at 14:01
• 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 Commented Apr 18, 2016 at 14:23
• @Sunhwa OK. I got it. Thanks for your advice ;) Commented Apr 18, 2016 at 14:39
• A good book is Mathematics for Economists by Simon and Blume Commented Apr 19, 2016 at 16:23

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

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.

• 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). Commented Apr 22, 2016 at 13:29

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, 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 which is more suited for Math majours than economics, so I recommend working through Spivak's Calculus 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 . This is what I will be reading this summer :D