Maths books review for graduate economics

I've covered pretty much half of Pemberton and Rau's 'Mathematics for Economists' and I'm a fresher in an undergrad course that is only 50% economics. Do you think I'd have the necessary prerequisites for a 1 year MSc Econ programme at a top university by the time I graduate?

To provide some context I'm at a top 5 university for economics, and will be taking an applied economics module next year (intro econometrics module) and in my 3rd year I will be taking a mathematical economics and econometrics course. Of course in addition to that my other economics modules (micro, macro, stats) are maths heavy too.

The maths I've covered so far is: vectors, matrices, square matrices, inverse and rank, systems of linear equations, determinants, quadratic forms, partial differentiation and its applications, homogenous functions, implicit relations, isoquants and indifference curves, critical points, global optima, concavity and non-negativity constraints, constrained optimisation and its applications, differential forms and difference equations. And I find it relatively easy (hoping for a 1st)

I know this is a bit off subject but I'd be grateful for your opinion And it might even stimulate further discussion about textbooks/prerequisites for a master's

Oh, and may I add that Pemberton and Rau if very clear and easy to understand. I'd definitely recommend it.

Dear RocknRap, this is not the goal of this particular thread (evaluate admission), you can creat your own thread about it and you'll receive a lot of precious comments there including mine of course .

Thank you for your review on P&R.

I think it's important to realise that every textbook is written in a different style, and while there are many that contain primarily the same content, some will suit your learning style and some won't.

From your list, I'm not a fan of Fundamental Methods of Mathematical Economics by Chiang. It was one of the recommended texts in my first year and I found it too much like a story and far too chatty.

I really liked EMEA by Sydsaeter and Hammond. It's a nice cook-book of sorts. I used it as my main text in first year since I felt its style was most akin to A-Level Maths, which of course I'd just come from doing.

It really depends on how mathematical your postgraduate programme is, however. Increasingly, the better your pure mathematical knowledge, the better prepared you will be for a Masters programme.

Although these are texts I am yet to use, I have been recommended them:
An Introduction to Mathematical Analysis for Economic Theory and Econometrics
Calculus: Concepts and Methods
Matrix Algebra by Abadir

For econometrics at the PhD level (or really good master's, e.g. LSE), it doesn't hurt to read real math books and not mathematics/calculus/matrix stuff for economists/engineers/housewives.

For linear algebra (in abstract vector spaces), one good place to start is Friedberg/Insel/Spense. For real analysis, a good introductory text is Bartle and Sherbert. One can then move on to more advanced texts such as Folland for (graduate) real analysis. For probability and statistics, standard texts include Hogg/Craig and Berger/Casella. These latter texts are not really rigorous but they are a good source of worked examples and the writing is clear.

Surely that wouldn't be the best way to go about it. It's like telling a 1st year economics students to read/use the same maths textbook as a maths students. Fair enough, there's quite a lot of maths involved in economics and some topics taught to maths student will be taught to an economics student. But surely topics like discrete maths, dynamics etc will be useless/unhelpful for an undergraduate economist.

And another thing to consider is economics is applied maths. You're not going to pass an economics degree by just solving maths problems without understanding the economics concept behind it.

I think it must be school specific. Some schools may want to put emphasis on one thing, others on the other, you have to know what they expect.
Also, to make this kind of evaluation one has to be very well familiar with all these books, or at least most. I do have Pemberton and Rau, and they seem ok, but I did not read any of the others, so I can not comment on them either way. I tried to use Schaum for my Discrete Math, though, and they did not help much, to be honest.

Yes Pemberton and Rau is good. Well written, friendly, covers most math needed, but I still believe it lacks of proofs and very tough problems.

I think that to warm yourself before going to another rigorous text is splendid and is perfect for if you forget something while you are studying, but to help you write maths in your thesis....mmmmm I am afraid that it is not enough.

I disagree. I think the sooner we get students on pure mathematics modules in calculus/analysis/linear algebra, the better. A pure mathematics module will give you a deeper and more profound understanding of the tools you're using, and further I feel they improve your overall mathematical ability when compared with mathematics for economics modules.

A prime example being log-linearised models - so often are they used in economics, yet at the same time they provide not only inefficient estimates but also inconsistent estimates (in the presence of heteroscedasticity) due to Jensen's inequality. Jensen's inequality has been known since 1906, and the resulting consequences soon thereafter, yet it's only within the last seven or so years that economists have started to look into the impact this is having on economic models.

As for knowing what sort of maths to use/learn, well true, but it's common sense to only focus on the relevant topics. You have lecturers who can guide you in this.

In regard to your final point, it's debatable, and depends entirely on your programme and university. That said, I agree not knowing the underlying economic theory would make for a very bad economist.

My concern, and or issue, is that far too often we're producing wishy-washy economists who know the 'theory' but don't understand the mathematics behind the models. A major problem is that increasingly we are finding applied economists who use log-linear models and don't account for Jensen's inequality, or they jump in front of Stata and run rreg for a robust regression, but fail to realise the strict assumptions they're placing on their data and model which often don't hold, thus again providing for inefficient/inconsistent estimates.

So I think, while you're a bad economist if you don't know the theory, in some respects you're potentially a worse economist if you don't understand the models deeply enough, or the mathematical/econometric techniques with which you test your hypotheses.