## What maths do I need before I start?

This depends on where you are going to study it, different institutions have different levels of mathematical emphasis. Core undergraduate level economics does not require a massive amount of maths, it is mainly a case of knowing how to manipulate algebra, understanding rules of logs and indices, and being comfortable with calculus. However at some institutions (LSE, Cambridge, UCL etc) they will expect you to take more advanced maths classes as well as your economics modules. This is because the more advanced texts (which you are unlikely to meet unless you go on to MSc or PhD) rely on some more advanced mathematics so they are preparing you for that. The institutions that expect you to do more advanced maths will be the ones who say they prefer you to have Further Maths A level.

But as I say, the actual maths you will need to get through undergraduate level economics is not too advanced so if maths isn’t your strongest point, don’t panic. A level will be sufficient. If you haven’t done A level maths or you struggled a bit then you need to do some preparation in the summer beforehands.

The important thing is to get the ‘fear’ of mathematics out of your system. You don’t want to be picking up an economics textbook, seeing a long set of algebraic equations and get scared off. It is just a ‘language’ that you need to learn.

I would definitely recommend spending the summer before you start university, getting on top of some topics. This is something to actually “do”, not just think about and end up putting it off till the last couple of weeks when you won’t have time to do any meaningful work. Get a plan, spend a bit of money on a book, and do a topic or so each week so you arrive at the start of your course confident in your maths and having not allowed it to go rusty over the summer.

I would recommend getting hold of one of these text books (an earlier edition, from amazon used books, will be fine, so you can save money that way, there is no need to have the latest shiny edition).

**MATHEMATICS FOR ECONOMICS AND BUSINESS: Ian Jacques**

This is the best book to start with if you haven’t done A level maths or if you are not very confident. It teaches you from scratch, all you really need for this is GCSE level. This one is a book that you can actually work through from cover to cover over the summer, doing all the exercises (the older editions tend to have answers in the back, newer ones you have to get their online access which you have to pay for!). The good thing about this is it is like A level standard but only picks out the parts of A level which you will need for economics. But even though it is seen as the ‘easy’ book, if you start your course with the level of knowledge that is in Jacques, then you will be fine.

**MATHS FOR ECONOMICS: Geoff Renshaw**

A bigger and meatier book than Jacques, this one is popular with universities as a core maths intro text but I find Jacques is more readable.

**MATHEMATICS FOR ECONOMISTS, AN INTRODUCTORY TEXTBOOK: Malcolm Pemberton and Nicholas Rau**

This is the one to get if you’ve done Maths or Further Maths and are more confident in your ability. This is a pretty good book to be honest. It is written by two UCL professors and is the recommended pre-reading for UCL’s MSc, so there is plenty of material in here. It starts from scratch again, covering all the basic topics you need, but has more advanced material that Jacques and Renshaw leave out, so this one will be more rewarding for students who want to stretch themselves or if you are going to one of the mathematical institutions and want to prepare for the maths classes there. It is a nice concise book which explains what you need with minimum words although because of that it kind of assumes a certain confidence with numbers and familiarity with A-level concepts. This is another one you can ‘work through’ in the summer, if you are good at maths or have taken Further Maths A-level, get this one instead of Jacques as your summer workbook. This will be an invaluable reference book during your course as well.

**FUNDAMENTAL METHODS OF MATHEMATICAL ECONOMICS: Alpha Chiang and Kevin Wainwright**

Kind of seen as the definitive text for university level maths in economics, this covers the basic topics but goes a long way beyond, this book is valid right up to MSc level. Probably will be the text that the more mathematical universities use for their maths classes. If you are good at maths and want to challenge yourself this will be a good investment, and allows you a bit of a sneak preview at what the more advanced levels of maths are like if you take economics further.

**MATHEMATICS FOR ECONOMISTS: Carl Simon and Lawrence Blume**

Pretty much everything I have said about Chiang and Wainwright applies to Simon and Blume, the two are pretty much interchangeable in standard. Some of the more maths oriented places will use Simon and Blume, some will use Chiang and Wainwright. Either way this is a book which goes up to MSc level so is suitable for the more advanced student. Students who would say maths isn’t their strong point and just want to do undergrad level economics should get Jacques, Renshaw or Pemberton/Rau rather than these last two as they might find the later chapters rather ‘off putting’.

Topics you need to know before you start:

**Sets and functions**

This is something you might have been introduced to earlier at school in GCSE or even before. You need to know concepts like set, domain, range, mapping, and you need to understand the concept of what a ‘function’ is, because you’ll often be dealing with formulae expressed in terms of a function of which you don’t know the specific form. Learn what a continuous or discontinuous function is, whether a function has an inverse, what a monotonic function is, when a function is concave or convex.

**Basic financial mathematics**

Simple stuff which has a lot of practical use in using your own personal finance – learn how to do percentages, including how to work out percentage gain/losses, and work out simple and compound interest, continuous compounding (you will need to have learned the exponential function, e, for this). Make sure you can do questions which involve annual interest rates being compounded at different intervals (eg not just annually, learn how to solve it when it’s monthly or weekly). These are popular in the type of maths questions that crop up on graduate scheme tests.

**Linear equations**

This is basic algebra. Make sure you’re comfortable rearranging equations as you will do it all the time in economics especially in macro. Get straight the order in which you do different operations (eg brackets, indices, division/multiplication, addition/subtraction), if you do operations in the wrong order you will always get wrong answers where you won’t be able to understand where you’ve gone wrong. Also make sure you know how to sketch graphs of linear equations, when you start doing microeconomics you will use a lot of linear demand and supply functions, so you need to know where the intercept is, what the slope of the line is, which way it slopes. You need to know how to solve simultaneous equations, eg three equations, three unknowns, solve them by substitution or elimination. As well as equations get familiar with inequalities.

**Quadratic equations**

You need to be able to solve these by factorisation where appropriate, or using the quadratic formula to find the roots. Again make sure you can sketch graphs of quadratics, know whether they are n or u shaped, where they intersect axes, and where they have a minimum or maximum point.

**Indices and Logarithms**

Understand what an index (‘power’) is and what the laws of indices are, and how you deal with indices when they come up in manipulating algebra. Logs will be really useful in a lot of situations, there are a few simple rules you need to get totally straight. You need to know what e is (as in the exponential function).

**Sequences**

3,5,7,9,11…whats the next number? Thats an arithmetic progression. What about 2,6,18,54….? That’s a geometric progression. You need to be able to recognise when progressons tend to a particular point and when they tend to infinity, when they converge and when they ‘explode’. Learn the formulae for summing an arithmetic or geometric progression. These come up all the time when you are dealing with investments and issues of intertemporal choice, and in early macro courses when you deal with ‘multipliers’.

**Differentiation**

Calculus is a big topic in economics. Microeconomics uses a lot of calculus. Learn the idea of what differentiation is, learn the different types of notation used to show the derivative, learn how to differentiate a simple function and then the standard rules, addition rule, subtraction rule, product rule, quotient rule, chain rule. Often you will have to combine these rules together to differentiate something (the chain rule is especially useful). You need to know how to differentiate the exponential function and natural logs. Know how to do a first and second derivative. You need to know how to find maximum or minimum points of a function by differentiation (economics is often about optimising things, maximising profit or minimising cost, so this comes up all the time). You should also learn partial and implicit differentiation, things like this needs to become second nature when you face it in economics (as though you were just doing basic adding and subtracting).

**Integration**

If you can differentiate its pretty straightforwards to learn how to integrate, its basically the process in reverse. Make sure you can solve indefinite and definite integrals and find the area under a curve.

**Matrices**

Also known as “Linear Algebra”. Matrices can be fiddly to work with at first but they are very useful. Learn basic vector arithmetic and the laws of vector arithmetic which always hold. Learn how to add and multiply matrices, what the identity matrix is, what a rank and determinant and inverse of a matrix are.