**Refresher Mathematics** for Economics 2021-22

*the master-economist must possess a rare combination of gifts. He must reach a high standard in several different directions and must combine talents not often found together. He must be mathematician,
historian, statesman, philosopherâ€”in some degree. He must understand symbols and speak in words.* â€” John Maynard Keynes

This is a pre-sessional resource to refresh mathematical skills and techniques in preparation for an undergraduate degree in economics.

** 1. Precalculus**

Refresh the essential mathematical skills that you will need throughout an economics course.

### 1.0. Why do economists need mathematical skills?

** 2. Univariate Calculus**

Refresh your knowledge about differentiation and integration of functions of one variable and how to use derivatives to understand the behaviour of functions, such as when they are increasing or decreasing, convex or concave, and where they might have local or global extremes.

2.1. Functions & inverses 2.2. Definition of derivative 2.3. Rules of differentiation 2.4. Slope, curvature and optimisation 2.5. Integrals### 2.0. Why is univariate Calculus useful for Economics?

** 3. Multivariate Calculus**

Refresh your knowledge about differentiation of functions of more than one variable and how to find partial derivatives or slopes of tangents to level curves.

3.1. Partial derivatives 3.2. Implicit differentiation### 3.0. How do economists use multivariate calculus?

** 4 Sequences and Series**

Refresh your knowledge about sequences and series (sums) of numbers. In particular, how to deal with arithmetic and geometric sequences and series.

4.1. Sequences 4.2. Series### 4.0. When can sequences and series help economists?

** 5. Matrices**

Refresh your knowledge about matrix arithmetic, determinants, inverses, and the relationship between matrices and systems of simultaneous linear equations.

5.1. Matrix arithmetic 5.2. Determinants & inverses 5.3. Matrices & simultaneous linear equations