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# BAEcon Economics and Social Statistics / Course details

Year of entry: 2021

## Course unit details:Adv Maths - BAEcon & BSc Econ

Unit code ECON10071 10 Level 1 Semester 1 Economics Yes

### Overview

This unit provides students with the essential mathematical toolkit required by economics students. At the core of the unit are constrained, multivariate optimisation problems. Such problems form a core element of many economics units and students who took Advanced Mathematics will be familiar with the required solution techniques.

Students will also be introduced to the principles of modelling dynamic variables. Simple difference equations will be introduced to model the rate of change of variables.

Students will be provided with detailed material through lectures, tutorial, reading and online videos. A discussion board will allow students to receive frequent feedback on their understanding.

### Pre/co-requisites

A Level Maths or very good AS level

### Aims

The aim of this course is to introduce mathematical techniques useful in the economic and social sciences to those students who have the appropriate advanced mathematical background.

### Learning outcomes

The objectives of this course are that students will be able to:

1. Solve simple linear equations, find roots a quadratic and understand the solution to non-linear equations.
2. Understand functions, continuity and basic differentiation.
3. Solve one and two-variable unconstrained and constrained optimisation problems using the Lagrangian method.
4. Demonstrate their understanding of linear univariate difference equations.

### Syllabus

The preliminary syllabus is organized around the following five Learning Modules (LM0-LM4).

LM0: Preliminaries and Pre-requisites. A review of your mathematical background and some observations on logic

LM1: Functions & Univariate Calculus. Functions, continuity. Roots of equations. Limits and basic differentiation. Stationary points and optimisation. Concavity and convexity.

LM2: Dynamics. Simple dynamics. Geometric Series. Linear difference equations

LM3: Vectors and Matrices. An introduction to vectors and matrices: their mathematical manipulation - addition, multiplication. Inverse matrix. Determinants. Rank. Quadratic Forms.

LM4: Bivariate Functions

Surfaces in 3D, contours. Partial functions and partial differentiation: the Jacobian and Hessian.
Optimisation; saddle points. Concavity/convexity. Finding maxima/minima of functions of two variables subject constraints; e.g., maximising utility subject to a budget constraint.

### Teaching and learning methods

Lectures and exercise classes.

### Employability skills

Analytical skills
Problem solving
Other
Using library, electronic and online resources.Numeracy, time management, improving own learning.

### Assessment methods

30% Mid-Term Online Tests

70% Final Exam

### Feedback methods

• Mock exam.
• Online quizzes.
• Tutorial feedback.
• PASS sessions.
• Office hours.
• Discussion boards.

Detailed prescribed reading is provided on the BLACKBOARD site.

The ESSENTIAL TEXT (available from Blackwell University Bookshop, Oxford Road, Manchester) is:

- ECON10071 Advanced Mathematics 2nd Edition

A Pearson Custom Publication

Compiled by Mario Pezzino

This text has been compiled specifically for this course from three sources:

Essential Mathematics for Economic Analysis (3rd Edition), by Knut Sydsæter and Peter Hammond

Further Mathematics for Economic Analysis (2nd Edition), by Knut Sydsæter, Peter Hammond, Atle Seierstad and Arne StrØm

A Guide to Game Theory, by Fiona Carmichael

The material covered is standard material and students can refer to many different textbooks and online resources for support.

### Study hours

Independent study hours
Independent study 0

### Teaching staff

Staff member Role
Ralf Becker Unit coordinator