BAEcon Development Studies

Year of entry: 2023

Course unit details:Advanced Mathematics

Unit code ECON20071 10 Level 2 Semester 1 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 matrix algebra, and 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

Unit title Unit code Requirement type Description
Introductory Mathematics ECON10061 Pre-Requisite Compulsory
ECON20071 Prerequisites: ECON10061

ECON10061 Intro Maths

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 equations 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

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

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

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

• 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.

• Dynamics. Simple dynamics. Geometric Series. Linear difference equations

Teaching and learning methods

Synchronous activities (such as Lectures or Review and Q&A sessions, and tutorials), and guided self-study

Employability skills

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

Assessment methods

70% Exam (2h)

30% Mid-term Online Test (1h)

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 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

This text will be available as a free online textbook from the unit's Blackboard page.

Teaching staff

Staff member Role
Panagiotis Sousounis Unit coordinator