Year of entry: 2022
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Course unit details:
|Unit level||Level 1|
|Teaching period(s)||Semester 1|
|Available as a free choice unit?||Yes|
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.
A Level Maths or very good AS level
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.
The objectives of this course are that students will be able to:
- Solve simple linear equations, find roots a quadratic and understand the solution to non-linear equations.
- Understand functions, continuity and basic differentiation.
- Solve one and two-variable unconstrained and constrained optimisation problems using the Lagrangian method.
- Demonstrate their understanding of linear univariate difference equations.
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
- Analytical skills
- Problem solving
- Using library, electronic and online resources.Numeracy, time management, improving own learning.
30% Mid-Term Online Tests
70% Final Exam
- 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.
|Ralf Becker||Unit coordinator|
For every 10 course unit credits we expect students to work for around 100 hours. This time generally includes any contact times (online or face to face, recorded and live), but also independent study, work for coursework, and group work. This amount is only a guidance and individual study time will vary