Advanced Mathematics for Economists
| Module title | Advanced Mathematics for Economists |
|---|---|
| Module code | BEE3054 |
| Academic year | 2023/4 |
| Credits | 15 |
| Module staff | Dr Stephen Nei (Convenor) |
| Duration: Term | 1 | 2 | 3 |
|---|---|---|---|
| Duration: Weeks | 0 | 11 | 0 |
| Number students taking module (anticipated) | 45 |
|---|
Module description
Summary:
This module is aimed at students who are considering a Masters and/or PhD in Economics. The module will cover a range of relevant mathematical tools and techniques that are typically required for further study in economics; the aim is to deepen and extend the mathematical preparation of 3rd year undergraduates by exposing them to rigorous higher level mathematics and providing them with the opportunity to develop proofs and apply new mathematical tools. Knowledge of elementary matrix theory and calculus is assumed.
The level of rigor will vary. Parts 1 and 2 will aim for thoroughness rather than for covering a huge range of material. Students should develop a feel for when a proof is complete and rigorous and when arguments are missing. In Part 3, emphasis is placed on learning how to quickly understand mathematical tools and be able to apply them, rather than on theoretical formalism. This is achieved sometimes at the expense of rigor. Where proofs are beyond the level of this course, references are given.
Additional Information:
Internationalisation
Mathematics is a global language, so the technical skills students acquire in this module can be used internationally.
Employability
By solving statistical mathematical problems and exercises, students are equipped with practical problem-solving skills, theoretical skills, and an understanding of mathematical relationships. All of these are highly valuable to employers.
Sustainability
All of the resources for this module are available on the ELE (Exeter Learning Environment).
Module aims - intentions of the module
This module is aimed at students who are considering a Masters and/or PhD in Economics. The module will cover a range of relevant mathematical tools and techniques that are typically required for further study in economics; the aim is to deepen and extend the mathematical preparation of 3rd year undergraduates by exposing them to rigorous higher level mathematics and providing them with the opportunity to develop proofs and apply new mathematical tools. Knowledge of elementary matrix theory and calculus is assumed.
The level of rigor will vary. Parts 1 and 2 will aim for thoroughness rather than for covering a huge range of material. Students should develop a feel for when a proof is complete and rigorous and when arguments are missing. In Part 3, emphasis is placed on learning how to quickly understand mathematical tools and be able to apply them, rather than on theoretical formalism. This is achieved sometimes at the expense of rigor. Where proofs are beyond the level of this course, references are given.
The assessment structure on this module is subject to review and may change before the start of the new academic year. Any changes will be clearly communicated to you before the start of the term and if you wish to change module as a result of this you can do so in the module change window.
Intended Learning Outcomes (ILOs)
ILO: Module-specific skills
On successfully completing the module you will be able to...
- 1. Understand and be able to do basic mathematical proofs
- 2. Demonstrate the ability to work with abstract mathematical concepts
- 3. Understand the mathematical aspects of economic modelling techniques
ILO: Discipline-specific skills
On successfully completing the module you will be able to...
- 4. Demonstrate the ability to read and work with current economic research papers
- 5. Critically analyse the logic of economic arguments
- 6. Work with economic models
ILO: Personal and key skills
On successfully completing the module you will be able to...
- 7. Develop logic and critical thinking
- 8. Develop and deepen higher level quantitative skills
Syllabus plan
This is an indicative outline: (further details will be available in week 1 of the module)
Part 1 (3 weeks)
- Numbers
- Sets
- Proofs and mathematical logic
In Part 1 we will provide the basics for the following material. The important properties of numbers and how they are described axiomatically (in particular, their order structure and completeness) will be discussed. Central notions of set theory will be developed and illustrated. Important methods of proofs (indirect proof, inductive proof) are illustrated in examples.
Part 2 (2 weeks)
- Set-theoretic Topology
- Fixed Points
- Sequences: Definition of Sequence and Subsequence, Bolzano-Weierstrass Theorem and Cauchy criterion
- Limits and Continuity: Definition of Continuity and Uniform Continuity, Intermediate Value, Differentiation
In Part 2 we will give a rigorous introduction to basic topological concepts (limit points, neighbourhoods, compact spaces, metric spaces etc.) and provide many examples of topological spaces. The emphasis is on teaching how to do rigorous proofs using abstract concepts.
Part 3 (5 weeks)
- Ordinary differential equations
- Eigenvectors and Eigenvalues
- First order differential equations systems:
- Other applications of mathematics to economics, such as discrete math and combinatorics.
In Part 3 we will introduce the most elementary notions of first and second differential equations. We will subsequently study systems of linear differential equations, their solutions in the various cases, stability conditions, phase diagrams and some economic applications. For this part only elementary matrix theory and basic calculus are needed.
Learning activities and teaching methods (given in hours of study time)
| Scheduled Learning and Teaching Activities | Guided independent study | Placement / study abroad |
|---|---|---|
| 33 | 117 | 0 |
Details of learning activities and teaching methods
| Category | Hours of study time | Description |
|---|---|---|
| Scheduled learning and teaching activity | 33 | Lectures |
| Guided independent study | 117 | Reading, research, reflection; preparation for lectures and assessments |
Formative assessment
| Form of assessment | Size of the assessment (eg length / duration) | ILOs assessed | Feedback method |
|---|---|---|---|
| Homework | Weekly sets | 1 -8 | Written and oral feedback/model solutions |
| Coursework proposal | 500 words | 1-8 | Written feedback |
Summative assessment (% of credit)
| Coursework | Written exams | Practical exams |
|---|---|---|
| 50 | 50 | 0 |
Details of summative assessment
| Form of assessment | % of credit | Size of the assessment (eg length / duration) | ILOs assessed | Feedback method |
|---|---|---|---|---|
| Coursework | 50 | 2,000 words | 1,3, 4, 5, 7 | Written and oral feedback |
| Examination | 50 | 2 hours | 4 - 6, 7 -8 | Written feedback |
Details of re-assessment (where required by referral or deferral)
| Original form of assessment | Form of re-assessment | ILOs re-assessed | Timescale for re-assessment |
|---|---|---|---|
| Coursework (50%) | 2,000 words (50%) | 1, 3, 4, 5, 7 | August/September re-assessment period |
| Examination (50%) | Examination (50%) (2 hours) | 1-8 | August/September re-assessment period |
Indicative learning resources - Basic reading
Basic Reading:
Parts 1 and 2: Logic, Set Theory, Topology
- John Nolt, Dennis Rohatyn and Achille Varzi: “Schaum's Outline of Logic”, McGraw-Hill; 2 edition (2011)
- Seymour Lipschutz: “Schaums Outline of General Topology”, McGraw-Hill; 1 edition (2011)
- Seymour Lipschutz: “Schaum's Outline of Set Theory and Related Topics”, McGraw-Hill; 2 edition (July 1, 1998)
Part 3: Differential Equations and Dynamic Optimisation
- Edward Dowling: “Schaum's Outline of Introduction to Mathematical Economics”,McGraw-Hill; 3 edition (2011)
- Knut Sydsaeter, Peter Hammond, Atle Seierstad, Arne Strom: “Further Mathematics for Economic Analysis” Prentice Hall; 2 edition (2008)
Indicative learning resources - Web based and electronic resources
ELE – College to provide hyperlink to appropriate pages
Indicative learning resources - Other resources
None
| Credit value | 15 |
|---|---|
| Module ECTS | 7.5 |
| Module pre-requisites | BEE2025 or BEE2026 or BEE1029 or BEE1034
|
| Module co-requisites | None |
| NQF level (module) | 6 |
| Available as distance learning? | No |
| Origin date | 01/09/2011 |
| Last revision date | 04/05/2023 |
