Mathematics for Economic Research
The module covers basic set theory and logic, and selected topics in advanced linear algebra and advanced real analysis at the level required for a PhD using mathematical methods. In the section on set theory the basic set theoretic operations are introduced, the notions of relations and functions as well as the basic axioms of set theory including the axiom of choice. The section on logic will introduce propositional logic, truth tables and basic first order logic. In the section on advanced linear algebra we will discuss abstract vector spaces, the existence of a basis of such a space, linear maps and their representations by matrices in the finite dimensional case, and the existence of Eigenvectors and Eigenvalues, with applications to dynamical systems. The section on advanced real analysis will discuss sequences and their convergence, completeness of the real number system, continuity of functions, topology on the Euclidian space, differentiability and Taylor series.
The whole content of this module is a neutral methodology that is applicable across disciplines and across geographic or national boundaries. It is taught by lectures with teaching and learning experience from many different countries.
All of the resources for this module are available on the ELE (Exeter Learning Environment).
The module will prepares for writing successfully a PhD at high academic standards.
Full module specification
|Module title:||Mathematics for Economic Research|
|Duration of module:||
Duration (weeks) - term 1: |
The module aims to make the students familiar with the rigorous standards of mathematical writing and doing proofs and arguments as required at the research level and to publish in leading peer-reviewed journals. The emphasis is hence on depth rather than on covering a wide range of topics.
ILO: Module-specific skills
- 1. Demonstrate and be able to derive rigorous mathematical proofs.
- 2. Demonstrate the ability to work with abstract mathematical concepts.
- 3. Compute the mathematical aspects of economic modelling techniques.
ILO: Discipline-specific skills
- 4. Demonstrate the ability to read and work with current economic research papers.
- 5. Critically analyze the logic of economic arguments.
- 6. Use and analyze economic models.
ILO: Personal and key skills
- 7. Solve logic and apply critical thinking.
- 8. Solve logic and apply higher level quantitative skills.
- 9. Apply essential research skills.
Learning activities and teaching methods (given in hours of study time)
|Scheduled Learning and Teaching Activities||Guided independent study||Placement / study abroad|
|32 hours||118 hours|
Details of learning activities and teaching methods
|Category||Hours of study time||Description|
|Contact hours||22||Lectures (2 hours per week)|
|Contact hours||10||Tutorials (1 hour per week)|
|Guided Independent Study||55 (5 per week)||Reading|
|Guided Independent Study||63 (approx. 6 hours per week)||Preparing problem set answers and preparing for examinations|
|Form of assessment||Size of the assessment (eg length / duration)||ILOs assessed||Feedback method|
|Homework||One set per week||1-9||Verbal in class|
Summative assessment (% of credit)
|Coursework||Written exams||Practical exams|
Details of summative assessment
|Form of assessment||% of credit||Size of the assessment (eg length / duration)||ILOs assessed||Feedback method|
|Presentation of homework solution||30||50 minutes||1-9||Verbal|
|Examination||70||2 hours||1-9||Detailed grading|
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|
|Presentation and Examination||Examination (100%) 2 hours||1-9||August reassessment period|
- Logic, Set Theory and proofs
- Vector spaces, basis, and dimension
- Abstract vector spaces and linear maps
- Eigenvectors and eigenvalues
- Dynamical systems
- Topology on the Euclidean space, completeness
- Properties of continuous functions
- Taylor polynomials
Indicative learning resources - Basic reading
Simon, CP and L. Blume: Mathematics for Economists, Part VI and VII, 1994, W.W. Norton & Company, New York, London
Rudin, W: Principles of Mathematical Analysis, 1978, McGraw Hill
Module has an active ELE page?
Last revision date