Research Methods I
This module provides an introduction to the techniques involved in optimization.
Full module specification
|Module title:||Research Methods I|
Only available to MRes Economics PhD pathway
|Duration of module:||
Duration (weeks) - term 1: |
This module aims to provide a thorough introduction to the techniques involved in optimisation required to take PhD level Economics courses. Topics include advanced calculus, dynamic programming, difference equations and linear algebra.
ILO: Module-specific skills
- 1. demonstrate and derive rigorous mathematical proofs.
- 2. work with abstract mathematical concepts.
- 3. solve economic optimisation problems.
ILO: Discipline-specific skills
- 4. read and work with current economic research papers.
- 5. critically analyse the logic of economic arguments.
- 6. use and analyse economic models.
ILO: Personal and key skills
- 7. demonstrate numeracy skills and handle logical and structured problem analysis.
- 8. demonstrate inductive and deductive reasoning.
- 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|
Details of learning activities and teaching methods
|Category||Hours of study time||Description|
|Scheduled learning and teaching activities||22||Lectures|
|Scheduled learning and teaching activities||10||Tutorials|
|Guided independent study||118||Reading, preparation for classes and assessments|
|Form of assessment||Size of the assessment (eg length / duration)||ILOs assessed||Feedback method|
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|
|Average of weekly problem sets||30||Weekly problem sets with 3 questions each||1-9||Oral/Written|
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|
|Problem sets and Examination||Examination 100% (2 hours)||1-9||August examination period|
- Basics of linear algebra: determinant, linear dependence and rank of a matrix, inverse of a matrix, determinant of a matrix, eigenvalues and eigenvectors, trace of a matrix, quadratic forms
- Calculus: differentiation, integration, Taylor expansion, concavity and convexity, quasi-concavity and quasi-convexity
- Optimization: unconstrained optimization, constrained optimization with equality constraints (Lagrange), constrained optimization with inequality constraints (Kuhn-Tucker)
- Comparative statics and fixed points: envelope theorem, implicit function theorem, correspondences, fixed point theorems
- Dynamic programming
- First-order differential equations
Indicative learning resources - Basic reading
- Knut Sydsæter, Peter Hammond, Arne Størm, and Andrés Carvajal (2016): Essential Mathematics for Economic Analysis, 5th edition, Pearson
- Knut Sydsaeter, Peter Hammond, Atle Seierstad, and Arne Strøm (2008): Further Mathematics for Economic Analysis, 2nd edition, Pearson
- Daniel Leonard and Ngo van Long (1991): Optimal Control Theory and Static Optimization in Economics, Cambridge University Press
- Jianjun Miao (2014): Economic Dynamics in Discrete Time, MIT Press
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