Undergraduate Course: Advanced Mathematical Economics (Continuing Professional Development) (ECNM10097)
Course Outline
| School | School of Economics |
College | College of Arts, Humanities and Social Sciences |
| Credit level (Normal year taken) | SCQF Level 10 (Year 4 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 20 |
ECTS Credits | 10 |
| Summary | This course is about the advanced mathematical tools that are used in economics research. Each mathematical topic is explored in the context of an important economic problem.
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| Course description |
The topics covered vary from year to year.
An example curriculum would be the following mathematics concepts illustrated in the context of general equilibrium theory:
- Naive Set Theory. This is the language of mathematics, and is widely used by economists. This is important for making precise hypotheses, such as "in every equilibrium, real wages increase over time", and for verifying these hypotheses with logically sound proofs. The main concepts are: sets, functions, logical connectives, quantifiers, countability, induction, proof by contradiction.
- Real Analysis and Metric Spaces. This branch of mathematics focuses on continuity and nearness (topology) while putting geometric concepts like distance and angles into the background. These ideas are useful for determining whether an optimal decision is possible, whether an equilibrium of an economy exists, and determining when optimal decisions change drastically when circumstances change. The main concepts are: open sets, continuity, limits, interior, boundary, closure, function spaces, sup metric, Cauchy sequences, connected spaces, complete spaces, compact spaces, Bolzano-Weierstrass theorem, Banach fixed point theorem, Brouwer fixed point theorem.
- Convex Analysis. This branch of geometry focuses on comparing extreme points and intermediate points that lie between extremes. These tools are useful for determining whether there is one or several optimal decisions in a particular situation, and determining in which direction optimal choices move when circumstances change. Convex analysis is related to the economic notions of increasing marginal cost and decreasing marginal benefit. The main concepts are: convex sets, convex and concave functions, quasi-convex and quasi-concave functions, supporting hyperplane theorem, separating hyperplane theorem.
- Dynamic Programming. This branch of mathematics is about breaking up a complicated optimisation problem involving many decisions into many simple optimisation problems involving few decisions. For example, a lifetime of choices can be broken up into simple choices made day-by-day. The main concepts are: value functions, Bellman equations, Bellman operators.
- Envelope Theorem. This is a calculus formula for calculating marginal values, such marginal benefit of saving money. The main concepts are: differentiable support functions, the Benveniste-Scheinkman theorem.
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
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Co-requisites | |
| Prohibited Combinations | |
Other requirements | None |
Information for Visiting Students
| Pre-requisites | None |
| High Demand Course? |
Yes |
Course Delivery Information
| Not being delivered |
Learning Outcomes
On completion of this course, the student will be able to:
- Mathematical maturity, i.e. the ability to: distinguish between definitions, conjectures, theorems, and proofs, generalise and specialise theorems and proofs, devise counter-examples, and determine whether objects conform to definitions and conditions of theorems. Experience in applying mathematical tools to derive economic conclusions.
- Research and investigative skills such as problem framing and solving and the ability to assemble and evaluate complex evidence and arguments.
- Communication skills in order to critique, create and communicate understanding and to collaborate with and relate to others.
- Personal effectiveness through task-management, time-management, teamwork and group interaction, dealing with uncertainty and adapting to new situations, personal and intellectual autonomy through independent learning.
- Practical/technical skills such as, modelling skills (abstraction, logic, succinctness), qualitative and quantitative analysis and general IT literacy.
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Reading List
Indicative readings:
* Boyd and Vandenburghe (2004), "Convex Optimization", Cambridge University Press.
* Luenberger (1968), "Optimization by Vector Space Methods", Wiley.
* de la Fuente (2000), "Mathematical Methods and Models for Economists", Cambridge University Press.
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Additional Information
| Graduate Attributes and Skills |
Research and Inquiry
B1. The ability to identify, define and analyse theoretical and applied economic problems and identify or devise approaches to investigate and solve these problems.
B3. The ability to critically assess existing understanding of economic and social issues, the limitations of that understanding and the limitations of their own knowledge and understanding of those issues.
B4. The ability to question the principles, methods, standards and boundaries of economic knowledge
Personal and Intellectual Autonomy
C1. The ability to be independent learners who take responsibility for their own learning, and are committed to continuous reflection, self-evaluation and self-improvement.
C4. The ability to collaborate and debate effectively to test, modify and strengthen their own views.
Communication
D1. The ability to make effective use of oral, written and visual means to critique, create and communicate understanding.
D2. The ability to further their own learning through effective use of feedback.
D3. The ability to use communication as a tool for collaborating and relating to others.
Personal Effectiveness
E1. The ability to manage tasks and also skills in time-management.
E4. The ability to work effectively with others, capitalising on their different thinking. |
| Keywords | AdvMath |
Contacts
| Course organiser | Dr Andrew Clausen
Tel: (0131 6)51 5131
Email: Andrew.Clausen@ed.ac.uk |
Course secretary | Mr Mathieu Donner
Tel: (0131 6)51 5958
Email: Mathieu.Donner@ed.ac.uk |
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