Undergraduate Course: Advanced Mathematical Economics (Visiting Students) (ECNM10124)
Course Outline
| School | School of Economics |
College | College of Arts, Humanities and Social Sciences |
| Credit level (Normal year taken) | SCQF Level 10 (Year 3 Undergraduate) |
Availability | Part-year visiting students only |
| 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. |
| 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 |
|
Co-requisites | |
| Prohibited Combinations | Students MUST NOT also be taking
Advanced Mathematical Economics (ECNM10085)
|
Other requirements | Only available to visiting students. Edinburgh-based students can enrol on ECNM10085. |
Information for Visiting Students
| Pre-requisites | Visiting students must have an equivalent of at least 4 semester-long Economics courses at grade B or above for entry to this course. This MUST INCLUDE courses in Intermediate Macroeconomics (with calculus); Intermediate Microeconomics (with calculus); and Probability and Statistics. If macroeconomics and microeconomics courses are not calculus-based, then, in addition, Calculus (or Mathematics for Economics) is required. |
| High Demand Course? |
Yes |
Course Delivery Information
|
| Academic year 2026/27, Part-year visiting students only (VV1)
|
Quota: 100 |
| Course Start |
Semester 1 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
200
(
Lecture Hours 20,
Seminar/Tutorial Hours 20,
Summative Assessment Hours 3,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
153 )
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| Assessment (Further Info) |
Written Exam
90 %,
Coursework
10 %,
Practical Exam
0 %
|
| Additional Information (Assessment) |
- Weekly homework 10%
- 3 Hour Examination in December 90%
Coursework involves weekly homework. Homework is due each week (except the first), and students get the full 10% if they attempt at least 5 of the 8, and lose 2% for each subsequent homework missed. |
| Feedback |
It is very important that students attend all tutorials, to receive feedback about their work and thinking. |
| No Exam Information |
Learning Outcomes
On completion of this course, the student will be able to:
- Demonstrate 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.
- Demonstrate communication skills in order to critique, create and communicate understanding and to collaborate with and relate to others.
- Develop 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.
- Acquire practical/technical skills such as, modelling skills (abstraction, logic, succinctness), qualitative and quantitative analysis and general IT literacy.
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Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | Not entered |
Contacts
| Course organiser | Dr Andrew Clausen
Tel: (0131 6)51 5131
Email: Andrew.Clausen@ed.ac.uk |
Course secretary | |
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