Postgraduate Course: Advanced Mathematical Economics (ECNM11072)
|School||School of Economics
||College||College of Humanities and Social Science
|Credit level (Normal year taken)||SCQF Level 11 (Postgraduate)
||Availability||Available to all students
|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.
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
* 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.
Entry Requirements (not applicable to Visiting Students)
||Other requirements|| None
Information for Visiting Students
Course Delivery Information
|Academic year 2018/19, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 20,
Seminar/Tutorial Hours 18,
Summative Assessment Hours 6,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
||Coursework (20%), Exam (80%).«br /»
- Mathematical Economics Project 20%«br /»
- 3 Hour Examinations in December and May 80% (using the best mark)«br /»
While we recommend that most Continuing Professional Development students take this as a full-year course, this course is also available in a one-semester format (without the May exam). For our internal record-keeping purposes, we call this option 'part-year visiting student' (because we offer the same format to exchange students), even though this is a Continuing Professional Development course.«br /»
||All tutorials will involve problem solving, and opportunities for formative feedback.
||Hours & Minutes
|Main Exam Diet S1 (December)||Advanced Mathematical Economics Class Exam||3:00|
|Main Exam Diet S2 (April/May)||Advanced Mathematical Economics Degree Exam||3:00|
| 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.
* 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
|Graduate Attributes and Skills
|Course organiser||Dr Andrew Clausen
Tel: (0131 6)51 5131
|Course secretary||Miss Sophie Bryan
Tel: (0131 6)50 9905