Undergraduate Course: Advanced Mathematical Economics (Continuing Professional Development) (ECNM10097)
|School||School of Economics
||College||College of Humanities and Social Science
|Credit level (Normal year taken)||SCQF Level 10 (Year 4 Undergraduate)
||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)
||Full-year visiting students (Continuing Professional Development students)«br /»
Coursework (10%) Degree exam (90%).«br /»
Coursework involves weekly homeworks. There would be homework due each week (except the first), and students would get the full 10% if they attempt at least 6 of the 9, and lose 2% for each subsequent homework missed. «br /»
There will be two exams: one in the December Diet and one in the April/May Diet. Candidates will be awarded the maximum of the marks obtained in these exams.«br /»
Part-year visiting students (Continuing Professional Development students)«br /»
- Weekly homework 10%«br /»
- Mathematical Economics Project 45% (optional)«br /»
- 3 Hour Examination in December 45%«br /»
Coursework involves weekly homeworks. There would be homework due each week (except the first), and students would get the full 10% if they attempt at least 6 of the 9, and lose 2% for each subsequent homework missed. The Mathematical Economics Project is worth 45%, but it is optional and only counts towards the final grade if this is favourable to the student. The examination in December is three hours.«br /»
- - - - - «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. 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 (Continuing Professional Development) (ECNM10097)||3:00|
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.
* 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
||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.
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.
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.
|Course organiser||Dr Andrew Clausen
Tel: (0131 6)51 5131
|Course secretary||Mr Mathieu Donner
Tel: (0131 6)51 5958