Postgraduate Course: Advanced Mathematical Economics (ECNM11072)
Course Outline
School  School of Economics 
College  College of Arts, Humanities and Social Sciences 
Credit level (Normal year taken)  SCQF Level 11 (Postgraduate) 
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. 
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, BolzanoWeierstrass 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,
quasiconvex and quasiconcave 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 daybyday. 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 BenvenisteScheinkman theorem.

Entry Requirements (not applicable to Visiting Students)
Prerequisites 

Corequisites  
Prohibited Combinations  
Other requirements  None 
Information for Visiting Students
Prerequisites  None 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2023/24, Available to all students (SV1)

Quota: None 
Course Start 
Semester 1 
Timetable 
Timetable 
Learning and Teaching activities (Further Info) 
Total Hours:
200
(
Lecture Hours 20,
Seminar/Tutorial Hours 18,
Summative Assessment Hours 6,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
152 )

Assessment (Further Info) 
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %

Additional Information (Assessment) 
Coursework (20%), Exam (80%).«br /»
«br /»
 Mathematical Economics Project 20%«br /»
 3 Hour Examinations in December and May 80% (using the best mark)«br /»
«br /»
While we recommend that most Continuing Professional Development students take this as a fullyear course, this course is also available in a onesemester format (without the May exam). For our internal recordkeeping purposes, we call this option 'partyear visiting student' (because we offer the same format to exchange students), even though this is a Continuing Professional Development course.«br /»

Feedback 
All tutorials will involve problem solving, and opportunities for formative feedback.

Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S1 (December)  Advanced Mathematical Economics Class Exam  3:00   Main Exam Diet S2 (April/May)   3:00  
Learning Outcomes
Mathematical maturity, i.e. the ability to: distinguish between definitions, conjectures, theorems, and proofs, generalise and specialise theorems and proofs, devise counterexamples, and determine whether objects conform to definitions and conditions of theorems. Experience in applying mathematical tools to derive economic conclusions.

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

Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  ADVMath 
Contacts
Course organiser  Dr Andrew Clausen
Tel: (0131 6)51 5131
Email: 
Course secretary  Ms Grace Oliver
Tel:
Email: 

