Undergraduate Course: Advanced Mathematical Economics (ECNM10085)
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  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.

Information for Visiting Students
Prerequisites  Visiting students must have an equivalent of at least 4 semesterlong 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 calculusbased, then, in addition, Calculus (or Mathematics for Economics) is required. 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2024/25, Available to all students (SV1)

Quota: 100 
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
90 %,
Coursework
10 %,
Practical Exam
0 %

Additional Information (Assessment) 
Coursework (10%) Degree exam (90%).
Coursework involves weekly homework. Homework is due each week (except the first), and students get the full 10% if they attempt at least 6 of the 9, and lose 2% for each subsequent homework missed.
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.
Partyear visiting students only (VV1)
 Weekly homework 10%
 Mathematical Economics Project 40% (optional)
 3 Hour Examination in December 50% (90% of the optional project is not undertaken)
Coursework involves weekly homework. Homework is due each week (except the first), and students 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 40%, 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. 
Feedback 
It is very important that students attend all tutorials, to receive feedback about their work and thinking. 
Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S1 (December)   3:00   Main Exam Diet S2 (April/May)   3:00  

Academic year 2024/25, Partyear visiting students only (VV1)

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 3,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
155 )

Assessment (Further Info) 
Written Exam
50 %,
Coursework
50 %,
Practical Exam
0 %

Additional Information (Assessment) 
Coursework (10%) Degree exam (90%).
Coursework involves weekly homework. Homework is due each week (except the first), and students get the full 10% if they attempt at least 6 of the 9, and lose 2% for each subsequent homework missed.
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.
Partyear visiting students only (VV1)
 Weekly homework 10%
 Mathematical Economics Project 40% (optional)
 3 Hour Examination in December 50% (90% of the optional project is not undertaken)
Coursework involves weekly homework. Homework is due each week (except the first), and students 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 40%, 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. 
Feedback 
It is very important that students attend all tutorials, to receive feedback about their work and thinking. 
Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S1 (December)   3:00   Resit Exam Diet (August)   3:00  
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 counterexamples, 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 taskmanagement, timemanagement, 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.

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 
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, selfevaluation and selfimprovement.
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 timemanagement.
E4. The ability to work effectively with others, capitalising on their different thinking. 
Additional Class Delivery Information 
10 * 2 hour lectures
9 * 2 hour tutorials 
Keywords  AdvMath 
Contacts
Course organiser  Dr Andrew Clausen
Tel: (0131 6)51 5131
Email: Andrew.Clausen@ed.ac.uk 
Course secretary  Miss Rico Chen
Tel:
Email: rico.chen@ed.ac.uk 

