# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2018/2019

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DRPS : Course Catalogue : School of Economics : Economics

# 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 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.
 Pre-requisites Co-requisites Prohibited Combinations Other requirements None
 Pre-requisites None
 Academic year 2018/19, 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 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 /» 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) 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.
 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
 Graduate Attributes and Skills Not entered Keywords ADVMath
 Course organiser Dr Andrew Clausen Tel: (0131 6)51 5131 Email: Andrew.Clausen@ed.ac.uk Course secretary Miss Sophie Bryan Tel: (0131 6)50 9905 Email: Sophie.Bryan@ed.ac.uk
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