# Mathematics for Economic Research

## Module description

The module covers basic set theory and logic, and selected topics in advanced linear algebra and advanced real analysis at the level required for a PhD using mathematical methods. In the section on set theory the basic set theoretic operations are introduced, the notions of relations and functions as well as the basic axioms of set theory including the axiom of choice. The section on logic will introduce propositional logic, truth tables and basic first order logic. In the section on advanced linear algebra we will discuss abstract vector spaces, the existence of a basis of such a space, linear maps and their representations by matrices in the finite dimensional case, and the existence of Eigenvectors and Eigenvalues, with applications to dynamical systems. The section on advanced real analysis will discuss sequences and their convergence, completeness of the real number system, continuity of functions, topology on the Euclidian space, differentiability and Taylor series.

Internationalisation

The whole content of this module is a neutral methodology that is applicable across disciplines and across geographic or national boundaries. It is taught by lectures with teaching and learning experience from many different countries.

Sustainability

All of the resources for this module are available on the ELE (Exeter Learning Environment).

Employability

The module will prepares for writing successfully a PhD at high academic standards.

## Full module specification

Module title: Mathematics for Economic Research BEEM132 M 2018/9 Professor Dieter Balkenborg - Convenor 15 7.5 None. None. Duration (weeks) - term 1: 11

## Module aims

The module aims to make the students familiar with the rigorous standards of mathematical writing and doing proofs and arguments as required at the research level and to publish in leading peer-reviewed journals. The emphasis is hence on depth rather than on covering a wide range of topics.

## ILO: Module-specific skills

• 1. Demonstrate and be able to derive rigorous mathematical proofs.
• 2. Demonstrate the ability to work with abstract mathematical concepts.
• 3. Compute the mathematical aspects of economic modelling techniques.

## ILO: Discipline-specific skills

• 4. Demonstrate the ability to read and work with current economic research papers.
• 5. Critically analyze the logic of economic arguments.
• 6. Use and analyze economic models.

## ILO: Personal and key skills

• 7. Solve logic and apply critical thinking.
• 8. Solve logic and apply higher level quantitative skills.
• 9. Apply essential research skills.

## Learning activities and teaching methods (given in hours of study time)

Scheduled Learning and Teaching ActivitiesGuided independent studyPlacement / study abroad
32 hours118 hours

## Details of learning activities and teaching methods

CategoryHours of study timeDescription
Contact hours22Lectures (2 hours per week)
Contact hours10Tutorials (1 hour per week)
Guided Independent Study55 (5 per week)Reading
Guided Independent Study63 (approx. 6 hours per week)Preparing problem set answers and preparing for examinations

## Formative assessment

Form of assessmentSize of the assessment (eg length / duration)ILOs assessedFeedback method
HomeworkOne set per week1-9Verbal in class

## Summative assessment (% of credit)

CourseworkWritten examsPractical exams
30700

## Details of summative assessment

Form of assessment% of creditSize of the assessment (eg length / duration)ILOs assessedFeedback method
Presentation of homework solution3050 minutes1-9Verbal
0
0
0
0

## Details of re-assessment (where required by referral or deferral)

Original form of assessmentForm of re-assessmentILOs re-assessedTimescale for re-assessment
Presentation and ExaminationExamination (100%) 2 hours1-9August reassessment period

None.

## Syllabus plan

1. Logic, Set Theory and proofs
2. Vector spaces, basis, and dimension
3. Abstract vector spaces and linear maps
4. Eigenvectors and eigenvalues
5. Dynamical systems
6. Topology on the Euclidean space, completeness
7. Properties of continuous functions
8. Taylor polynomials

## Indicative learning resources - Basic reading

Simon, CP and  L. Blume: Mathematics for Economists, Part VI and VII, 1994, W.W. Norton & Company, New York, London

Rudin, W: Principles of Mathematical Analysis, 1978, McGraw Hill

Yes

04/04/2016

09/10/2017