Advanced Mathematics and Optimization
Level of Study
Objectives and Content
The course will make students better suited to meeting the demands in mathematics, which they will face in other upper-bachelor and master-level economics courses.
The course deals with linear algebra, the functions of several variables, comparative statistics and optimization with several variables and restrictions. In optimization, the Lagrange and Kuhn-Tucker methods are the main points of focus.
A student who has completed the course should have the following learning outcomes defined in terms of knowledge, skills and general competence:
The student can ...
- comprehend the following conversions and concepts within linear algebra: Addition, subtraction and scalar multiplication of vectors, vector length, distance between vectors and inner product between vectors, lines and planes, hyperplanes in parametric and non-parametric representation, linear independence.
- give a description of: square shapes, positive and negative semidefinite matrices, convex amounts and functions.
- distinguish constraint and no constrain optimization problems as well as dynamic and non-dynamic optimization problems.
- reflect on the necessary conditions for global or local maxima`s and minima`s.
- discuss the application of the envelope theory for optimization problems in economics.
The student can ...
- apply addition and multiplication of matrices, the identity matrix, inverse matrix and linear equation system on matrix form. The student should be able to determine the rank of an array to classify linear equation systems. They should also be able to calculate determinants and be able to use Cramer's rules for linear equations.
- apply partial derivative, total differential, gradient vector and directional derivative as well as implicit derivation, second order partial derivative and hesseian matrix. The student should be able to use comparative statistics on an equation system.
- apply Lagrange and Kuhn-Tucker methods for solving optimization problems with restrictions.
Required Previous Knowledge
Credit Reduction due to Course Overlap
Complete overlap with ECON141
Access to the Course
Teaching and learning methods
Lectures: approx. 36 hours, mathematics tasks: approx. 18 hours, seminars: approx. 18 hours
Compulsory Assignments and Attendance
Forms of Assessment
Written exam (4 hours)
Updated: Change of assessment form from 4 hour written exam to 2 hour take home exam as part of the measures to limit the risk of corona infection.
Examination Support Material
Matematisk formelsamling av K Sydsæter, A. Strøm og P. Berck eller Mathematical Formulas for Economists of B. Luderer, V. Nollau and K. Vetters. Kalkulator: Berre følgjande enkle, ikkje-programmerbare kalkulatorar utan grafisk display vert tillate brukt ved skriftlege prøvar:
Alle modellar av typane:
- Casio FX-82, Casio FX-82ES PLUS eller Casio FX-82EX
- Hewlett-Packard HP30
- Texas instruments TI-30
Institutt for økonomi kan gjennomføre stikkprøvar av hjelpemidla i eksamenslokalet.
Assessment in teaching semester. Only students who have a valid document of absence will be entitled to take a new exam the following semester.
All courses are evaluated according to UiB's system for quality assurance of education.
Department of Economics
Type of assessment: Take-home examination
- Assignment handed out
- 19.11.2021, 09:00
- Submission deadline
- 19.11.2021, 11:00
- Withdrawal deadline
- Examination system
- Digital exam