# ELE 3719 Mathematics elective APPLIES TO ACADEMIC YEAR 2015/2016Norwegian version

ELE 3719 Mathematics elective

Responsible for the course
Pål Lauritzen

Department
Department of Economics

Term
According to study plan

ECTS Credits
7,5

Language of instruction
Norwegian

Introduction
This course gives an introduction to selected topics in mathematics and probability theory.

Learning outcome
Acquired knowledge
Upon completing this course, the student should have acquired mathematical knowledge in selected topics that are important for finance, economics and statistics. The student should:

• Know important concepts in linear algebra and vector calculus, such as matrices, vectors, determinants and quadratic forms, and know how to use these in optimization and multivariate statistics.
• Understand probability models from a mathematical point of view.
• Know the concept differential equation, and know how differential equations can be used for modelling.
• Understand foundations of calculus of variations and optimal control theory, and know how this theory can be used in economics.

Acquired skills
Upon completing this course, the student should have acquired skills including:
• Mastery of calculations with matrices, vectors and determinants, find eigenvalues and eigenvectors, and ability to use this in applications.
• Ability to compute with probabilities and probability models in one or several variables, and to use this in applications.
• Ability to solve selected types of differential equations, with and without initial conditions.
• Ability to solve selected optimization problems.

Reflection
Upon completing this course, the student should have strengthened his/her analytical thinking, and have realized the value of precise and systematic work.

Prerequisites
The course builds on MET 1180 Mathematics, or MET 2910 Mathematics.

Books:
Stirzaker, David. 1999. Probability and random variables : a beginner's guide. Cambridge University Press. Kapittel 1-6

Books:
Sydsæter, Knut ... [et al.]. 2014. Further mathematics for economic analysis. 3rd ed. Financial Times/Prentice-Hall. Kap. 1, 5-6, 8

Course outline
• Linear algebra and vector calculus
• Probability theory
• Differential equations
• Optimal control theory

Computer-based tools
Not used in this course.

The course has 45 hours of lectures. There will be work programmes with problems that the student should solve. Some of the problems will subsequently be solved in class.

Some time in class will be set aside for the students to work on basic problems in topics recently covered in lectures. This will activate the students and increase the learning outcome through the presentation of solutions to the problems.

 Activity Workload Participation in class 45 Independent work on problems 100 Reading of literature 50 Examination 5 Total recommended use of time 200h

Examination
A five hour individual written examination concludes the course.
Examination code(s)
ELE 37191 - Wiritten examination, accounts for 100% of the final grade in ELE 3719 Mathematics elective - 7.5 credits.

Examination support materials
BI approved exam calculator. Examination support materials at written examinations are explained under examination information in the student portal @bi. Please note use of calculator and dictionary in the section on support materials (https://at.bi.no/EN/Pages/Exa_Hjelpemidler-til-eksamen.aspx).

Re-sit examination
A re-sit is held in connection with the next scheduled course.