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Course syllabus - Optimization and simulation

Scope

7.5 credits

Course code

MAA139

Valid from

Autumn semester 2026

Education level

First cycle

Progressive Specialisation

G1F (First cycle, has less than 60 credits in first-cycle course/s as entry requirements)

Main area(s)

Mathematics/Applied Mathematics

Organisation

Department of Business and Mathematics

Ratified

2017-12-12

Revised

2025-12-19

Literature lists

Course literature is preliminary up to 8 weeks before course start. Course literature can be valid over several semesters.

    • Ratified date: 2025-05-20
    • Latest update: 2025-05-27

    Other Materials

    Kurslitteraturen finns tillgänglig via lärplattformen Canvas.

Objectives

The aim of the course is to provide basic knowledge of optimization theory and methods of simulations, as well as develop skills in modelling and solving problems in the appropriate field of technology using efficient algorithms and simulations.

Learning outcomes

Upon completion of the course the student is expected to be able to:

  1. construct mathematical models for linear optimization problems
  2. describe and apply the theory of linear programming, including the concepts of convexity and duality
  3. generate continuous and discrete stochastic variables
  4. describe and apply the theory of Monte Carlo-modelling and Monte Carlo-simulation
  5. analyse problems in the appropriate field of technology and be able to present the results by well-structured reports and oral presentations

Course content

  • Background and basic ideas of linear programming
  • Linear modelling
  • Convexity, in particular with respect to the domain of definition
  • Duality
  • Solution methods of linear optimization problems, such as the Simplex method
  • Estimation of expected values using stochastic processes, generation of discrete and continuous stochastic variables and processes following different distributions
  • Ideas and theory of Monte Carlo-methods, speed of convergence independent of dimension
  • Modelling and implementation of problems in the appropriate field of technology

Specific requirements

Probability Theory and Statistical Inference, 7.5 credits (at least 3.5 credits must be passed at the start of the course), Numerical Methods, 7.5 credits, and Programming, 7.5 credits, or equivalent.

Examination

INL2, Assignment, 1.5 credits, written reports and/or oral presentations concerning learning outcomes 1-5, grades Fail (U) or Pass (G).
TEN1, Written examination, 3 credits, written examination concerning learning outcomes 1, 2 and 5, grades Fail (U), 3, 4 or 5.
TEN2, Written examination, 3 credits, written examination concerning learning outcomes 3-5, grades Fail (U), 3, 4 or 5.

Grade för the course as a whole is given by the average grade of TEN1 and TEN2 rounded up.

A student who has a certificate from MDU regarding disability study support, can request adaptions for the examination. It is the examiner who takes decisions on any adaptions, based on the certificate and other conditions.

Grade

Grading scale: 5, 4, 3