Print Course syllabus
Course syllabus - Computer algebra with applications
Scope
7.5 credits
Course code
MAA155
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
2016-12-19
Revised
2025-11-03
Literature lists
Course literature is preliminary up to 8 weeks before course start. Course literature can be valid over several semesters.
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Books
Other Materials
Additional course material might be shared on Canvas.
Objectives
The purpose of the course is to give an introduction to algorithms (and the theory underlying them) for algebraic computations on a computer, and to introduce the students to some computer algebra system that is used in practice.
Learning outcomes
After passing the course the students should be able to
- describe data structures and algorithms that can be used for basic computations with numbers and polynomials
- describe the pros and cons of symbolic methods as compared to numerical methods
- read and write pseudo-code
- describe and apply algorithms for Gröbner basis computations, and know something about the areas of application of Gröbner bases
- apply other methods for solving polynomial equations and systems of polynomial equations in simple cases
- describe algorithms for factoring polynomials in Z
- formalize a mathematical formula in machine-readable format
- use some software package for computer algebra
Course content
- Symbolic representation of and computation with integers, rational numbers, complex numbers and polynomials. To some extent, also algebraic numbers. Differences between symbolic and numerical representations.
- Pseudo-code
- Algorithms for modular arithmetic with integers and polynomials
- Gröbner bases and their use in solving equations
- To some extent, other methods for solving polynomial equations and systems of polynomial equations
- Applications of polynomial equations in mechanics and robotics
- Factorization of polynomials in Z
- Machine-readable encoding of mathematics. Introduction to the subset of XML that is required for that purpose.
- Use of software for computer algebra.
Specific requirements
Discrete Mathematics, 7.5 credits and Basic Vector Algebra, 7.5 credits or equivalent.
Examination
INL1, Assignment, 2.5 credits, written assignments concerning learning outcomes 1-8, grades Fail (U) or Pass (G).
TEN1, Examination, 5 credits, written examination concerning learning outcomes 1-7, grades Fail (U), 3, 4 or 5.
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