Experimental Mathematics (XM)

Course content

The participants will gain the ability to use computers to formulate and test hypotheses concerning suitable mathematical objects through a systematic search for counterexamples. Key concepts covered are: The experimental method, introduction to programming in Maple, from hypothesis to proof, formulating and testing hypotheses, visualization, pseudorandomness, iteration, symbolic inversion, time/memory vs. precision, applications of linear algebra and graph theory.


MSc Programme in Mathematics

Learning outcome


The experimental method, basic elements of programming in Maple, visualization, pseudo-randomness, iteration, symbolic inversion, time/memory vs. precision, relevant tools in linear algebra. 



  • To employ Maple as a programming tool via the use of procedures, control structures, and data structures in standard situations
  • To convert pseudocode to executable Maple code.
  • To maintain a log documenting the investigation



  • To formulate and test hypotheses concerning suitable mathematical objects through a systematic search for counterexamples.
  • To design algorithms for mathematical experimentation by use of pseudocode.
  • To examine data and collections of examples arising from experiments systematically and formulate hypotheses based on the investigation.
  • To use pseudorandomness in repeatable computations.
  • To weigh the use of available resources and time versus the needed precision.
  • To determine whether a given problem is suited for an experimental investigation.
  • To use the results of an experimental investigation to formulate theorems, proofs and counterexamples.

4 lectures, 4 problem sessions, and 4 computer labs per week corresponding to 7 weeks, but taught over 8 weeks and with a reduced schedule for the last 3 weeks to make room for project work.

Eilers & Johansen: Introduction to Experimental Mathematics, Cambridge University Press.

LinAlg, Algebra 1, and Analyse 1. Familiarity with Maple use as in MatIntro and LinAlg is expected. No knowledge of programming in Maple is required.

General mathematical qualifications equivalent to the two first years of a BSc degree is recommended.

Feedback by final exam (In addition to the grade)
7,5 ECTS
Type of assessment
Oral examination, 30 minutes
without preparation time
Only certain aids allowed

At the oral exam the student may only bring his or her final project, possibly annotated and/or prepared for presentation.

Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners.
Criteria for exam assessment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 28
  • Preparation
  • 60
  • Theory exercises
  • 28
  • Practical exercises
  • 28
  • Project work
  • 62
  • English
  • 206