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
MSc Programme in Mathematics with a minor subject

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
Type of assessment details
Without preparation time
Exam registration requirements

Two assignments must be handed in. The first assignment is individual and must be approved before the student can participate in the oral exam. The second assignment forms the basis for the oral exam.

Only certain aids allowed

At the oral exam it is only allowed to bring the second assignment, possibly annotated and/or prepared for presentation.

Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners.

1 hour oral exam covering theory and all assignments. No preparation time, but all aids allowed. 

If the first assignment was not approved before the ordinary exam, it must be resubmitted at the latest two weeks before the beginning of the re-exam week. It must be approved before the re-exam.

The student may also choose to resubmit a new version of the second assignment in order to obtain feedback before the oral exam. This must also be resubmitted at the latest two weeks before the beginning of the re-exam week.

Criteria for exam assessment

The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.

Single subject courses (day)

  • Category
  • Hours
  • Lectures
  • 28
  • Preparation
  • 59
  • Theory exercises
  • 28
  • Practical exercises
  • 28
  • Project work
  • 62
  • Exam
  • 1
  • English
  • 206


Course number
7,5 ECTS
Programme level
Full Degree Master

1 block

Block 2
No limit
Study Board of Mathematics and Computer Science
Contracting department
  • Department of Mathematical Sciences
Contracting faculty
  • Faculty of Science
Course Coordinators
  • Søren Eilers   (6-696d70697677447165786c326f7932686f)
  • Joachim Kock   (4-6d71656d426f63766a306d7730666d)
S.E./phone +45 35 32 07 55, office 04.2.18
Saved on the 22-09-2023

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