NMAB21005U Introduction to Experimental Mathematics (IXM)

Volume 2021/2022

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.

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.

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.
4 lectures, 4 problem sessions, and 4 computer labs per week corresponding to 7 weeks, but taught over 8 weeks with a reduced schedule for the last 3 weeks to make room for project work.
The IXM course is recommended for BSc students who wish to continue with an experimental BSc project. The participants may choose to continue with the same project as the one studied in the final mandatory project in the course.
  • Category
  • Hours
  • Lectures
  • 28
  • Preparation
  • 60
  • Theory exercises
  • 28
  • Practical exercises
  • 28
  • Project work
  • 62
  • Total
  • 206
Feedback by final exam (In addition to the grade)
7,5 ECTS
Type of assessment
Oral examination, 30 minutes
without preparation time
Exam registration requirements

Two assignments must be handed in and approved before the student can participate in the oral exam. The oral exam is based on the content of the last assignment.

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
passed/not passed
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 compulsory assignments were not approved before the ordinary exam they must be resubmitted at the latest two weeks before the beginning of the re-exam week. They must be approved before the re-exam.



Criteria for exam assesment

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