# NMAK16008U Experimental Mathematics (XM)

Volume 2021/2022
Education

MSc Programme in Mathematics

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.

Learning Outcome

Knowledge:

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

Skills:

• 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

Competence:

• 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 and with a reduced schedule for the last 3 weeks to make room for project work.
• Category
• Hours
• Lectures
• 28
• Preparation
• 60
• Theory exercises
• 28
• Practical exercises
• 28
• Project work
• 62
• Total
• 206
Written
Individual
Collective
Credit
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.

Aid
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
Censorship form
No external censorship
Several internal examiners.
Re-exam

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.