# 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.

Education

MSc Programme in Mathematics

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.

4 lectures, 4 problem sessions, and 4 computer labs per week for 7 weeks.

LinAlg, Algebra 1, and Analyse 1. Beyond what is learned in MatIntro and LinAlg, no knowledge of programming in Maple is required.

Written
Individual
Collective
Feedback by final exam (In addition to the grade)
ECTS
7,5 ECTS
Type of assessment
Oral examination, 30 minutes
without preparation time
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.
##### 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
• Theory exercises
• 28
• Practical exercises
• 28
• Preparation
• 60
• Project work
• 62
• English
• 206