Introduction to Experimental Mathematics (IXM)
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.
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 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.
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.
- 7,5 ECTS
- Type of assessment
Oral examination, 30 minutes
- Type of assessment details
- Without preparation time
- 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
- passed/not passed
- Censorship form
- No external censorship
Several internal examiners.
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)
- Theory exercises
- Practical exercises
- Project work
- Course number
- 7,5 ECTS
- Programme level
- Block 2
- No limit
- Study Board of Mathematics and Computer Science
- Department of Mathematical Sciences
- Faculty of Science
- Søren Eilers (6-676b6e677475426f63766a306d7730666d)
- Joachim Kock (4-7c80747c517e7285793f7c863f757c)
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