NMAA13033U Experimental Mathematics (XM)
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.
- 7,5 ECTS
- Type of assessment
- Oral examination, 30 minutes---
- Exam registration requirements
- Three assignments must be handed in and approved before the student can participate in the orel 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 third project, possibly annotated.
- Marking scale
- passed/not passed
- Censorship form
- No external censorship
Several internal examiners.
- 1hour oral exam covering theory and all three assignments.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
- Theory exercises
- Practical exercises
- Project work