## Admission requirements

The student should have finished a bachelor in mathematics, having followed courses on ordinary differential equations and modeling. Knowledge of partial differential equations may not be needed for all research projects. The student is required to provide motivation to start the traineeship. Admittance is determined based on fit of knowledge to the available research project(s), which is determined after a mandatory interview of the envisioned supervisor with the student.

## Description

Research starts with research questions, both in science and business. More often than not, these questions are formulated in natural language rather than in mathematical formalism. In order to see whether these are tractable by mathematical techniques, they must first be translated into a mathematical model, followed by analysis and/or simulation of the resulting model to answer the original questions.

This traineeship is aimed at development of skills of the student needed to work effectively and efficiently in a multi- or interdisciplinary research team, in science or industry, while being embedded in such a research group. Among others, it introduces the student to making the translation from original (non-mathematical) research question in a real-life scientific or industry context to mathematical models, the assessment of the tractability of the models, the actual mathematical analysis or simulation and the presentation and translation of mathematical results back to answers concerning the initial question(s).

The student will be supervised during his traineeship by a member from the research team (at university or industry) and a supervisor from the Mathematical Institute.

## Course objectives

Develop the skills to concretize research questions for translating into mathematical models.

Translate into appropriate mathematical model(s).

Analyze and/or simulate the developed model(s).

Translate mathematical results to answers relevant the research group or company and to the initial research question.

## Mode of instruction

The student will be embedded within the research group at the university or at the company that provides the initial research question. (S)he will have a daily supervisor within that group and a supervisor from the Mathematical Institute (MI) with whom regular meetings will be planned to discuss the progress during the traineeship and any mathematical issues that may arise.

## Assessment method

(1) A written report with management summary, on the initial research question, the modeling, analysis and simulation that has been performed, and discussion of the results obtained (75%). It is assessed by both the daily supervisor from the research group and the supervisor from MI. Marks from both are averaged. (2) An oral presentation of the results and applied methods for the research team in which the student has been embedded and the supervisor from MI (25%). It is considered a practical. Marks from both supervisor are averaged.

A retake exam is offered as an oral exam in which only part (1) can be improved.

## Literature

Literature will be selected case-by-case, based on the initial research question provided by the research group and the particular modelling approach chosen.

## Contact

Possible supervisors at MI:

Dr. S.C. Hille (shille@math.leidenuniv.nl)

Dr. V. Rottschäfer (vivi@math.leidenuniv.nl)

Dr. H.G.J. van Mil (h.g.j.van.mil@math.leidenuniv.nl)