## Seminar Mathematical Methods for Medicine

**Organizers:**

Prof. Dr. Vincent Heuveline, Saskia Haupt

**Location:**

INF 205/SR 5

**Date:**

Mo. 16:00-18:00 ct

**Description:**

In the recent years, an increasing number of mathematical models have been developed in order to describe numerous biological and medical phenomena. This is especially the case in the area of cancer research leading to the emergence of the so called mathematical oncology. Hereby, the goal is to understand the development of cancer, called tumorigenesis or carcinogenesis, and the progression of tumor tissue as well as the formation of metastases. In particular, the aim is to reflect, check and refine the medical understanding of the underlying processes which lead to cancer.

During this seminar, we will have a closer look at the above mentioned three main areas of current research in mathematical oncology, starting with the description of the first mutated cell over the growing tumor until the formation of metastases. Depending on the interests and prior knowledge of the participants, we will look at different mathematical approaches: stochastic modeling, ordinary differential equations, partial differential equations, graph theory. The goal is to answer the following questions:

- How can each of these processes be modeled mathematically?
- Which mathematical tools can be used for modeling?
- Which numerical methods are needed for solving these problems?
- How can we compare the different models?
- What is the medical importance of the mathematical results?

**Language:**

English or German is both fine for presentations (beamer) and the written seminar work. However, the material for preparation of the seminar topics provided by the organizers is in English.

**Formalities:**

In this seminar, 12 different topics are provided. Each interested student (Bachelor or Master) can create a list of three topics of his choice (prioritized). The 12 topics will be distributed in order to match the interests of the participants as good as possible. **The maximum number of students is 12.** Therefore, if more students should be interested the topics will be distributed by random selection of the students which attend the **preliminary discussion on 15th October 2018.** Later applications can only be considered if not all topics have been distributed.

**Preliminary discussion:**

Monday, 15.10.2018, INF 205 (Mathematikon), SR 5, 16:00 - 18:00 pm.

**Prerequisites:**

The prerequisites for each seminar talk depend on the chosen topics. The latter are based on:

- Knowledge in numerical mathematics (esp. ordinary and partial differential equations)
- Knowledge in stochastic (esp. random variables, probability densities, stochastic processes, expectation, Markov processes)
- Knowledge in graph theory (esp. directed acyclic graphs, trees)
- Knowledge in programming is optional