On Wednesday, September 18, 2024, a teacher training course on the above-mentioned topic
will take place at the Institute of Mathematics at Clausthal University of Technology,
Erzstraße 1, from 9.30 am to 4.30 pm, in cooperation with the Competence Center for Teacher Training Braunschweig
(KLBS), to which we cordially invite you. The cost of participation is 25 euros
per participant and will be charged via the KLBS.

Registration is possible at nlc.info direct link:
https://nlc.info/app/edb/event/44128

Program (subject to change):
The Mathematics Day will feature three presentations by experts
followed by a discussion:

Dr. Raj Spielmann
Mathematical models in biology
With the increasing possibilities of biotechnology, e.g. the CRISPR/Cas method or "optimizations" of metabolic rate, the need for critical examination is growing. This requires an understanding of evolutionary biological processes and interactions, which are often formulated mathematically. The laws allow conclusions to be drawn about the risks that could be expected when manipulating one parameter on other life functions. The first part of the lecture shows correlations between mass, metabolic rate and life cycles (lifespan, duration of reproductive capacity, duration of a heartbeat, etc.) when comparing biological species, with multiples of ¼ appearing as exponents. Relationships between the formulas help to understand the dependence of metabolic rate and life cycles. This can be used to explain environmental adaptations and evolutionary trends. Further consequences are species-dependent limits on lifespan and immunities. In the second part, hereditary diseases are examined in interaction with natural selection. In the case of diseases with a protective function, such as sickle cell anemia against malaria, the setting of optimal balances in nature is demonstrated. The examples show the importance of interdisciplinary thinking, which is becoming increasingly important in a highly technological society. At the same time, it becomes clear that mathematics is also indispensable for physicians and biologists. The associated tools include probabilities and mathematical statistics, number sequences, series as well as differential and integral calculus.

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PD Dr. Philipp Öffner (Institute of Mathematics, Clausthal University of Technology)
From theory to practice: Numerical methods and their importance in mathematical biology and chemistry
The modeling of dynamic systems plays a central role in mathematical biology. Many of these models use ordinary differential equations (ODEs) to describe biological or chemical processes over time. A well-known example is the SIR model for the spread of infectious diseases such as COVID-19. However, the analytical solution of such equations is often not possible, especially for complex or non-linear models, so numerical methods are essential for solving them. The aim is to work with methods that are as efficient and accurate as possible in order to achieve meaningful results quickly. In my lecture, I will model real problems describing biological or chemical processes and emphasize the importance of ordinary differential equations in this context. The SIR model will serve as an example to illustrate this. The Euler method (Euler polygonal method) is presented as the first numerical tool, whereby some basic theoretical concepts and the practical implementation are explained using examples. Further examples are used to show the challenges and problems that can arise when solving numerically. Starting from the Euler method, we will get to know more advanced methods that ensure that the numerical solutions preserve important properties of the system and fulfill the laws of nature. The lecture aims to emphasize the importance of these numerical techniques in mathematical biology and chemistry in order to be able to apply them to illustrative examples in the classroom.

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Dr. Niklas Sapountzoglou (Institute of Mathematics, TU Clausthal)
Growth processes and evolutionary problems in biology
Mathematical modeling plays a major role in the natural sciences, especially in biology - for example, in predicting the growth of a forest, the population of animal species, the weather of tomorrow or the course of a pandemic. We present different growth processes and explain examples of where these growth processes occur in biology. Furthermore, we describe the associated evolution problems for these examples, i.e. time-dependent differential equations with an initial value, and try to derive the resulting growth processes.
We will learn about the predator-prey model (or Lotka-Volterra model) and the SIR model for modeling epidemics. The lecture concludes with some remarks and hints on the accuracy and significance of mathematical models of evolutionary problems and how to classify the results of these models.

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Program:

09:30 - 09:45	Welcome
09:45 - 10:30	Mathematical models in biology (part 1) Dr. Raj Spielmann
10:30 - 11:00	Coffee break
11:00 - 11:45	Mathematical models in biology (part 2) Dr. Raj Spielmann
11:45 - 13:30	Lunch break
13:30 - 14:30	From theory to practice: Numerical methods and their importance in mathematical biology and chemistry PD Dr. Philipp Öffner
14:30 - 15:00	Coffee break
15:00 - 16:00	Growth processes and evolutionary problems in biology Dr. Niklas Sapountzoglou
16:00 - 16:30	Discussion and closing remarks

 

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Materials:

• Lecture by Dr. Raj Spielmann
• Lecture by Prof. Dr. Philipp Rudolf Öffner
• Lecture by Dr. Niklas Sapountzoglou