# Lecture "Applied Mathematics in Biology: Single-cell omics"

Modern molecular biology has become a data-intensive subject, with plenty of opportunity for mathematically trained researchers (e.g., mathematicians, physicists, engineers, computer scientists) to contribute. Most notably, new technolgies for single-cell transcriptomics are currently transforming biological research, making it possible to assess the gene-expression profile (and therefore the biological state) of thousands of cells in a sample. Analysing such data, comparing across samples, and reaching conlusions leverages modern ideas in high-dimensional statistics and machine learning.

Therefore, we need more researchers with math and CS background in biology. This lecture invites students from the exact sciences to learn about molecular biology.

Prerequisites:
- Knowledge of linear algebra and basic calculus, ideally also some basic stochastics or statistics (You don't need very advanced knowledge, introductory lectures suffice; but you will need good mathematical thinking.)
- Some programming skills in at least one language
- For biology, high school-level knowledge is sufficient; you'll learn more, though.

Goal of the lecture:
There is much demand for researchers with solid math or CS background in molecular biology. The field hence offers exciting opportunities for graduates with a fascination for the complexity of life and a willingness to learn the language of biology. This course aims to offer a first step in this direction.

Contents:
- Brief introduction to molecular biology: genes and gene expression, the so-called "central dogma", basic cellular and organismal functions
- methods to study gene expression at single-cell level ("scRNASeq"), as example for cutting-edge experimental techniques in today's biological research
- workflows to scRNASeq data analysis, and ways to interpret the data
- the math behind this: principal componant analysis, principal curves, diffusion distances, trajectory inference, statistical inference for comparisons, etc.
- practical examples from basic and medical research
- performing numerical computations using R and/or Python
- working with "big data"

Lecturer: Dr. Anders
I have obtained my PhD in theoretical physics and then moved to bioinformatics and biostatistics. I am a junior professor at the BioQuant center within the University's biology department. Our research focuses on developing mathematical methods to analyse omics data, i.e., molecular-biology data obtained with so-called high-throughput methods, where thousands to millions of data values are obtained in parallel for each sample. I consider our research as "translating" from the abstract language of mathematics and statistics research to the real-world needs of modern biology research, thus building bridges between these fields.