Search result: Catalogue data in Autumn Semester 2021
Mathematics Master  
Application Area Only necessary and eligible for the Master degree in Applied Mathematics. One of the application areas specified must be selected for the category Application Area for the Master degree in Applied Mathematics. At least 8 credits are required in the chosen application area.  
Biology  
Number  Title  Type  ECTS  Hours  Lecturers  

636001700L  Computational Biology  W  6 credits  3G + 2A  T. Vaughan  
Abstract  The aim of the course is to provide uptodate knowledge on how we can study biological processes using genetic sequencing data. Computational algorithms extracting biological information from genetic sequence data are discussed, and statistical tools to understand this information in detail are introduced.  
Objective  Attendees will learn which information is contained in genetic sequencing data and how to extract information from this data using computational tools. The main concepts introduced are: * stochastic models in molecular evolution * phylogenetic & phylodynamic inference * maximum likelihood and Bayesian statistics Attendees will apply these concepts to a number of applications yielding biological insight into: * epidemiology * pathogen evolution * macroevolution of species  
Content  The course consists of four parts. We first introduce modern genetic sequencing technology, and algorithms to obtain sequence alignments from the output of the sequencers. We then present methods for direct alignment analysis using approaches such as BLAST and GWAS. Second, we introduce mechanisms and concepts of molecular evolution, i.e. we discuss how genetic sequences change over time. Third, we employ evolutionary concepts to infer ancestral relationships between organisms based on their genetic sequences, i.e. we discuss methods to infer genealogies and phylogenies. Lastly, we introduce the field of phylodynamics, the aim of which is to understand and quantify population dynamic processes (such as transmission in epidemiology or speciation & extinction in macroevolution) based on a phylogeny. Throughout the class, the models and methods are illustrated on different datasets giving insight into the epidemiology and evolution of a range of infectious diseases (e.g. HIV, HCV, influenza, Ebola). Applications of the methods to the field of macroevolution provide insight into the evolution and ecology of different species clades. Students will be trained in the algorithms and their application both on paper and in silico as part of the exercises.  
Lecture notes  Lecture slides will be available on moodle.  
Literature  The course is not based on any of the textbooks below, but they are excellent choices as accompanying material: * Yang, Z. 2006. Computational Molecular Evolution. * Felsenstein, J. 2004. Inferring Phylogenies. * Semple, C. & Steel, M. 2003. Phylogenetics. * Drummond, A. & Bouckaert, R. 2015. Bayesian evolutionary analysis with BEAST.  
Prerequisites / Notice  Basic knowledge in linear algebra, analysis, and statistics will be helpful. Programming in R will be required for the project work (compulsory continuous performance assessments). We provide an R tutorial and help sessions during the first two weeks of class to learn the required skills. However, in case you do not have any previous experience with R, we strongly recommend to get familiar with R prior to the semester start. For the DBSSE students, we highly recommend the voluntary course „Introduction to Programming“, which takes place at DBSSE from Wednesday, September 12 to Friday, September 14, i.e. BEFORE the official semester starting date Link For the Zurichbased students without R experience, we recommend the R course Link, or working through the script provided as part of this R course.  
636000700L  Computational Systems Biology  W  6 credits  3V + 2U  J. Stelling  
Abstract  Study of fundamental concepts, models and computational methods for the analysis of complex biological networks. Topics: Systems approaches in biology, biology and reaction network fundamentals, modeling and simulation approaches (topological, probabilistic, stoichiometric, qualitative, linear / nonlinear ODEs, stochastic), and systems analysis (complexity reduction, stability, identification).  
Objective  The aim of this course is to provide an introductory overview of mathematical and computational methods for the modeling, simulation and analysis of biological networks.  
Content  Biology has witnessed an unprecedented increase in experimental data and, correspondingly, an increased need for computational methods to analyze this data. The explosion of sequenced genomes, and subsequently, of bioinformatics methods for the storage, analysis and comparison of genetic sequences provides a prominent example. Recently, however, an additional area of research, captured by the label "Systems Biology", focuses on how networks, which are more than the mere sum of their parts' properties, establish biological functions. This is essentially a task of reverse engineering. The aim of this course is to provide an introductory overview of corresponding computational methods for the modeling, simulation and analysis of biological networks. We will start with an introduction into the basic units, functions and design principles that are relevant for biology at the level of individual cells. Making extensive use of example systems, the course will then focus on methods and algorithms that allow for the investigation of biological networks with increasing detail. These include (i) graph theoretical approaches for revealing largescale network organization, (ii) probabilistic (Bayesian) network representations, (iii) structural network analysis based on reaction stoichiometries, (iv) qualitative methods for dynamic modeling and simulation (Boolean and piecewise linear approaches), (v) mechanistic modeling using ordinary differential equations (ODEs) and finally (vi) stochastic simulation methods.  
Lecture notes  Link  
Literature  U. Alon, An introduction to systems biology. Chapman & Hall / CRC, 2006. Z. Szallasi et al. (eds.), System modeling in cellular biology. MIT Press, 2010. B. Ingalls, Mathematical modeling in systems biology: an introduction. MIT Press, 2013  
636000900L  Evolutionary Dynamics  W  6 credits  2V + 1U + 2A  N. Beerenwinkel  
Abstract  Evolutionary dynamics is concerned with the mathematical principles according to which life has evolved. This course offers an introduction to mathematical modeling of evolution, including deterministic and stochastic models, with an emphasis on tumor evolution.  
Objective  The goal of this course is to understand and to appreciate mathematical models and computational methods that provide insight into the evolutionary process in general and tumor evolution in particular. Students should analyze and evaluate models and their application critically and be able to design new models.  
Content  Evolution is the one theory that encompasses all of biology. It provides a single, unifying concept to understand the living systems that we observe today. We will introduce several types of mathematical models of evolution to describe gene frequency changes over time in the context of different biological systems, focusing on asexual populations. Viruses and cancer cells provide the most prominent examples of such systems and they are at the same time of great biomedical interest. The course will cover some classical mathematical population genetics and population dynamics, and also introduce several new approaches. This is reflected in a diverse set of mathematical concepts which make their appearance throughout the course, all of which are introduced from scratch. Topics covered include the quasispecies equation, evolution of HIV, evolutionary game theory, evolutionary stability, evolutionary graph theory, tumor evolution, stochastic tunneling, genetic progression of cancer, diffusion theory, fitness landscapes, branching processes, and evolutionary escape.  
Lecture notes  No.  
Literature   Evolutionary Dynamics. Martin A. Nowak. The Belknap Press of Harvard University Press, 2006.  Evolutionary Theory: Mathematical and Conceptual Foundations. Sean H. Rice. Sinauer Associates, Inc., 2004.  
Prerequisites / Notice  Prerequisites: Basic mathematics (linear algebra, calculus, probability)  
Competencies 

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