Mathematical and computational methods in natural sciences.

General data

Course ID:	1100-4PM23
Erasmus code / ISCED:	11.953 Kod klasyfikacyjny przedmiotu składa się z trzech do pięciu cyfr, przy czym trzy pierwsze oznaczają klasyfikację dziedziny wg. Listy kodów dziedzin obowiązującej w programie Socrates/Erasmus, czwarta (dotąd na ogół 0) – ewentualne uszczegółowienie informacji o dyscyplinie, piąta – stopień zaawansowania przedmiotu ustalony na podstawie roku studiów, dla którego przedmiot jest przeznaczony. / (0588) Natural sciences, mathematics and statistics, inter-disciplinary programmes The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title:	Mathematical and computational methods in natural sciences.
Name in Polish:	Metody modelowania matematycznego i komputerowego w naukach przyrodniczych
Organizational unit:	Faculty of Physics
Course groups:	(in Polish) ZFBM, II stopień; Projektowanie molekularne i bioinformatyka
ECTS credit allocation (and other scores):	(not available) Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	English
Main fields of studies for MISMaP:	biology chemistry computer science mathematics physics
Mode:	Classroom
Short description:	Contemporary trends and research strategies for complex systems in natural sciences will be described using methods of theoretical physics and computational sciences, including simulation techniques. Practical applications of the discussed theoretical models will be presented.
Full description:	Topics. Contemporary trends and research strategies of complex systems in natural sciences using theoretical physics, computational sciences and simulation techniques. Contemporary computer architectures. Classical and quantum computers. World and Polish supercomputing centers and a review of research and services carried out. Methods for determining the structure of complex (bio)molecular systems. Structural databases. Multiscale modeling methods and simulations of complex physical, chemical and biological systems and processes as an indispensable element of research in order to understand their structure and function. Review of the leading methods and computational environments used in (bio)molecular and material sciences. Selected quantum methods for generating potential energy, including ab initio and DFT methods. Hellmann-Feynman theorem and molecular forces. Analytical approximations of the potential energy. Relations of physics of (bio)molecular systems and nanosystems. Dynamical systems. Phase space trajectories. Classification of dynamical systems. Correlation functions, including time correlation functions. Selected molecular dynamics algorithms: classical molecular dynamics (MD), quantum molecular dynamics (QD) and quantum-classical molecular dynamics (QCMD). Numerical stability of MD algorithms. Simulations of systems in thermodynamic equilibrium: basic statistical systems and thermodynamic properties, microscopic models of pressure and temperature, free energy simulations, thermodynamic integration. Microscopic and mesoscopic models of molecular fields. Poisson-Boltzmann equation. Diffusion processes. Fokker-Planck equation. Brown's dynamics. Hydrodynamic interactions. Simulations of kinetic processes, including metabolic and signaling pathways. Physics and evolution. Genetic algorithms. In silico neural networks and their applications. Analysis of signals. Causality relations in the dynamics of complex systems. New challenges.
Bibliography:	• B. Lesyng, Notes to lectures, e-mailed using USOS. • Molecular Conceptor, computer course available in the laboratory. • SCIGRESS, a computational environment for studying complex (bio)molecular and material systems (https://www.fqs.pl/en/chemistry/products/scigress/). • A. Hinchliffe, Molecular Modeling for Beginers, Wiley, West Sussex, 2008. • T. Schlick, Molecular Modeling and Simulation. An Interdisciplinary Guide. Springer, New York, Dordrecht, Heidelberg, London, 2010 • A. H. Zewail, Physical Biology. From Atoms to Medicine, Imperial College Press, 2008. • K.A. Dill, S. Bromberg, Molecular Driving Forces. Statistical Thermodynamics in Chemistry and Biology, Garland Science, 2003. • U. Forys, Mathematics in Biology, WNT, 2005. • L. Susskind, The Theoretical Minimum. What You Need to Know to Start Doing Physics, Basic Books, 2013. • L. Susskind, Quantum Mechanics. The Theoretical Miniumum. Penguin Random House, UK, 2014.
Learning outcomes:	The purpose of the lecture and presentations, as well as exercises, is to provide students with a review of methods, trends and strategies for studying complex systems in life sciences using mathematical and computational models, including the use of multi-scale methods of theoretical physics and computational sciences. The lecture should provide a good, substantive background for a better understanding of complex systems and processes, enabling own research.
Assessment methods and assessment criteria:	Written exam. 4-problems/questions to solve. 20 points to get. A minimum of 10 points to obtain a positive grade. From 11 points to 20 points, a linear scale for converting points into scores.

This course is not currently offered.

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