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Mathematical modeling in environmental science

General data

Course ID:	WF-OB-MODM
Erasmus code / ISCED:	07.2 The subject classification code consists of three to five digits, where the first three represent the classification of the discipline according to the Discipline code list applicable to the Socrates/Erasmus program, the fourth (usually 0) - possible further specification of discipline information, the fifth - the degree of subject determined based on the year of study for which the subject is intended. / (unknown)
Course title:	Mathematical modeling in environmental science
Name in Polish:	Modelowanie matematyczne w naukach o środowisku
Organizational unit:	Center for Ecology and Ecophilosophy
Course groups:	(in Polish) Przedmioty obowiązkowe dla 2 roku studiów II stopnia magisterskich
ECTS credit allocation (and other scores):	0 OR 3.00 (depends on study program) 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:	Polish
Subject level:	intermediate
Learning outcome code/codes:	OB2_W12 OB2_U01 OB2_U09 OB2_U13 OB2_K07
Short description:	The aim is to learn basis of mathematical modelling in biology using NetLogo programming language and translating description of biological problems into mathematical and programming languages.The lecture will be illustrated by basics ecological models. YTheir features will be disccused. Basic information from mathematics and computer use are recommended.
Full description:	Modelling in biology. Mathematics as an language for natural sciences. Description of time and space in mathematical models. Statictical or empirical models. Vollenweide'sr model as an example. Habitat models on example of scenariuos Vistulla valley transformations. Model LARCH and RAMAS. NetLogo as a usful programming tool. Population growth - linear, exponential and logistic model. Deterministic chaos. Stochastic models of small populations. Stability - its mathematical formulation and ecological interpretations. Are ecological systems stable? Stability and complexity question. Dynamics of two competing population. Predator-prey system dynamics. Oscillations and limit cycles. Models of matter cycling in ecosystems. Phosporus cycling in a lake as an example of ecosystem's functioning model. Forest dynamics models. Cellural automata. Individual-based modeling and its differences with classical modeling. Fractal modelling - unitary and modular organisms. Speciation and extinction of species.
Bibliography:	Uchmański J. 1992. Klasyczna ekologia matematyczna.PWN. Uchmański J. 2022. Modele matematyczne w ekologii. Wydawnictwa UKSW. Białynicki-Birula I., Białynicka-Birula I. 2002 Modelowanie rzeczywistości. Prószyński i S-ka Bodnar M. 2008. Zbiór zadań z matematyki dla biologów. Wydawnictwa Uniwersytetu Warszawskiego, Warszawa Czarnowski D. S., Romanowski J. M., Stiepanowa N. W. 1974. Co to jest biofizyka matematyczna. PWN. Foryś U. 2005. Matematyka w biologii. Wydawnictwa Naukowo-Techniczne, Warszawa. Murray J.D. 1989. Mathematical biology. Springer-Verlag. Murray J. D. 2006. Wprowadzenie do biomatematyki. Wydawnictwo Naukowe PWN, Warszawa. Wit R. 1994. Wykłady o modelowaniu w fizyce medycznej. Uniwersytet Jagielloński. Wrzosek D. 2008. Matematyka dla biologów. Wydawnictwa Uniwersytetu Warszawskiego, Warszawa
Efekty kształcenia i opis ECTS:	Knowledge EF1 - Student knows basic models used in ecology Abilities EK2 - Student is able to build simple model of an ecological process. Competence EK3 - Student knows that application of maqthematical and compouters methods is useful in ecology and nature protection.
Assessment methods and assessment criteria:	Score on basis of the end test. The presence and activity during lectures are also important.

Classes in period "Winter semester 2021/22" (past)

Time span:	2021-10-01 - 2022-01-31	Selected timetable range: weekly course term Go to timetable MO TU W TH WAR FR
Type of class:	Workshops, 30 hours, 30 places more information
Coordinators:	Janusz Uchmański
Group instructors:	Janusz Uchmański
Course homepage:	https://teams.microsoft.com/l/team/19%3a086ba876377e4260830775a8fb378f80%40thread.tacv2/conversations?groupId=2c17b0f6-9ca0-424c-85c1-d57846f4a939&tenantId=12578430-c51b-4816-8163-c7281035b9b3
Students list:	(inaccessible to you)
Credit:	Course - examination Workshops - examination
(in Polish) E-Learning:	(in Polish) E-Learning z podziałem na grupy
Short description:	The aim is to learn basis of mathematical modelling in biology using NetLogo programming language and translating description of biological problems into mathematical and programming languages.The lecture will be illustrated by basics ecological models. YTheir features will be disccused. Basic information from mathematics and computer use are recommended.
Full description:	Modelling in biology. Mathematics as an language for natural sciences. Description of time and space in mathematical models. Statictical or empirical models. Vollenweide'sr model as an example. Habitat models on example of scenariuos Vistulla valley transformations. Model LARCH and RAMAS. NetLogo as a usful programming tool. Population growth - linear, exponential and logistic model. Deterministic chaos. Stochastic models of small populations. Stability - its mathematical formulation and ecological interpretations. Are ecological systems stable? Stability and complexity question. Dynamics of two competing population. Predator-prey system dynamics. Oscillations and limit cycles. Models of matter cycling in ecosystems. Phosporus cycling in a lake as an example of ecosystem's functioning model. Forest dynamics models. Cellural automata. Individual-based modeling and its differences with classical modeling. Fractal modelling - unitary and modular organisms. Speciation and extinction of species.
Bibliography:	Białynicki-Birula I., Białynicka-Birula I. 2002 Modelowanie rzeczywistości. Prószyński i S-ka Bodnar M. 2008. Zbiór zadań z matematyki dla biologów. Wydawnictwa Uniwersytetu Warszawskiego, Warszawa Czarnowski D. S., Romanowski J. M., Stiepanowa N. W. 1974. Co to jest biofizyka matematyczna. PWN. Foryś U. 2005. Matematyka w biologii. Wydawnictwa Naukowo-Techniczne, Warszawa. Murray J.D. 1989. Mathematical biology. Springer-Verlag. Murray J. D. 2006. Wprowadzenie do biomatematyki. Wydawnictwo Naukowe PWN, Warszawa. Uchmański J. 1992. Klasyczna ekologia matematyczna. PWN. Wit R. 1994. Wykłady o modelowaniu w fizyce medycznej. Uniwersytet Jagielloński. Wrzosek D. 2008. Matematyka dla biologów. Wydawnictwa Uniwersytetu Warszawskiego, Warszawa
Wymagania wstępne:	High school level of mathematics

Classes in period "Winter semester 2022/23" (past)

Time span:	2022-10-01 - 2023-01-31	Selected timetable range: weekly course term Go to timetable MO TU W TH WAR FR
Type of class:	Workshops, 30 hours, 30 places more information
Coordinators:	Janusz Uchmański
Group instructors:	Janusz Uchmański
Course homepage:	https://teams.microsoft.com/l/team/19%3a086ba876377e4260830775a8fb378f80%40thread.tacv2/conversations?groupId=2c17b0f6-9ca0-424c-85c1-d57846f4a939&tenantId=12578430-c51b-4816-8163-c7281035b9b3
Students list:	(inaccessible to you)
Credit:	Course - examination Workshops - examination
(in Polish) E-Learning:	(in Polish) E-Learning z podziałem na grupy
Short description:	The aim is to learn basis of mathematical modelling in biology using NetLogo programming language and translating description of biological problems into mathematical and programming languages.The lecture will be illustrated by basics ecological models. YTheir features will be disccused. Basic information from mathematics and computer use are recommended.
Full description:	Modelling in biology. Mathematics as an language for natural sciences. Description of time and space in mathematical models. Statictical or empirical models. Vollenweide'sr model as an example. Habitat models on example of scenariuos Vistulla valley transformations. Model LARCH and RAMAS. NetLogo as a usful programming tool. Population growth - linear, exponential and logistic model. Deterministic chaos. Stochastic models of small populations. Stability - its mathematical formulation and ecological interpretations. Are ecological systems stable? Stability and complexity question. Dynamics of two competing population. Predator-prey system dynamics. Oscillations and limit cycles. Models of matter cycling in ecosystems. Phosporus cycling in a lake as an example of ecosystem's functioning model. Forest dynamics models. Cellural automata. Individual-based modeling and its differences with classical modeling. Fractal modelling - unitary and modular organisms. Speciation and extinction of species.
Bibliography:	Białynicki-Birula I., Białynicka-Birula I. 2002 Modelowanie rzeczywistości. Prószyński i S-ka Bodnar M. 2008. Zbiór zadań z matematyki dla biologów. Wydawnictwa Uniwersytetu Warszawskiego, Warszawa Czarnowski D. S., Romanowski J. M., Stiepanowa N. W. 1974. Co to jest biofizyka matematyczna. PWN. Foryś U. 2005. Matematyka w biologii. Wydawnictwa Naukowo-Techniczne, Warszawa. Murray J.D. 1989. Mathematical biology. Springer-Verlag. Murray J. D. 2006. Wprowadzenie do biomatematyki. Wydawnictwo Naukowe PWN, Warszawa. Uchmański J. 1992. Klasyczna ekologia matematyczna. PWN. Wit R. 1994. Wykłady o modelowaniu w fizyce medycznej. Uniwersytet Jagielloński. Wrzosek D. 2008. Matematyka dla biologów. Wydawnictwa Uniwersytetu Warszawskiego, Warszawa
Wymagania wstępne:	High school level of mathematics

Classes in period "Winter semester 2023/24" (past)

Time span:	2023-10-01 - 2024-01-31	Selected timetable range: weekly course term Go to timetable MO TU W TH WAR FR
Type of class:	Workshops, 30 hours, 30 places more information
Coordinators:	Janusz Uchmański
Group instructors:	Janusz Uchmański
Course homepage:	https://teams.microsoft.com/l/team/19%3a086ba876377e4260830775a8fb378f80%40thread.tacv2/conversations?groupId=2c17b0f6-9ca0-424c-85c1-d57846f4a939&tenantId=12578430-c51b-4816-8163-c7281035b9b3
Students list:	(inaccessible to you)
Credit:	Course - examination Workshops - examination
(in Polish) E-Learning:	(in Polish) E-Learning z podziałem na grupy
Short description:	The aim is to learn basis of mathematical modelling in biology using NetLogo programming language and translating description of biological problems into mathematical and programming languages.The lecture will be illustrated by basics ecological models. YTheir features will be disccused. Basic information from mathematics and computer use are recommended.
Full description:	Modelling in biology. Mathematics as an language for natural sciences. Description of time and space in mathematical models. Statictical or empirical models. Vollenweide'sr model as an example. Habitat models on example of scenariuos Vistulla valley transformations. Model LARCH and RAMAS. NetLogo as a usful programming tool. Population growth - linear, exponential and logistic model. Deterministic chaos. Stochastic models of small populations. Stability - its mathematical formulation and ecological interpretations. Are ecological systems stable? Stability and complexity question. Dynamics of two competing population. Predator-prey system dynamics. Oscillations and limit cycles. Models of matter cycling in ecosystems. Phosporus cycling in a lake as an example of ecosystem's functioning model. Forest dynamics models. Cellural automata. Individual-based modeling and its differences with classical modeling. Fractal modelling - unitary and modular organisms. Speciation and extinction of species.
Bibliography:	Białynicki-Birula I., Białynicka-Birula I. 2002 Modelowanie rzeczywistości. Prószyński i S-ka Bodnar M. 2008. Zbiór zadań z matematyki dla biologów. Wydawnictwa Uniwersytetu Warszawskiego, Warszawa Czarnowski D. S., Romanowski J. M., Stiepanowa N. W. 1974. Co to jest biofizyka matematyczna. PWN. Foryś U. 2005. Matematyka w biologii. Wydawnictwa Naukowo-Techniczne, Warszawa. Murray J.D. 1989. Mathematical biology. Springer-Verlag. Murray J. D. 2006. Wprowadzenie do biomatematyki. Wydawnictwo Naukowe PWN, Warszawa. Uchmański J. 1992. Klasyczna ekologia matematyczna. PWN. Wit R. 1994. Wykłady o modelowaniu w fizyce medycznej. Uniwersytet Jagielloński. Wrzosek D. 2008. Matematyka dla biologów. Wydawnictwa Uniwersytetu Warszawskiego, Warszawa
Wymagania wstępne:	High school level of mathematics

Classes in period "Winter semester 2024/25" (past)

Time span:	2024-10-01 - 2025-01-31	Selected timetable range: weekly course term Go to timetable MO TU W TH WAR FR
Type of class:	Workshops, 30 hours, 30 places more information
Coordinators:	Janusz Uchmański
Group instructors:	Janusz Uchmański
Course homepage:	https://teams.microsoft.com/l/team/19%3a086ba876377e4260830775a8fb378f80%40thread.tacv2/conversations?groupId=2c17b0f6-9ca0-424c-85c1-d57846f4a939&tenantId=12578430-c51b-4816-8163-c7281035b9b3
Students list:	(inaccessible to you)
Credit:	Course - examination Workshops - examination
(in Polish) E-Learning:	(in Polish) E-Learning z podziałem na grupy
Type of subject:	optional with unlimited choices
(in Polish) Grupa przedmiotów ogólnouczenianych:	(in Polish) nie dotyczy
Short description:	The aim is to learn basis of mathematical modelling in biology using NetLogo programming language and translating description of biological problems into mathematical and programming languages.The lecture will be illustrated by basics ecological models. YTheir features will be disccused. Basic information from mathematics and computer use are recommended.
Full description:	Modelling in biology. Mathematics as an language for natural sciences. Description of time and space in mathematical models. Statictical or empirical models. Vollenweide'sr model as an example. Habitat models on example of scenariuos Vistulla valley transformations. Model LARCH and RAMAS. NetLogo as a usful programming tool. Population growth - linear, exponential and logistic model. Deterministic chaos. Stochastic models of small populations. Stability - its mathematical formulation and ecological interpretations. Are ecological systems stable? Stability and complexity question. Dynamics of two competing population. Predator-prey system dynamics. Oscillations and limit cycles. Models of matter cycling in ecosystems. Phosporus cycling in a lake as an example of ecosystem's functioning model. Forest dynamics models. Cellural automata. Individual-based modeling and its differences with classical modeling. Fractal modelling - unitary and modular organisms. Speciation and extinction of species.
Bibliography:	Białynicki-Birula I., Białynicka-Birula I. 2002 Modelowanie rzeczywistości. Prószyński i S-ka Bodnar M. 2008. Zbiór zadań z matematyki dla biologów. Wydawnictwa Uniwersytetu Warszawskiego, Warszawa Czarnowski D. S., Romanowski J. M., Stiepanowa N. W. 1974. Co to jest biofizyka matematyczna. PWN. Foryś U. 2005. Matematyka w biologii. Wydawnictwa Naukowo-Techniczne, Warszawa. Murray J.D. 1989. Mathematical biology. Springer-Verlag. Murray J. D. 2006. Wprowadzenie do biomatematyki. Wydawnictwo Naukowe PWN, Warszawa. Uchmański J. 1992. Klasyczna ekologia matematyczna. PWN. Wit R. 1994. Wykłady o modelowaniu w fizyce medycznej. Uniwersytet Jagielloński. Wrzosek D. 2008. Matematyka dla biologów. Wydawnictwa Uniwersytetu Warszawskiego, Warszawa
Wymagania wstępne:	High school level of mathematics

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