Matematical Modelling in Biology and Medicine
General data
Course ID: | WM-MA-Z-S1-E5-Mmwbim |
Erasmus code / ISCED: | (unknown) / (unknown) |
Course title: | Matematical Modelling in Biology and Medicine |
Name in Polish: | Modelowanie matematyczne w biologii i medycynie |
Organizational unit: | Faculty of Mathematics and Natural Sciences. School of Exact Sciences. |
Course groups: | |
ECTS credit allocation (and other scores): |
6.00
|
Language: | Polish |
(in Polish) Dyscyplina naukowa, do której odnoszą się efekty uczenia się: | mathematics |
Subject level: | elementary |
Learning outcome code/codes: | LECTURE MA1_W01, MA1_W03 EXERCISES MA1_K01, MA1_K02 |
Preliminary Requirements: | (in Polish) Analiza I i II, Algebra Liniowa, RRZ, Rachunek P-stwa |
Full description: |
The aim of the course is to introduce the basics of classical mathematical modeling in biology, epidemiology and medicine. In particular, the student will learn biological and medical applications of integrals and derivatives; equations and systems of ordinary differential equations modeling the development of populations, epidemics, and diseases; discrete models in genetics based on Markov chains. The student will also acquire basic skills in understanding models, their construction, their application in practice and their mathematical analysis. |
Efekty kształcenia i opis ECTS: |
The student knows and understands: (MA1_W01, MA1_W03) W1.1 - using the derivative as the rate of change or gradient of a given quantity, W1.2 - construction, applications and limitations of polynomial regression; W2 - differential equation (dimension 1 or higher) which is a biological and epidemiological model, the concept of steady states, their stability and their importance in models; including models: exponential and logistic, L-V, SIR, their variants; other models; W3 - basic discrete models which are numerical schemes for solving RRZ and discrete models based on Markov chains. The student is able to (MA_W03, MA1_U01) U1 - solve problems requiring the use of derivatives, integrals, research on the course of function variability in biological and epidemiological applications, U2 - perform basic analysis of the RRZ-based model, its steady states, stability, interpret mathematical conclusions in a real context; U3 - carry out basic analysis of a model based on a Markov-type process, its absorbing states, expected value; The student is ready: (MA1_K01, MA1_K02) K1 - prepare a paper presenting a new issue, K2 - participate in a scientific discussion. |
Assessment methods and assessment criteria: |
For all effects, the following assessment criteria are adopted for all forms of verification: grade 5: fully achieved (no obvious shortcomings) grade 4.5: achieved almost fully and criteria for awarding a higher grade are not met grade 4: largely achieved and the criteria for a higher grade are not met grade 3.5: largely achieved - with a clear majority of positives - and the criteria for granting a higher grade are not met grade 3: achieved for most of the cases covered by the verification and criteria for a higher grade are not met grade 2: not achieved for most of the cases covered by the verification |
Classes in period "Winter semester 2022/23" (past)
Time span: | 2022-10-01 - 2023-01-31 |
Navigate to timetable
MO TU W TH FR SA WYK
CW
|
Type of class: |
Classes, 20 hours
Lectures, 20 hours
|
|
Coordinators: | Maria Gokieli | |
Group instructors: | Maria Gokieli | |
Students list: | (inaccessible to you) | |
Examination: |
Course -
examination
Classes - graded credit Lectures - examination |
|
(in Polish) E-Learning: | (in Polish) E-Learning (pełny kurs) z podziałem na grupy |
|
(in Polish) Opis nakładu pracy studenta w ECTS: | (in Polish) WYKŁAD uczestnictwo w zajęciach - 20 h konsultacje - 6 h egzamin - 4 h samodzielna lektura - 10 h przygotowanie do egzaminu - 10 h razem 50 h czyli 2 ECTS ĆWICZENIA uczestnictwo w zajęciach - 20 h przygotowanie referatów - 15 h prace domowe - 15 h razem 50 h czyli 2 ECTS |
Classes in period "Winter semester 2023/24" (past)
Time span: | 2023-10-01 - 2024-01-31 |
Navigate to timetable
MO TU W TH FR SA WYK
CW
SU WYK
CW
|
Type of class: |
Classes, 20 hours
Lectures, 20 hours
|
|
Coordinators: | Maria Gokieli, Paweł Pęczkowski | |
Group instructors: | Paweł Pęczkowski | |
Students list: | (inaccessible to you) | |
Examination: | examination | |
(in Polish) E-Learning: | (in Polish) E-Learning |
|
(in Polish) Opis nakładu pracy studenta w ECTS: | LECTURE participation in classes - 20 h consultations - 6 h exam - 4 hours independent reading - 10 h preparation for the exam - 10 hours total 50 hours, i.e. 2 ECTS EXERCISES participation in classes - 20 h preparation of papers - 15 hours housework - 15 h total 50 hours, i.e. 2 ECTS |
|
Type of subject: | obligatory |
|
(in Polish) Grupa przedmiotów ogólnouczenianych: | (in Polish) nie dotyczy |
|
Full description: |
The aim of the course is to introduce the basics of classical mathematical modeling in biology, epidemiology and medicine. In particular, the student will learn biological and medical applications of integrals and derivatives; equations and systems of ordinary differential equations modeling the development of populations, epidemics, and diseases; discrete models in genetics based on Markov chains. The student will also acquire basic skills in understanding models, their construction, their application in practice and their mathematical analysis. |
|
Bibliography: |
Required literature J. Stewart, Calculus, PWN 2020 U. Foryś, Mathematical modeling in biology and medicine, https://mst.mimuw.edu.pl/wyklady/mbm/wyklad.pdf Additional literature U. Foryś, Mathematics in biology, WNT 2005 J.D. Murray, Introduction to biomathematics, PWN 2006 A. Garfinkel, J. Shevtsov, Y. Guo, Modeling Life - The Mathematics of Biological Systems, Springer 2017 |
|
Wymagania wstępne: |
3rd year. nst. |
Copyright by Cardinal Stefan Wyszynski University in Warsaw.