Mathematics
General data
Course ID: | 1000-111MAT |
Erasmus code / ISCED: |
11.1
|
Course title: | Mathematics |
Name in Polish: | Matematyka |
Organizational unit: | Faculty of Mathematics, Informatics, and Mechanics |
Course groups: |
Requisite courses for first-year students of Biology Requisite subjects for first-year students of Biotechnology Requisite subjects for first-year students of Environmental Protection |
Course homepage: | https://www.mimuw.edu.pl/~darekw/ |
ECTS credit allocation (and other scores): |
3.00
|
Language: | Polish |
Main fields of studies for MISMaP: | biology |
Type of course: | obligatory courses |
Mode: | Classroom |
Short description: |
Students will study basic mathematical notions such as sets, number, relation and functions. We will describe basic types of functions and give the introduction to mathematical analysis. The introduction to theory of ordinary differential equations will be presented as a basis to mathematical modelling of bioloqical phenomena. Moreover, probability theory will be a basis of the probabilistic models. |
Full description: |
We will start the lecture from the description of basic mathematical notions such as sets, numbers, relations, functions. Next, we will describe basic types of functions: linear, exponential and logarythmic as well as logarithms and its applications. The main part on the lecture will be devoted to mathematical analysis. We will define the notion of limit (in the context of sequences and functions), continuity and differentiability of one variable functions. We will try to understand geometrical and physical interpretations of derivative. Next we will describe an extremum and study the dependence between extrema and convexity (concavity) of the function. The theoretical part of the lecture will end with the description of primitive function and the notion of integral and its geometrical interpretation. In the last part of the lecture we will focus on mathematical modelling of biological phenomena. Therefore, it will be necessary to introduce the notion of ordinary differential equations. On the basis we will study some models of population dynamics (equation of Malthus, logistic equation, competition, predation, symbiosis). We will introduce some basic notions of the probability theory and define Markov chains and its applications for models of evolution. |
Bibliography: |
(in Polish) Dariusz Wrzosek, Matematyka dla biologów, Wydawnictwa UW, Warszawa 2008 Marek Bodnar, Zbiór zadań z matematyki dla biologów, Wydawnictwa UW, Warszawa 2008 |
Learning outcomes: |
(in Polish) Wiedza i umiejętności:
|
Assessment methods and assessment criteria: |
The final note will be based on the result of the written exam and students' work during classes. |
Classes in period "Winter semester 2024/25" (past)
Time span: | 2024-10-01 - 2025-01-26 |
Go to timetable
MO CW
CW
TU CW
CW
W CW
CW
TH CW
CW
FR |
Type of class: |
Classes, 45 hours
|
|
Coordinators: | Dariusz Wrzosek | |
Group instructors: | Marcin Choiński, Paweł Cygan, Anna Lisiecka, Waldemar Pałuba, Magdalena Szafrańska-Łęczycka, Dariusz Wrzosek | |
Students list: | (inaccessible to you) | |
Credit: |
Course -
Examination
Classes - Examination |
Classes in period "Winter semester 2025/26" (future)
Time span: | 2025-10-01 - 2026-01-25 |
Go to timetable
MO CW
CW
TU CW
CW
W CW
CW
TH CW
CW
FR |
Type of class: |
Classes, 45 hours
|
|
Coordinators: | Dariusz Wrzosek | |
Group instructors: | Mirosław Lachowicz, Anna Lisiecka, Marcin Małogrosz, Waldemar Pałuba, Tomasz Piasecki, Dariusz Wrzosek | |
Students list: | (inaccessible to you) | |
Credit: |
Course -
Examination
Classes - Examination |
Copyright by University of Warsaw.