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Algebra with geometry I

General data

Course ID: 1100-1AF10 Erasmus code / ISCED: 11.101 / (unknown)
Course title: Algebra with geometry I Name in Polish: Algebra z geometrią I
Organizational unit: Faculty of Physics
Course groups: (in Polish) Astronomia, fizyka, I stopień; przedmioty do wyboru z grupy matematyka
(in Polish) Nanoinżynieria; przedmioty dla I roku
(in Polish) Nauczanie fizyki; przedmioty dla I roku
(in Polish) ZFBM - Zastosowania fizyki w biologii i medycynie; przedmioty dla I roku
Astronomy (1st level); 1st year courses
Physics (1st level); 1st year courses
ECTS credit allocation (and other scores): 5.00
Language: Polish
Main fields of studies for MISMaP:

physics

Prerequisites (description):

Finished high school.

Mode:

Classroom

Short description:

The purpose of the course is to explain basic notions of algebra such as complex numbers, polynomials, groups, vectors and matrices.

Full description:

The purpose of the course is to explain notions that appear in mathematics and physics throughout the entire period of studies. These abstract notions will be illustrated with various examples to make them maximally comprehensible and to demonstrate their usefulness in physics.

1. Complex numbers, number fields.

2. Third degree algebraic equations.

3. Basic properties of polybomials, the greatest common divisor.

4. The notion of a group, permutation groups, permutation sign and the decomposition of permutation into cycles.

5. Vector spaces, linear independence, basis, subspaces, sums and intersections of subspaces.

6. Linear maps, kernel, image, the matrix of a linear map.

7. Determinant.

Bibliography:

1. S. Zakrzewski, Algebra i geometria, Warsaw University publication.

2. P. Urbański, Algebra liniowa i geometria, Warsaw University publication.

Learning outcomes:

After having completed the course students should:

a) be familiar with the notion of complex numbers and calculations involving complex numbers;

b) understand the notions of a vector space, linear independance, a basis;

c) understand the notion of a linear map and a matrix;

d) be able to solve systems of linear equations;

e) be able to compute determinants and find the inverese matrix.

Assessment methods and assessment criteria:

Midterms and written exam -- computational part;

oral exam -- theoretical part.

Practical placement:

none

Classes in period "Winter semester 2020/21" (past)

Time span: 2020-10-01 - 2021-01-31
Choosen plan division:


magnify
see course schedule
Type of class: Class, 30 hours, 150 places more information
Lecture, 30 hours, 150 places more information
Coordinators: Maciej Nieszporski
Group instructors: Marcin Badziak, Marcin Kościelecki, Maciej Nieszporski, Adam Szereszewski
Students list: (inaccessible to you)
Examination: Course - Examination
Lecture - Examination

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

Time span: 2021-10-01 - 2022-02-20
Choosen plan division:


magnify
see course schedule
Type of class: Class, 30 hours, 150 places more information
Lecture, 30 hours, 150 places more information
Coordinators: Maciej Nieszporski
Group instructors: Julia Lange, Maciej Nieszporski, Janusz Rosiek, Adam Szereszewski, Piotr Wrzosek
Students list: (inaccessible to you)
Examination: Course - Examination
Lecture - Examination
Course descriptions are protected by copyright.
Copyright by University of Warsaw.