Algebra with geometry I
General data
Course ID:  11001AF10  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:  20201001  20210131 
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:  20211001  20220220 
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 
Copyright by University of Warsaw.