(in Polish) Algebra z elementami logiki WM-P-PSM-AEL
The course aims to familiarize students with the basics of algebra, matrix calculus and its applications, and three-dimensional analytic geometry. Students acquire skills in analyzing and solving linear systems, finding eigenvalues and eigenspaces, and modular arithmetic.
(in Polish) Grupa przedmiotów ogólnouczenianych
Subject level
Learning outcome code/codes
Type of subject
Preliminary Requirements
Course coordinators
Learning outcomes
Lecture: The student knows and understands:
W1: the concepts of a group, a ring, and a field, the differences between them, and basic examples,
W2: the concepts of a matrix and a vector and their basic properties,
W3: the properties of determinants and the geometric interpretation of determinants, the definitions and properties of the scalar, vector, and mixed product of vectors,
W4: basic theorems and laws concerning matrices,
W5: vector and matrix notation in the analysis of systems of linear equations,
W6: knows the definition of a field of complex numbers and operations within this field, as well as basic properties of complex numbers,
W7: the definitions of a line and a plane in the space R^3, various ways of representing them and their properties,
W8: the definitions of linear spaces and transformations, the concept of eigenvalues.
Exercises: The student is able to:
U1: use the concepts of polynomial, vector, matrix, and scalar product,
U2: calculate determinants and apply their properties to solve problems,
U3: solve systems of linear equations with constant coefficients and use the geometric interpretation of solutions,
U4: perform calculations in operations mod n and in the field of complex numbers,
U5: determine the eigenvectors of matrices, verify the linear independence of vectors, and determine the basis of a linear space.
Assessment criteria
Assessment of work during tutorials is ongoing – worksheets and teamwork.
Only one absence from the tutorial is permitted! Final test during the last class (91% - 100% - 5.0; 81% - 90% - 4.5; 71% - 80% - 4.0; 61% - 70% - 3.5; 51% - 60% - 3.0). Only those who successfully complete the exercises are admitted to the test.
The following evaluation criteria are adopted for all effects in all forms of verification:
5.0: fully achieved (without any noticeable shortcomings),
4.5: almost fully achieved and the criteria for a higher rating are not met,
4.0: achieved to a large extent and the criteria for a higher rating are not met,
3.5: achieved to a large extent – with a clear predominance of positives – and the criteria for a higher rating are not met,
3.0: achieved for the majority of cases included in the review and the criteria for a higher rating are not met,
2.0: not achieved for the majority of cases included in the review.
Practical placement
no
Bibliography
1. Wojciech Guzicki, Piotr Zakrzewski, Wykłady ze wstepu do matematyki. Wprowadzenie do teorii mnogości, Wydawnictwo Naukowe PWN, Warszawa, 2005.
2. Tadeusz Koźniewski, Wykłady z algebry liniowej I, Wydanie piąte, Wadawnictwa Uniwersytetu Warszawskiego, Warszawa, 2008.
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: