Karta przedmiotu

Linear algebra with analytical geometry

Some basic information about the module

Cycle of education:

2019/2020

The name of the faculty organization unit:

The faculty Mathematics and Applied Physics

The name of the field of study:

Engineering and data analysis

The area of study:

sciences

The profile of studing:

The level of study:

first degree study

Type of study:

full time

discipline specialities :

The degree after graduating from university:

engineer

The name of the module department :

Departament of Discrete Mathematics

The code of the module:

12292

The module status:

mandatory for teaching programme

The position in the studies teaching programme:

sem: 1 / W30 C30 L15 / 5 ECTS / E

The language of the lecture:

Polish

The name of the coordinator:

Małgorzata Wołowiec-Musiał, PhD

office hours of the coordinator:

poniedziałek 10:30-12:00, czwartek 10:30-12:00

semester 1:

Adrian Michalski, PhD

semester 1:

Paweł Bednarz, PhD

semester 1:

Natalia Paja, PhD

The aim of studying and bibliography

The main aim of study:
The aim of the course is to familiarize students with the basics of linear algebra and analytic geometry.

The general information about the module:
The module consists of 30 hours of lectures, 30 hours of classes and 15 hours of laboratories. It ends with an exam.

Bibliography required to complete the module

Bibliography used during lectures
1	T. Jurlewicz, Z. Skoczylas	Algebra i geometria analityczna. Definicje, twierdzenia, wzory	Oficyna Wydawnicza GiS, Wrocław.	2014.
2	M. Zakrzewski	Markowe wykłady z matematyki. Algebra z geometrią	Oficyna Wydawnicza GiS, Wrocław.	2015.

Bibliography used during classes/laboratories/others
1	T. Jurlewicz, Z. Skoczylas	Algebra i geometria analityczna. Przykłady i zadania	Oficyna Wydawnicza GiS, Wrocław.	2008.
2	J. Stankiewicz, K.Wilczek	Algebra z geometrią. Teoria, przykłady, zadania	Oficyna Wydawnicza PRz, Rzeszów.	2006.
3	P.N. de Souza, R.J. Fateman, J. Moses, C. Yapp	The Maxima Book	http://maxima.sourceforge.net.	-

Bibliography to self-study
1	M. Gewert, Z, Skoczylas	Algebra i geometria analityczna. Kolokwia i egzaminy	Oficyna Wydawnicza GiS, Wrocław.	2009.
2	T. Świrszcz	Algebra liniowa z geometrią	Oficyna Wydawnicza Politechniki Warszawskiej, Warszawa.	2012.

Basic requirements in category knowledge/skills/social competences

Formal requirements:
The student satisfies the formal requirements set out in the study regulations.

Basic requirements in category knowledge:
basic knowledge of mathematics at the high school level

Basic requirements in category skills:
ability to use basic mathematical tools at the high school level

Basic requirements in category social competences:
preparation for taking substantively justified mathematical actions to solve the posed problem

Module outcomes

MEK	The student who completed the module	Types of classes / teaching methods leading to achieving a given outcome of teaching	Methods of verifying every mentioned outcome of teaching	Relationships with KEK	Relationships with PRK
MEK01	can make operations on complex numbers and can find roots of complex polynomials	lecture, class, laboratory	written test, written exam	K-W01+ K-U01++	P6S-UW P6S-WG
MEK02	can make matrix operations and calculate the determinant and the rank of a matrix	lecture, class, laboratory	written test, written exam	K-W01+ K-U01++	P6S-UW P6S-WG
MEK03	can solve systems of linear equations using matrix algebra	lecture, class, laboratory	written test, written exam	K-W01+ K-U01++ K-K02+	P6S-KK P6S-KO P6S-UW P6S-WG
MEK04	can describe lines and planes in space and recognize conic curves by its equations	lecture, class, laboratory	written test, written exam	K-W01+ K-U01++ K-K01+	P6S-KK P6S-UW P6S-WG
MEK05	can make in CAS Maxima calculations on complex numbers, matrices, and solve systems of linear equations, can draw conic curves in 2D and lines and planes in 3D	laboratory	practical test on a computer	K-W02+ K-U01++ K-K01+	P6S-KK P6S-UW P6S-WG

The syllabus of the module

Sem.	TK	The content	realized in	MEK
1	TK01	The Cartesian product of sets. Set of comlex numbers: standard and polar form of a complex number, power and roots of complex numbers.	W1-W6, C1-C4, L1-L3	MEK01 MEK05
1	TK02	Complex polynomials: calculations on complex polynomials, roots of complex polynomials, the fundamental theorem of algebra. Partial fraction decomposition of a rational function.	W7-W10, C5-C8, L4-L6	MEK01 MEK05
1	TK03	Matrices and determinants: operations on matrices, definitions, rules of computation and properties of determinants, the concepts of the inverse matrix and the rank of a matrix, some applications of matrices in practice.	W11-W16, C9-C12, L7-L8	MEK02 MEK05
1	TK04	Systems of linear equations, Cramer's system, solvability of any system of linear equations, theorem of Kronecker-Capelli, Gaussian elimination.	W17-W20, C13-C16 L9-10	MEK03 MEK05
1	TK05	Analytic geometry in the three-dimensional space: vector calculus, inner product, cross product and, mixed product of vectors, equations of lines and planes, relations between lines and planes in space.	W21-W26, C17-C22, L11-L12	MEK04 MEK05
1	TK06	Definition and examples of vector spaces. Linear independence of vectors and basis of a vector space. Conic sections and some mechanical curves.	W27-W30, C23-C26, L13-14	MEK04 MEK05
1	TK07	Tests involving module outcomes realized during lectures, classes and laboratories.	C27-C30, L15	MEK01 MEK02 MEK03 MEK04 MEK05

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 1)		contact hours: 30.00 hours/sem.	complementing/reading through notes: 3.00 hours/sem. Studying the recommended bibliography: 7.00 hours/sem.
Class (sem. 1)	The preparation for a Class: 2.00 hours/sem. The preparation for a test: 8.00 hours/sem.	contact hours: 30.00 hours/sem.	Finishing/Studying tasks: 10.00 hours/sem.
Laboratory (sem. 1)	The preparation for a Laboratory: 2.00 hours/sem. The preparation for a test: 3.00 hours/sem.	contact hours: 15.00 hours/sem.	Finishing/Making the report: 5.00 hours/sem.
Advice (sem. 1)	The preparation for Advice: 1.00 hours/sem.	The participation in Advice: 2.00 hours/sem.
Exam (sem. 1)	The preparation for an Exam: 10.00 hours/sem.	The written exam: 2.00 hours/sem.

The way of giving the component module grades and the final grade

The type of classes	The way of giving the final grade
Lecture	A credit for the lecture is based on the written exam.
Class	A credit for the class is based on at least two written tests involving module outcomes realized during the class. Student's activity during the class can raise the grade.
Laboratory	A credit for the laboratory is based on the practical test on a computer.
The final grade

Sample problems

Required during the exam/when receiving the credit
(-)

Realized during classes/laboratories/projects
(-)

Others
(-)

Can a student use any teaching aids during the exam/when receiving the credit : no

The contents of the module are associated with the research profile yes

1	U. Bednarz; M. Wołowiec-Musiał	Generalized Fibonacci–Leonardo numbers	2024
2	U. Bednarz; A. Włoch; M. Wołowiec-Musiał	New Types of Distance Padovan Sequences via Decomposition Technique	2022
3	U. Bednarz; M. Wołowiec-Musiał	Distance Fibonacci Polynomials—Part II	2021
4	U. Bednarz; M. Wołowiec-Musiał	Distance Fibonacci Polynomials	2020