1. SylabUZ
2. Wydział Matematyki, Informatyki i Ekonometrii
3. semestr zimowy 2019/2020
4. Computer science and econometrics - pierwszego stopnia z tyt. licencjata
5. Algebra liniowa 1

Wygeneruj PDF dla tej strony

Algebra liniowa 1 - opis przedmiotu

Cel przedmiotu

The aim of the course is to acquaint the student with the basic of linear algebra.

Wymagania wstępne

Zapisz zmiany

Secondary school mathematics.

Zakres tematyczny

Lecture

1.  Complex numbers: the conjugate of a complex number, the modulus, the trigonometric form, the geometrical interpretation of operations, de Moivre's formula, the root of complex numbers. The fundamental theorem of algebra. (6 hours)
2. Matrices: operations on matrices, the determinant of a matrix and its properties, the inverse matrix, the rank of a matrix. (6 hours)
3. Solving systems of linear equations. The Kronecker-Cappelli theorem, the Cramer's theorem. The Gauss elimination method. (4 hours)
4. Analytical geometry in R3. The dot product and the cross product. The equation of a plane and a line. Quadric surfaces. (6 hours)
5. Relations and their properties. An equivalence relation and equivalence classes. A partial order relation, partially ordered sets. Lattices. (5 hours)
6. Algebraic structures: Boolean algebras, groups and fields. Examples. (3 hours)

Class

1. Complex numbers: the conjugate of a complex number, the modulus, the trigonometric form, the geometrical interpretation of operations, de Moivre's formula, the root of complex numbers. The fundamental theorem of algebra. (6 hours)
2. Matrices: operations on matrices, the determinant of a matrix and its properties, the inverse matrix, the rank of a matrix. (6 hours)
3. Solving systems of linear equations. The Kronecker-Cappelli theorem, the Cramer's theorem. The Gauss elimination method. (6 hours)
4. Analytical geometry in R³. The dot product and the cross product. The equation of a plane and a line. Quadric surfaces. (6 hours)
5. Relations and their properties. An equivalence relation and equivalence classes. A partial order relation, partially ordered sets. Lattices. (2 hours)

Metody kształcenia

Traditional lecturies and solving problems under the supervision of the instructor.

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

In order to be allowed to take the exam a student has to have a positive class grade and active participation in classes.

In order to pass the exam a student has to have a positive exam grade.

The final grade is an arithmetic average of the class grade  and the exam grade.

Literatura podstawowa

1. Robert A. Beezer, A First Course in Linear Algebra.

2. Thomas W. Judson, Abstract Algebra:Theory and Applications.

3. Jim Hefferon, Linear Algebra.

Literatura uzupełniająca

Uwagi

Zmodyfikowane przez dr Alina Szelecka (ostatnia modyfikacja: 21-11-2020 06:10)