1. SylabUZ
2. Wydział Matematyki, Informatyki i Ekonometrii
3. semestr zimowy 2023/2024
4. Computer science and econometrics - pierwszego stopnia z tyt. licencjata
5. Linear Algebra 1

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Linear Algebra 1 - opis przedmiotu

Cel przedmiotu

The aim is for the student to achieve skills and competencies in understanding the basic mathematical topics listed in the thematic scope of the subject and to use the acquired knowledge as linear algebra tools in econometrics and computer science.

Wymagania wstępne

Zapisz zmiany

Secondary school mathematics.

Zakres tematyczny

Lecture

1. Complex numbers: conjugate of a complex number, the modulus, the trigonometric form, the geometrical interpretation of operations, de Moivre's formula, and 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, and 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 (for information). (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, and the root of complex numbers. (6 hours)
2. Matrices: operations on matrices, the determinant of a matrix and its properties, the inverse matrix, and 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 (for information). (6 hours)
5. Relations and their properties. (2 hours)

Metody kształcenia

Traditional lecture; discussion lecture; and problem lecture.

Exercises: solving typical tasks illustrating the subject matter, exercises on the application of theory, and solving problem tasks.

Efekty uczenia się i metody weryfikacji osiągania efektów uczenia się

Opis efektu	Symbole efektów	Metody weryfikacji	Forma zajęć

Warunki zaliczenia

The condition for taking the exam is a positive grade from the exercises obtained in two written tests (with tasks of varying grades of difficulty, allowing for checking whether the student has achieved the learning outcomes to a minimum level) and for active participation in the classes.

The condition for passing the course is a positive grade on the exam.

The final grade is the arithmetic mean of the grade from the exercises and the grade from the exam (written or oral).

Literatura podstawowa

1. Robert A. Beezer, A First Course in Linear Algebra.
2. Thomas W. Judson, Abstract Algebra: Theory and Applications.

Literatura uzupełniająca

1. Serge Lang, Linear Algebra, Undergraduate Texts in Mathematics, 1987.
2. Serge Lang, Introduction to Linear Algebra, Undergraduate Texts in Mathematics, 1986.

Uwagi

Zmodyfikowane przez dr Ewa Synówka (ostatnia modyfikacja: 10-04-2024 19:04)