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
Secondary school mathematics.
Zakres tematyczny
Lecture
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)
Matrices: operations on matrices, the determinant of a matrix and its properties, the inverse matrix, and the rank of a matrix. (6 hours)
Solving systems of linear equations. The Kronecker-Cappelli theorem, the Cramer's theorem. The Gauss elimination method. (4 hours)
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)
Relations and their properties. An equivalence relation and equivalence classes. A partial order relation, partially ordered sets. Lattices. (5 hours)
Algebraic structures: Boolean algebras, groups, and fields. Examples. (3 hours)
Class
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)
Matrices: operations on matrices, the determinant of a matrix and its properties, the inverse matrix, and the rank of a matrix. (6 hours)
Solving systems of linear equations. The Kronecker-Cappelli theorem, the Cramer's theorem. The Gauss elimination method. (6 hours)
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)
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
Robert A. Beezer, A First Course in Linear Algebra.
Thomas W. Judson, Abstract Algebra: Theory and Applications.
Literatura uzupełniająca
Serge Lang, Linear Algebra, Undergraduate Texts in Mathematics, 1987.
Serge Lang, Introduction to Linear Algebra, Undergraduate Texts in Mathematics, 1986.
Uwagi
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