Lecture 1 - Preliminaries Presentation of various algebraic objects with particular emphasis on differences and relationships between them. Definitions of number sets: natural numbers, integers, rational numbers, irrational numbers, real numbers, complex numbers, vectors and matrices. Relationships between the objects: the representation of a set of vectors as a matrix, the representation of a complex number as a vector. Lecture 2 - Properties of number sets Divisibility of integers, the congruence modulo, Chinese Remainder Theorem, different number systems. Lecture 3 - Complex numbers Algebra of complex numbers, algebraic and geometric representation. Modulus and argument, trigonometric form, de Moivre's formula.

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Definicje, twierdzenia, wzory; [5] Mostowski A. Additional information registration calendar, class conductors, localization and schedules of classes , might be available in the USOSweb system:. Organized by: Faculty of Mathematics and Computer Science. Lecture, discussion, working in groups, heuristic talk, directed reasoning, self-study. The evaluation of the lecture is the evaluation of a multiple-choice test to check the learning outcomes in terms of: e1 - e8.

The positive evaluation of the two colloquia is a prerequisite for admission to the test. The positive evaluation of the test is a prerequisite to get the final grade. In special cases, the assessment may be increased by half a degree. The greatest common divisor. Euclidean algorithm. Prime numbers. Modular arithmetic. Diophantine equations. Groups, rings, fields. Ring of polynomials. Matrices, determinants. Vector spaces. Vector space Rn. Linear independence. Basis of linear space. Systems of linear equations.

Gauss-Jordan elimination method. Theorem of Cramer. Theorem of Kronecker-Capelli. Linear transformations. Matrix representation of linear transformation.

Lines, planes, hyperplanes in Rn. The purpose of this course is to present basic concepts and facts from number theory and algebra of fundamental importance in the further education of information technology - including issues relating to divisibility, modular arithmetic, matrix calculus and analytic geometry.

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## JURLEWICZ SKOCZYLAS ALGEBRA LINIOWA 2 PRZYKADY ZADANIA PDF

Matrixes and determinants, solving of linear equations system, fundamental definitions of 3D-analytical geometry. Differential and integral calculations for one-variable functions. Matrix calculations. Inverse matrix. System of linear equations — formula of Cramer, Kronecker-Capelli. Method of the Gauss elimination and triangulization. Vector calculations, scalar, vector and mixed product.

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## Calculus and linear algebra

Composition of a function and inverse function. Monotonicity of a sequence of numbers. Comparison test for convergence of infinite series. Power series. Continuity of a function.

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## Algebra Liniowa 2 - Przykłady I Zadania, Jurlewicz, Skoczylas, Gis 2003

Author: Teresa Jurlewicz, Zbigniew Skoczylas. Definicje, twierdzenia, wzory; [5] Mostowski A. Jurlewiczz of Exact Sciences. The main aim of study: The whole-number operations of addition, subtraction, multiplication and division and their properties form the foundation of arithmetic. Faculty of Mathematics and Computer Science. Faculty of Mathematics and Natural Sciences. Copyright by Cardinal Stefan Wyszynski University.