Objectives of the course: Introduction to linear algebra. Basic algebraic structures groups, fields, linear spaces and properties of algebraic operations. Applications of matrices, elementary matrix operations, determinants and vectors to the analysis of the following three, stricly connected problems:. Cartesian products. Relations orderings, partitions and equivalence relations. Groups, fields, linear spaces.
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Definicje, twierdzenia, wzory;  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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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.
Algebra Liniowa 1 - Kolokwia i Egzaminy - Gewert Skoczylas