ECTS
ECTS Course Catalogue
Course details
Course code: ICSS10123o15Semester: 2015/2016 winter
Name: Algebra
Major: Safety Engineering
Study Type: first cycle
Course type: compulsory
Study Semester: 1
ECTS points: 7
Hours (Lectures / Tutorials / Other): 30 / 28 / 0
Lecturer: dr hab. Wiesław Szulczewski, prof. nadzw.
Language of instruction: Polish
Learning outcomes: Knowledge: The student understands the importance of mathematics and its applications. They know the basic theorems of the known branches of mathematics. They know the selected concepts and methods of mathematical logic, algebra and geometry. IB1A_W1 Skills: The student is able to deal with linear spaces, vectors, matrices. They can calculate determinants and know their properties. They solve systems of linear equations with constant coefficients. They compute the eigenvalues and eigenvectors of a matrix. IB1A_U1 Social competence: The student understands their limitations in gaining knowledge and understands the need for further education. IB1A_K1
Competences:
Prerequisites: Knowledge of mathematics at secondary school level
Course content: Foundations of mathematical logic. Complex numbers. Complex polynomials. Fundamental theorem of algebra. Rational functions and partial fraction decomposition. Matrices and determinants. Matrix equations. Rank of a matrix. Systems of linear equations. Eigenvalues and eigenvectors, characteristic polynomials of a matrix. Analytical geometry in plane. Linear transformations. Vector space. Analytical geometry in space. Selected classes of curves and surfaces of second order.
Recommended literature: 1. Mostowski A., Stark M., 1975, Elementy algebry wyższej, PWN, Warszawa. 2. Mostowski A., Stark M., 1976, Algebra liniowa, PWN, Warszawa. 3. Jurlewicz T., Skoczylas Z., 1999 (and later editions), Algebra liniowa 1. Definicje, twierdzenia, wzory, Oficyna Wydawnicza GIS, Wrocław, 4. Jurlewicz T., Skoczylas Z., 1999 (and later editions), Algebra liniowa 1. Przykłady i zadania, Oficyna Wydawnicza GIS, Wrocław. 5. Leja F., 1976, Geometria analityczna, PWN, Warszawa. Krysicki W., Włodarski L., 1998 (and later editions), Analiza matematyczna w zadaniach, Część I, PWN, Warszawa. 6. S. Smolik, 2004, Zadania z zastosowań matematyki dla Akademii Rolniczych, SGGW, Warszawa.
Assessment methods: Tutorial's final mark is based on test results and activity throughout the semester. Written-oral exam. To get a positive mark it is obligatory to get at least 50% of the possible points.
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