docAlgebra z Geometri ˛a Analityczn ˛a
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Algebra z Geometri ˛a Analityczn ˛a
Zał nr 4 do ZW Faculty of Fundamental Problems of Technology COURSE CARD Name in polish : Algebra z Geometria˛ Analityczna˛ Name in english : Algebra and Analytic Geometry Field of study : Computer Science Specialty (if applicable) : Undergraduate degree and form of : engineering, stationary Type of course : compulsory Course code : E1_T02 Group rate : Yes Lectures Exercides Laboratory Project Number of classes held in schools (ZZU) 60 30 The total number of hours of student work- 120 90 load (CNPS) Assesment pass For a group of courses final course mark X Number of ECTS credits 4 3 including the number of points correspond3 ing to the classes of practical (P) including the number of points correspond- 4 3 ing occupations requiring direct contact (BK) PREREQUISITES FOR KNOWLEDGE, SKILLS AND OTHER POWERS This course has no pre-specified requirements. COURSE OBJECTIVES Seminar C1 Learning properties of basic notions of algebra, linear algebra and analytic geometry C2 Achievement of practical competence in applications of basic notions of algebra, linear algebra and analytic geometry 1 COURSE LEARNING OUTCOMES The scope of the student’s knowledge: W1 Student knows notion and examples of groups, rings and fields. Student knows notion of polynomials and Fundamental Theorem of Algebra. W2 Students knows theorem of Kronecker-Capelli, notion of basis and dimension of linear space, and linear subspaces. W3 Student knows notion of matrix, image, kernel, eigenvalue and eigenvector of linear transformation. Student knows notion of direct orthogonal sum of linear subspace and its orthogonal complement in Eucliden space. W4 Student knows criterion of Sylvester for quadratic forms. Student knows singular value decomposition of matrix, norms of matrices. Student knows equations of lines, planes and conics. The student skills: U1 Student is able to perform operations in simple groups, field of complex numbers and on polynomials. U2 Student is able to solve systems of linear equations, compute inverses, determine coefficients of vector in basis and dimension of linear subspace. U3 Student is able to compute eigenvalues and eigenvectors of matrix, describe kernels of linear transformations. Student is able to determine matrix of change of basis. Student is able to apply orthogonalization of GramSchmidt and to compute orthogonal projection on linear subspace. U4 Student is able to check positivity of quadratic forms. Student is able to investigate location of points, lines and planes, and to compute norms of vectors and matrices. U5 Student is able to apply Octave to solving simple problems of linear algebra, geometry and scientific computing. The student’s social competence: K1 Student knows applications of complex number in scinces and technique. K2 Student knows basic applications of matrices in science and technique. COURSE CONTENT 2 Wy1 Wy2 Wy3 Wy4 Wy5 Wy6 Wy7 Wy8 Wy9 Wy10 Wy11 Wy12 Wy13 Wy14 Wy15 Wy16 Wy17 Wy18 Wy19 Wy20 Ćw1 Ćw2 Ćw3 Ćw4 Ćw5 Ćw6 Ćw7 Ćw8 Ćw9 Ćw10 Ćw11 Ćw12 Ćw13 Ćw14 Ćw15 Ćw16 Type of classes - lectures Groups, rings and fields Field of complex numbers Polynomials and their roots Matrices Introduction to Octave Determinants and inverses Systems of linear equations and Gauss elimination Linear spaces Arbitrary systems of linear equations Applications of systems of linear equations Test I Eigenvalues and eigenvectors of matrix Linear transformations Euclidean spaces Applications of orthogonal projections in approximation Elements of analytic geometry in R2 and R3. Quadratic forms Conics Test II SVD decomposition of matrix and its applications Type of classes - exercises Introduction Operations in groups Operations with complex numbers given in different forms and roots Polynomials and their decompositions Simple commands in Octave Test Matrices, determinants and elementary transformations Gauss elimination and Cramer’s rule Bases and dimensions of linear spaces and subspaces Solving system of linear equations with arbitrary rectangular matrix Eigenvalues and eigenvectors of matrix, similarity transformation of matrix to diagonal form Linear transformations and their ranges and kernels Test Gram-Schmidt ortogonalization and application of orthogonal projection in approximation Change of basis and positive definite quadratic forms Determining mutual positions of points, lines and planes. Applied learning tools 1. Traditional lecture 2. Solving tasks and problems 3. Solving programming tasks 4. Consultation 5. Self-study students EVALUATION OF THE EFFECTS OF EDUCATION ACHIEVEMENTS 3 4h 4h 4h 2h 2h 4h 4h 4h 2h 2h 2h 2h 6h 4h 2h 4h 2h 2h 2h 2h 2h 2h 2h 2h 1h 1h 2h 2h 2h 2h 2h 2h 1h 3h 2h 2h Value Number of training effect F1 F2 W1-W4, K1-K2 U1-U5, K1-K2 Way to evaluate the effect of education two tests on lectures two tests on exercises, report, activity of student during exercises P=50%*F1+50%*F2 BASIC AND ADDITIONAL READING 1. J. Klukowski, I. Nabiałek, Algebra dla studentów, WNT 2005. 2. B. Gleichgewicht, Algebra, PWN 1976, Oficyna Wyd. GiS 2002. 3. G. Banaszak, W. Gajda, Elementy algebry liniowej, cz˛eść I i II, WNT 2002. 4. T. Jurlewicz, Z. Skoczylas, Algebra i geometria analityczna, Oficyna Wyd. GiS 2005. 5. T. Jurlewicz, Z. Skoczylas, Algebra liniowa 2, Oficyna Wyd. GiS, Wrocław 2006. 6. J. Rutkowski, Algebra abstrakcyjna w zadaniach, PWN 2000. 7. P. Krzyżanowski, Obliczenia inżynierskie i naukowe. Szybkie, skuteczne, efektowne, PWN 2011. 8. H. Anton, Ch. Rorres. Elementary Linear Algebra, Applications Version, Wiley 2005. 9. G. Strang, Introduction to Linear Algebra, Wellesley-Cambridge Press 2009. 10. C.D. Meyer, Matrix Analysis and Applied Linear Algebra, SIAM 2000. SUPERVISOR OF COURSE dr hab. Krystyna Zi˛etak 4 RELATIONSHIP MATRIX EFFECTS OF EDUCATION FOR THE COURSE Algebra and Analytic Geometry WITH EFFECTS OF EDUCATION ON THE DIRECTION OF COMPUTER SCIENCE Course train- Reference to the effect of the learning out- Objectives of The con- Number ing effect comes defined for the field of study and the course** tents of the teaching specialization (if applicable) course** tools** W1 K1_W01 C1 Wy1-Wy20 145 W2 K1_W01 C1 Wy1-Wy20 145 W3 K1_W01 C1 Wy1-Wy20 145 W4 K1_W01 C1 Wy1-Wy20 145 U1 K1_U31 C2 Ćw1-Ćw16 2345 Ćw1-Ćw16 U2 K1_U31 C2 2345 U3 K1_U31 C2 Ćw1-Ćw16 2345 U4 K1_U31 C2 2345 Ćw1-Ćw16 Ćw1-Ćw16 U5 K1_U12 C2 2345 K1 K1_K01 K1_K12 K1_K13 K1_K14 C1 C2 Wy1-Wy20 12345 Ćw1-Ćw16 K2 K1_K01 K1_K12 K1_K14 C1 C2 Wy1-Wy20 12345 Ćw1-Ćw16 5 of
