| Study program / study programs: Advanced data analytics |
| Course: Mathematical Foundations of Data Analysis |
| Teacher(s): Tanja Stojadinović |
| Course status: Elective |
| ECTS points: 10 |
| Prerequisites: – |
| Course objective: Acquisition of general and specific knowledge of Linear Algebra and Numerical Analysis. |
| Learning outcomes: Upon completion of the course, students have the basic knowledge of linear algebra and numerical methods. They are able to solve problems in these fields and to apply acquired concepts and techniques in other fields. |
| Course structure and content: System of linear equations and Gaussian elimination Vectors in Rn; linear combinations, linear spans, linear dependence; basis and dimension Matrices; matrix addition and scalar multiplication; transpose Elementary row operations; echelon matrices, rank of a matrix Matrix multiplication; invertible matrices Determinant; properties of determinants; minors and cofactors; adjoint of a matrix Linear mappings; kernel and image of a linear mapping Matrix representation of a linear map Eigenvalues and eigenvectors; diagonalization Inner product spaces; orthogonality, orthonormal sets; orthogonal projection, applications Numerical methods for solving systems of linear equations; direct methods and iterative methods Numerical methods for computing eigenvalues and eigenvectors Polynomial interpolation and other methods for function approximation Fourier transformation; discrete Fourier transformation; fast Fourier transformation |
| Literature/Readings: А. Lipkovski, Linearna algebra i analitička geometrija, 2nd edition, Zavod za udžbenike i nastavna sredstva, Beograd, 2007 S. Lipschutz, Schaum’s Outline of Theory and Problems of Linear Algebra, 2nd ed, Mc Graw-Hill, New York, 1991 D. Radunović, Numeričke metode, Akademska misao, Beograd, 2004 F. B. Hildebrand, Introduction to Numerical Analysis, 2nd edition, Dover Publications, INC, New York, 2013 G.Shanker Rao, Mathematical Methods, I.K. International Publishing House, 2013. |
| The number of class hours per week: Lectures: 4 Labs: 0 Workshops: 0 Research study: 3 Other classes: 0 |
| Teaching methods: Frontal, group, practical |
| Evaluation/Grading (maximum 100 points): Pre-exam requirements (Exercises, lab tests): 40 Final exam (Written-oral exam): 60 |
