Advanced Mathematics of Data Science - Interactive curriculae of TU Ilmenau
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| module properties Advanced Mathematics of Data Science in degree program Master Mathematik und Wirtschaftsmathematik 2022 | |
|---|---|
| module number | 201320 |
| examination number | 2400927 |
| department | Department of Mathematics and Natural Sciences |
| ID of group | 2414 (Mathematics of Data Science) |
| module leader | Prof. Dr. Jana de Wiljes |
| term | winter term only |
| language | Englisch |
| credit points | 5 |
| on-campus program (h) | 45 |
| self-study (h) | 105 |
| obligation | elective module |
| exam | written examination performance, 120 minutes |
| details of the certificate | |
| link to Moodle course | |
| teacher | |
| signup details for alternative examinations | |
| maximum number of participants | |
| previous knowledge and experience | basics of the analysis, Linear Algebra, Probability Theory, Python programming or Matlab programming, Mathematics of Data Science |
| learning outcome | Upon completing this course, students have gained a deep understanding of advanced mathematical techniques and their applications in data science. Specifically, they: 1) have Master concentration inequalities, which are crucial for understanding the behavior of random variables and probabilistic bounds, helping students to analyze uncertainty in high-dimensional data. 2) Understand the VC-Dimension (Vapnik- Chervonenkis Dimension), a fundamental concept in learning theory, which provides a measure of the capacity of a statistical model and plays a key role in understanding model complexity and generalization. 3) Have developed expertise in Support Vector Machines (SVMs), including the mathematical formulation and geometric intuition behind these powerful classification tools, as well as their implementation and optimization in practical scenarios. 4) have gain advanced skills in algorithm development and analysis, enabling them to design and optimize algorithms for complex data problems. 5) have learned to evaluate algorithmic performance and computational complexity in data science applications. 6) are able to critically assess cutting-edge research in data science, can apply advanced techniques to real-world problems, and can present research findings with clarity and rigor. |
| content | Topics Covered: |
| media of instruction and technical requirements for education and examination in case of online participation | projector, assignments, ,Slides, jupyter notebooks, personal computer with Python or Matlab to work on the programming part of the exercises |
| literature / references | Concentration Inequalities: A Nonasymptotic Theory of Independence" by Stéphane Boucheron, Gábor Lugosi, and Pascal Massart |
| evaluation of teaching | |