Mathematics of Data Science - Interactive curriculae of TU Ilmenau

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module properties module number 201319 - common information
module number	201319
department	Department of Mathematics and Natural Sciences
ID of group	2414 (Mathematics of Data Science)
module leader	Prof. Dr. Jana de Wiljes
language	Englisch
term	Sommersemester
previous knowledge and experience	basics of the analysis, Linear Algebra, Probability Theory, Python programming or Matlab programming
learning outcome	After completing this course, students are a solid understanding of the core mathematical methods foundational to Data Science. They are familiar with both the theoretical and practical aspects of various mathematical techniques used in data analysis. Specifically, they: 1) Understand fundamental concepts from linear algebra, calculus, and probability theory as they relate to data science. 2) Grasp the principles of multivariate analysis, including the theory behind covariance, correlation matrices, and dimensionality reduction techniques. 3) Are able to critically assess the advantages and disadvantages of various mathematical methods for different types of data analysis problems. 4) Have developed an understanding of different data models and be able to select appropriate models for specific applications. 5) Have gained experience in methodically investigating selected models, developing algorithms, and applying them to real-world problems. 6) Understand the relevance of mathematical techniques to areas like theoretical computer science and be able to make connections between fields. 7) Are able to read, present, and critically discuss current research papers in the field of data science
content	Topics covered: . Mathematical foundations (linear algebra, calculus, probability) . Multivariate analysis (covariance, correlation, differentiation techniques in higher dimensions . Dimensionality reduction techniques (PCA, SVD, Hypothesis testing) . K-means clustering Spectral clustering
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	"An Introduction to Multivariate Statistical Analysis" by T.W. Anderson "Elements of Statistical Learning" by Trevor Hastie, Robert Tibshirani, and Jerome Friedman "Mathematical Statistics: Basic Ideas and Selected Topics" by Peter J. Bickel and Kjell A. Doksum "Spectral Methods for Data Science: Theory and Algorithms" by T. Tony Cai, Xiaodong Li, and Harrison H. Zhou "Pattern Recognition and Machine Learning" by Christopher M. Bishop
evaluation of teaching

Details reference subject
module name	Mathematics of Data Science
examination number	2400926
credit points	5
SWS	4 (2 V, 2 Ü, 0 P)
on-campus program (h)	45
self-study (h)	105
obligation	obligatory 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