Mathematics of Data Science - Interaktive Studienpläne der TU Ilmenau

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

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

"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