1. Simovici, Dan A., and Chabane Djeraba. "Mathematical tools for data mining." SpringerVerlag, London (2008).
2. Cover, Thomas M. Elements of information theory. John Wiley & Sons, 1999.
Mathematics for Computer Science
| Language of instruction | angličtina, čeština |
|---|---|
| Code | 460-4164 |
| Abbreviation | MPI |
| Course title | Mathematics for Computer Science |
| Coordinating department | Department of Computer Science |
| Course coordinator | doc. Mgr. Pavla Dráždilová, Ph.D. |
Summary
The course provides a systematic overview of mathematical concepts that form the basis of modern data analysis, machine learning, information processing, and signal processing. The teaching is structured to gradually build understanding from abstract algebraic structures through data space geometry to practical methods of compression, classification, and transformation.
In the introductory blocks, students will learn about sets, algebras with two operations, and conceptual sets, which serve as a formal framework for representing knowledge and relationships. This is followed by an extension to fuzzy sets and rough sets, which allow for modeling uncertainty and incompleteness of data.
The next part of the course focuses on metric and topological structures, similarities, and dissimilarities, which form the basis for geometric data modeling. In this context, the issues of dimensionality, eigenvalues, and vectors are discussed, as well as dimension reduction methods such as PCA and SVD.
This part is followed by lectures focused on data clustering – from the mathematical foundations of algorithms to methods of evaluating cluster quality. The course also covers information theory, including entropy, Kullback-Leibler divergence, mutual information, and coding principles. Students will learn about code sets, variable-length codes, and statistical coding.
In the introductory blocks, students will learn about sets, algebras with two operations, and conceptual sets, which serve as a formal framework for representing knowledge and relationships. This is followed by an extension to fuzzy sets and rough sets, which allow for modeling uncertainty and incompleteness of data.
The next part of the course focuses on metric and topological structures, similarities, and dissimilarities, which form the basis for geometric data modeling. In this context, the issues of dimensionality, eigenvalues, and vectors are discussed, as well as dimension reduction methods such as PCA and SVD.
This part is followed by lectures focused on data clustering – from the mathematical foundations of algorithms to methods of evaluating cluster quality. The course also covers information theory, including entropy, Kullback-Leibler divergence, mutual information, and coding principles. Students will learn about code sets, variable-length codes, and statistical coding.
Literature
Advised literature
1. Deisenroth, Marc Peter, A. Aldo Faisal, and Cheng Soon Ong. Mathematics for machine learning. Cambridge University Press, 2020.