Objectives and competences
Students enhance their knowledge of fundamental mathematical tools in data science. They become proficient in applying theoretical knowledge from the fields of linear algebra and mathematical analysis, as well as using the MATLAB program to solve problems and study models and algorithms. They conduct critical evaluation based on solid theoretical foundations.
Content (Syllabus outline)
1. Matrices, basics notions
2. Invertible matrices and generalized matrix inverses
3. Eigenvalues and eigenvectors, matrix decompositions and matrix diagonalization
4. Vector spaces, linear mappings, and matrix representation of linear mappings
5. Partial derivatives of functions of several variables and multivariate chain rule, maxima, minama, and Lagrange multipliers, gradients of vector-valued functions, higher order derivatives, linearization and multivariate Taylor series, gradient descent
6. Applications
Learning and teaching methods
Lectures, guided classes in computer room, solving exercises, presentations of solutions to tasks, teachers' consultations, independent study of the required literature
Intended learning outcomes - knowledge and understanding
In this course, students:
1. Review basic concepts in the fields of linear algebra and mathematical analysis.
2. Gain knowledge of the mathematical foundations of data science.
3.Systematically upgrade their knowledge of linear algebra and mathematical analysis and become proficient in applying theoretical knowledge in concrete mathematical models. (PILO 1a, PILO 2a)
4. Are able to select appropriate mathematical tools for solving complex problems and seek the most efficient paths to solutions. (PILO 1a, PILO 2a)
5. Acquire the ability to search for and synthesize new information on the use of mathematics in data science in literature and through modern digital methods, as well as the ability to integrate them into an appropriate professional framework. (PILO 3a)
6. Conduct critical evaluation of mathematical tools in data science, apply them in practice, and sensibly present their results. (PILO 3b)
7. Gain practical experience and become users of the MATLAB program. (PILO 3a)
8. Are aware of their own ethical and professional responsibilities in the field of applied mathematical tools in data science. (PILO 4a)
The PILO label (i.e., Programme Intended Learning Outcomes) defines the contribution of each listed intended learning outcome of a course towards achieving the general and/or subject-specific competencies or learning outcomes acquired through the programme.
Intended learning outcomes - transferable/key skills and other attributes
In this course, students:
1. Review basic concepts in the fields of linear algebra and mathematical analysis.
2. Gain knowledge of the mathematical foundations of data science.
3.Systematically upgrade their knowledge of linear algebra and mathematical analysis and become proficient in applying theoretical knowledge in concrete mathematical models. (PILO 1a, PILO 2a)
4. Are able to select appropriate mathematical tools for solving complex problems and seek the most efficient paths to solutions. (PILO 1a, PILO 2a)
5. Acquire the ability to search for and synthesize new information on the use of mathematics in data science in literature and through modern digital methods, as well as the ability to integrate them into an appropriate professional framework. (PILO 3a)
6. Conduct critical evaluation of mathematical tools in data science, apply them in practice, and sensibly present their results. (PILO 3b)
7. Gain practical experience and become users of the MATLAB program. (PILO 3a)
8. Are aware of their own ethical and professional responsibilities in the field of applied mathematical tools in data science. (PILO 4a)
The PILO label (i.e., Programme Intended Learning Outcomes) defines the contribution of each listed intended learning outcome of a course towards achieving the general and/or subject-specific competencies or learning outcomes acquired through the programme.
Readings
Obvezna študijska literatura (Compulsory textbook):
Deisenroth, M. P., Faisal, A. A., Ong, C. S. (2020). Mathematics for machine learning, Cambridge University Press, Cambridge, United Kingdom. Pridobljeno 26. aprila 2023: https://mml-book.github.io/book/mml-book.pdf.
Dodatna študijska literatura (Additonal textbook):
Aggarwal, C. C. (2020). Linear algebra and optimization for machine learning, Springer Nature Switzerland, Cham, Switzerland. Pridobljeno 26. aprila 2023: https://link.springer.com/book/10.1007/978-3-030-40344-7.
Additional information on implementation and assessment - active participation (20%)
- Written exam (80%)
Written exam - at least 80% attendance in laboratory exercises and independent solving and brief presentation of solutions to mathematical problems.
Written exam - written exam with at least one question from linear algebra and at least one question from mathematical analysis.
