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Lecturer(s)
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Valdman Jan, doc. Dr.rer.nat.
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Revilla Rimbach Tomas Augusto, Ph.D.
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Course content
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1 - Linear Algebra: matrices, linear independence, (reduced) row echelon form . 2 - Analytic Geometry: norms, inner products, orthogonality, orthogonal projections. 3 - Matrix Decompositions: eigenvalues, eigenvectors, Cholesky-, eigen-, singular- decompositions. 4 - Vector Calculus: partial Differentiation and Gradients, Higher-Order Derivatives, Multivariate Taylor Series. 5 - Optimization: Gradient descent, Constrained Optimization and Lagrange Multipliers, Convex Optimization. 6 - Probability and Distributions: Bayes' Theorem, Gaussian distribution. 7 - Applications: Linear Regression, Principal Component Analysis. The topics of tutorials follow the lecture topics. Additional study materials: Materials for lectures and tutorials will be in USB LMS Moodle and MS Teams
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), E-learning
- Semestral paper
- 70 hours per semester
- Preparation for credit
- 50 hours per semester
- Preparation for exam
- 30 hours per semester
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Learning outcomes
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This course provides basic tools from linear algebra, calculus, optimization and probability necessary for understanding algorithms in Artificial intelligence and Data Science.
Understanding of elements of linear algebra, vector analysis and probablity theory required for formulation of algorithms in AI and DS.
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Prerequisites
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Knowledge of basic undergraduate mathematics and knowledge of some programming language (eg. Mathematica, Matlab, Python).
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Assessment methods and criteria
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Oral examination, Written examination
To pass the course, a student must obtain at least 50 points out of 100 in a maximum of 4 tests (each test accounts for 25 points) to pass credits. So, test number 3 and 4 are two repetitive (remedial) credit attempts. Then, a student must pass a final exam (both written and/or oral).
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Recommended literature
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DAVID C. LAY, STEVEN R. LAY, JUDI J. MCDONALD. Linear Algebra and Its Applications, Pearson; 5th edition 2014, ISBN: 978-0321982384.
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MARC PETER DEISENROTH, A. ALDO FAISAL, CHENG SOON ONG. Mathematics for Machine Learning, Cambridge University Press; 1st edition 2020, ISBN 978-1108470049.
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STEPHEN BOYD, LIEVEN VANDENBERGHE. Convex Optimization, Cambridge University Press, 1st edition 2004, ISBN: 978-0521833783.
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