| Ziele |
(*)Calculus is essential for designing and understanding algorithms in AI and machine learning. Most methods in machine learning are based on some optimization principle. These optimization techniques are related to gradient-based methods, quadratic optimization or convex optimization. Many machine learning algorithms are based on and described by matrix algebra like neural networks, projection methods like PCA and ICA and many more.
The objective of this subject is an in-depth training in calculus and linear algebra with some topics from algebra. Particular topics are set theory, sequences and series, functions and limits, differentiation and integration, vector spaces, matrices, normed and Hilbert spaces, calculus in higher dimensions, differential equations, and integral transformations. Furthermore, the students acquire skills in unconstraint and constraint optimization with a focus on first and second order gradient descent methods, quadratic optimization, and convex optimization.
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