| (*)Students have an advanced understanding of mathematical concepts essential to artificial intelligence, including linear algebra, measure theory, functional analysis, and potentially differential equations. They are able to apply these mathematical techniques to solve AI-relevant problems, such as data representation, dimensionality reduction, and optimization within functional and normed spaces.
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(*)- Computing Eigenvalues, Eigenvectors, and Performing SVD (k4)
Students can calculate eigenvalues and eigenvectors of matrices and apply the singular value decomposition (SVD) to analyze and transform data effectively.
- Applying Concepts of Measure and Integration Theory (k4)
Students are able to understand and utilize the foundational principles of measure theory and integration to perform rigorous mathematical analyses relevant to AI.
- Understanding and Applying Functional Analysis (k4)
Students can work with normed spaces and Hilbert spaces, applying concepts from functional analysis to understand functions, sequences, and operators in AI contexts.
- Solving Basic Differential Equations (k3)
If covered, students can apply techniques to solve simple differential equations, recognizing their role and relevance in modeling continuous processes within AI applications.
- Linking Mathematical Theory to AI Applications (k5)
Students are capable of connecting mathematical concepts like SVD, measure theory, and functional analysis to practical applications in AI, such as dimensionality reduction, optimization, and data transformations.
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(*)Students have acquired knowledge of advanced linear algebra concepts, including eigenvalues, eigenvectors, and the singular value decomposition (SVD), as well as foundational topics in measure theory and functional analysis. They know how these mathematical tools are applied in AI for data representation, dimensionality reduction, and working within normed and Hilbert spaces, and they gain a basic understanding of differential equations if time permits.
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