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Explores orthogonality, dot product properties, vector norms, and angle definitions in vector spaces.
Characteristic Polynomials and Similar Matrices
Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.
Sequences: Definition and Convergence
Explains the concept of limits and convergence criteria for sequences of function values.
Elliptic Partial Differential Equations
Covers the model problem of elliptic PDEs with weak formulation and classical solutions.
Cartesian Products and Equivalence Relations
Introduces Cartesian products, equivalence relations, and functions, emphasizing the importance of order and discussing injective, surjective, and bijective functions.
Partial Derivatives: Definitions and Applications
Explores the definitions and applications of partial derivatives in functions of several variables, emphasizing the importance of specifying the choice of variables.
Ethics and Law of AI
Delves into different ethical theories and thought experiments in the context of AI, exploring the challenges of defining AI.
Advanced Analysis II: Eigenvalues and Compact Sets
Covers the reconstruction of a table using diagonal matrices and explores extreme values and set definitions.
Linear Algebra Basics
Covers the basics of linear algebra, including rank, differentiable applications, and submersions.

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