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Lecture
Cyclic Sequences: Counting and Equivalence
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Tangent vectors without embedding space: Making tangent spaces linear
Explores making tangent spaces linear, defining tangent vectors without an embedding space and their operations, as well as the equivalence of different tangent space notions.
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Explores cryptanalysis in public-key systems and the power of interaction in interactive proofs, covering CO-NP, NP classes, P vs. NP, and more.
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Covers the basics of Turing machines, including states, tape manipulation, and problem-solving capabilities.
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Explores conditional entropy and Huffman coding for efficient data compression techniques.
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Tensor Products and Symmetric Power
Covers tensor products, symmetric power, and exterior power of vector spaces, including properties and applications.