1. Eigenvectors from eigenvalues A survey of a basic identity in linear algebra

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  2. simple lie algebra classification (1) from root system to admissible configuration,

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  3. Linear algebra advanced basic: Zorn's lemma, exchange lemma, dimension

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  4. simple lie algebra classification (2) show all possible coexter and Dynkin diagrams

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  5. Prove fundamental theorem of algebra by analysis

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  6. Introduction to lie groups, lie algebra and its representation

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  7. Lie algebra definition and terminology: Solvable, Nilpotent etc

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  8. integral of x^n lnx from 0 to 1

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  9. Inner product space and p norm

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