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  1. Hilbert Basis theorem state and proof (algebraic geometry)

    Hilbert Basis theorem state and proof (algebraic geometry)

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  7. The existence proof of eigenvectors and eigenvalues

    The existence proof of eigenvectors and eigenvalues

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  10. Prove normal matrix is unitary diagonalizable

    Prove normal matrix is unitary diagonalizable

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  11. Hermitian matrix is diagonalizable and orthonormal basis

    Hermitian matrix is diagonalizable and orthonormal basis

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  12. Prove Method of infinite Descent (Vieta's jumping) : (x^2+y^2+1)/xy=3

    Prove Method of infinite Descent (Vieta's jumping) : (x^2+y^2+1)/xy=3

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  14. sum of the reciprocals of the primes is divergent

    sum of the reciprocals of the primes is divergent

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  15. Gaussian integer and Fermat theorem

    Gaussian integer and Fermat theorem

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  16. 7 is the only Prime followed by a Cube? What's more? how about quartic

    7 is the only Prime followed by a Cube? What's more? how about quartic

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  17. Integral of 1/(e^x+1) and integral of 1/(e^x-1)

    Integral of 1/(e^x+1) and integral of 1/(e^x-1)

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  18. Integral of e^ax cos(bx) and Integral of e^ax sin(bx) no integration by part

    Integral of e^ax cos(bx) and Integral of e^ax sin(bx) no integration by part

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

    integral of x^n lnx from 0 to 1

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  20. integral of lnx ln(1-x) from 0 to 1

    integral of lnx ln(1-x) from 0 to 1

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  21. Complex contour: Integral of ln(x)/(x^2+1) and ln(x)^2/(x^2+1)

    Complex contour: Integral of ln(x)/(x^2+1) and ln(x)^2/(x^2+1)

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  22. Permutation group (Symmetric group)

    Permutation group (Symmetric group)

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  23. Integral of 1/(x^2+1) by using complex number

    Integral of 1/(x^2+1) by using complex number

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  24. Complex contour integral: e^{-x}cos(x)/sqrt(x), e^{-x}sin(x)/sqrt(x) from 0 to infinity

    Complex contour integral: e^{-x}cos(x)/sqrt(x), e^{-x}sin(x)/sqrt(x) from 0 to infinity

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  25. Euclid-Euler theorem: Perfect numbers

    Euclid-Euler theorem: Perfect numbers

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