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  1. 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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  2. the field of quotients of an integral domain

    the field of quotients of an integral domain

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  5. Show e really exists in one page

    Show e really exists in one page

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

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

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  7. Gaussian integer and Fermat theorem

    Gaussian integer and Fermat theorem

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  8. Ring theory lecture - definition

    Ring theory lecture - definition

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  9. Counting formula in Group theory

    Counting formula in Group theory

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  10. Permutation group (Symmetric group)

    Permutation group (Symmetric group)

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  11. Construction in categories: product/coproduct, equalizer/coequalizer, Pushout/pullbacks

    Construction in categories: product/coproduct, equalizer/coequalizer, Pushout/pullbacks

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  12. More easy mathematical induction exercise

    More easy mathematical induction exercise

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  14. Hermitian matrix is diagonalizable and orthonormal basis

    Hermitian matrix is diagonalizable and orthonormal basis

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  15. Correspondence theorem in Group theory and third isomorphism theorem

    Correspondence theorem in Group theory and third isomorphism theorem

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  16. Goldbach's theorem: Fermat numbers are coprime

    Goldbach's theorem: Fermat numbers are coprime

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  17. How to put 20 equilateral triangles on sphere

    How to put 20 equilateral triangles on sphere

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  18. Field theory (Abstract Algebra)

    Field theory (Abstract Algebra)

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  21. 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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  22. Power series definition for exponential function, logarithmic function, trigonometric function

    Power series definition for exponential function, logarithmic function, trigonometric function

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  24. Prove normal matrix is unitary diagonalizable

    Prove normal matrix is unitary diagonalizable

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  25. sin(x+y)sin(x-y)=(sinx+siny)(sinx-siny)

    sin(x+y)sin(x-y)=(sinx+siny)(sinx-siny)

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