Advanced Algebra I

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syllabus

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Lecture Notes:

       all (tex, pdf) : all the notes up to present in one file.

  • Set Theory
  •        lecture 1:  Set theory: Zorn's Lemma, Cardinality.

  • Group Theory
  •         lecture 2:  Basic group theory

            lecture 3:  Group actions and sylow's theorems.

            lecture 4:  Symmetry. Abelian groups.

            lecture 5:  Nilpotent and solvable groups, normal series.

            lecture 6:  Some simple groups.

  • Field Theory
  •         lecture 7:  Basic properties. Field extensions.

            lecture 8:  Irreducibility. Algebraic closed fields and algebraic closure.

            lecture 9:  Splitting fields and normal extensions. Finite dimensional Galois extensions.

            lecture 10:  Galois group of a polynomial.

            lecture 11:  Finite fields. Cyclotomic extensions.

            lecture 12:  Solving cubic polynomials. Radical extensions.

            lecture 13:  Separability and inseparability. Transcendental extensions.

  • Homological algebra
  •         lecture 14:  Categories and functors. Complexes and some examples.

            lecture 15:  Exact sequences.

            lecture 16:  Injective.

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    Homeworks:

    hw1(tex, pdf)   hw2(tex, pdf)    hw3(tex, pdf)    hw4(tex, pdf)    hw5(tex, pdf)    hw6(tex, pdf)    hw7(tex, pdf)     hw8(tex, pdf)

    hw9(tex, pdf)     hw10(tex, pdf)    hw11(tex, pdf)   hw12(tex, pdf)    hw13(tex, pdf)    hw14(tex, pdf)    hw15(tex, pdf)

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