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Lecture Notes:
all (tex, pdf) : all the notes up to present in one file.
lecture 1: Set theory: Zorn's Lemma, Cardinality.
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.
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.
lecture 14: Categories and functors. Complexes and some examples.
lecture 15: Exact sequences.
lecture 16: Injective.
¡@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)