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Math 446/546 SPRING 2012, List of lectures
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On this page I will post content of all lectures. All handouts also will be posted here.
Monday, April 2: Ideals and Factor Rings. Fraleigh, Section 26.
Wednesday, April 4: Prime and maximal ideals;
ideals in the ring of polynomials.
Fraleigh, Section 27.
Please find your homework.
Friday, April 6: Extensions of fields. Fraleigh, Section 29.
Monday, April 9: Simple, finite, algebraic and
finitely generated extensions. Fraleigh, Section 31.
Wednesday, April 11: Algebraically closed fields and algebraic closure.
Fraleigh, Section 31.
New homework.
Friday, April 13: Existence of algebraic closure. Finite fields.
Fraleigh, Sections 31 and 33.
Monday, April 16: Geometric constructions and constructible numbers.
Fraleigh, Section 32.
Wednesday, April 18: Isomorphism theorems. Subnormal and normal series.
Fraleigh, Sections 34-35.
New homework.
Friday, April 20: Jordan-Holder theorem. Solvable and nilpotent groups.
Fraleigh, Section 35.
Monday, April 23: Actions of p-groups. Cauchy's theorem.
Fraleigh, Section 36.
We will have MIDTERM on Friday!!!
Please find practice problems!
Wednesday, April 25: The Sylow theorems.
Fraleigh, Section 36.
Please find solutions for the practice problems.
New homework.
Friday, April 27: MIDTERM. The solutions are
here.
Monday, April 30: Applications of Sylow theory. Fraleigh, Section 37.
Wednesday, May 2: Conjugacy classes. p-groups are nilpotent. Alternating
groups are simple.
Fraleigh, Section 37.
New homework.
Friday, May 4: Free abelian groups. Fraleigh, Section 38.
Monday, May 7: Smith normal form. Free groups. Fraleigh, Sections 38-39.
Wednesday, May 9: Generators and relations for groups. Semi-direct product.
Fraleigh, Section 40. New homework.
Friday, May 11: Automorphisms of fields and extensions of homomorphisms.
Fraleigh, Sections 48-49.
Monday, May 14: Splitting fields. Fraleigh, Section 50.
Wednesday, May 16: Index of extension. Separable extensions and
perfect fields. Fraleigh, Sections 49 and 51.
New homework.
Friday, May 18: Primitive element theorem. Galois extensions.
Fraleigh, Sections 51 and 53.
Monday, May 21: Main theorem of Galois theory.
Fraleigh, Section 53.
We will have MIDTERM on Friday!!!
Please find practice problems!
Wednesday, May 23: Galois theory examples.
Fraleigh, Sections 53-54.
Please find solutions for the practice problems.
New homework.
Friday, May 25: MIDTERM. The solutions are
here.
Monday, May 28: Memorial Day.
Wednesday, May 30: Galois groups for finite fields. Discriminant and
low degree polynomials. Fraleigh, Sections 53 and 54.
Last homework.
Friday, June 1: Fundamental theorem of algebra via Galois theory.
Cyclotomic extensions. Fraleigh, Section 55.
Monday, June 4: Radical extensions and solvable Galois groups
Fraleigh, Section 56.
Wednesday, June 6: Kummer's theory. Solvable extensions are radical.
Friday, June 8: Dedekind theory.
Please find practice problems for the final!
Please find solutions for the practice problems.
THE END.