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Math 444/544 FALL 2015, 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, September 28: Sets with operations. Integers.
Section 1.6.
Wednesday, September 30: Euclidean algorithm and greatest common divisor.
Section 1.6.
Please find your homework.
Friday, October 2: Modular Arithmetic.
Section 1.7.
Monday, October 5: Polynomials. Section 1.8.
Wednesday, October 7: Rings and fields. Section 1.11.
New homework.
Friday, October 9: Symmetries. Sections 1.1-1.4.
Monday, October 12: More examples of groups. Permutations.
Sections 1.5 and 1.10.
Wednesday, October 14: Beginnings of systematic theory of groups. Section 2.1.
New homework.
Friday, October 16: Groups of small order. Isomorphisms and structural
properties of groups. Section 2.1.
Monday, October 19: Subgroups. Subgroup generated by subsets;
cyclic subgroups. Section 2.2.
We will have MIDTERM on Friday!!!
Wednesday, October 21: Cyclic groups and their subgroups. Section 2.2.
New homework.
Friday, October 23: MITERM. The solutions are
here.
Monday, October 26: The dihedral groups. Section 2.3.
Wednesday, October 28: Homomorphisms and their kernels.
Section 2.4. New homework.
Friday, October 30: Sign of permutation.
Cosets and Lagrange theorem. Sections 2.4-2.5.
Monday, November 2: Proof of Lagrange Theorem. Centralizers and
conjugacy classes. Sections 2.5-2.6.
Wednesday, November 4: Quotient groups. Section 2.7.
New homework.
Friday, November 6: Homomorphism theorems. Section 2.7.
Monday, November 9: More on isomorphisms theorems. Section 2.7.
Wednesday, November 11: Direct products. Section 3.1.
New homework.
Friday, November 13: Finite abelian groups: decomposition into direct
product of p-groups. Section 3.6.
Monday, November 16: Semidirect products. Section 3.2.
We will have MIDTERM on Friday!!!
Wednesday, November 18: Examples of semi direct products.
Automorphisms of cyclic groups. Section 3.2.
New homework.
Friday, November 20: MIDTERM. Please find solutions
here.
Monday, November 23: Finite abelian groups are products of cyclic p-groups.
Section 3.6.
Wednesday, November 25: Factors in decomposition of finite abelian group into
product of cyclic p-groups are unique. Section 3.6.
Monday, November 30: Group of units in Z_n. Section 3.6.
Wednesday, December 2: Conjugacy classes and class equation; groups of order
p^2, 8, 12. Section 5.4.
Friday, December 4: More on conjugacy classes: conjugacy classes in the alternating
group. Group A_5 is simple. Section 5.4.
Please find practice problems for the final!
Please find solutions for practice problems!
END