Math 444/544 FALL 2015, List of lectures

  • 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