Math 445/545 WINTER 2016, List of lectures

  • On this page I will post content of all lectures. All handouts also will be posted here.
  • Monday, January 4: Group actions on sets. Section 5.1.
  • Wednesday, January 6: Burnside lemma. Section 5.2. Please find your homework.
  • Friday, January 8: Group actions on groups and some applications. Sections 5.3-5.4.
  • Monday, January 11: Sylow theorems. Section 5.4.
  • Wednesday, January 13: Applications of Sylow theorems. Section 5.4. New homework.
  • Friday, January 15: Symmetries of regular polyhedra. Chapter 4.
  • Monday, January 16: Martin Luther King holiday.
  • Wednesday, January 18: Orthogonal and special orthogonal groups. Symmetries of icosahedron. Chapter 4. New homework.
  • Friday, January 20: Free abelian groups and their bases. Section 3.5.
  • Monday, January 23: Subgroups of free abelian groups and Smith normal form of matrices. Section 3.5. We will have MIDTERM on Friday!!!
  • Wednesday, January 25: More on Smith normal form. Rings. Sections 3.5 and 6.1. New homework.
  • Friday, January 27: MIDTERM. The solutions are here.
  • Monday, February 1: Rings and ring homomorphisms. Sections 6.1 and 6.2.
  • Wednesday, February 3: Kernels of homomorphisms and ideals. Section 6.2. New homework.
  • Friday, February 5: Quotient rings. Section 6.3.
  • Monday, February 8: Correspondence theorems for ideals. Simple commutative rings. Section 6.3.
  • Wednesday, February 10: Integral domains and fields of fractions. Section 6.4. New homework.
  • Friday, February 12: Factorization in rings. Section 6.5.
  • Monday, February 15: Euclidean domains are PID and UFD. Section 6.5.
  • Wednesday, February 17: More on UFD. Sections 6.5-6.6. New homework.
  • Friday, February 19: Irreducibility of Polynomials. Section 6.8.
  • Monday, February 22: Irreducible polynomials. Section 6.8. We will have MIDTERM on Friday!!!
  • Wednesday, February 24: Notherian rings. New homework.
  • Friday, February 26: MIDTERM. The solutions are here.
  • Monday, February 29: Linear algebra: existence of a basis. Section 3.3.
  • Wednesday, March 2: Linear algebra: Linear algebra: dimension. Section 3.3. Last homework.
  • Friday, March 4: Linear algebra: dual space. Section 3.4.
  • Monday, March 7: Duality for subspaces and quotient spaces. Matrices. Section 3.4.
  • Wednesday, March 9: Matrices up to similarity. Sections 3.4 and 8.3. Please find practice problems for the final!
  • Friday, March 11: Jordan normal form of matrices. Section 8.7. Please find solutions for the practice problems.
  • END