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Math 445/545 WINTER 2016, 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, 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