Math 445/545 WINTER 2012, List of lectures

• On this page I will post content of all lectures. All handouts also will be posted here.
• Monday, January 9: Ring of polynomials. Fraleigh, Section 22.
• Wednesday, January 11: Factorization of polynomials over a field. Fraleigh, Section 23. Please find your homework.
• Friday, January 13: Subgroup of multiplicative group of a field is cyclic. Primitive roots. Fraleigh, Section 23.
• Monday, January 16: Martin Luther King holiday.
• Wednesday, January 18: Irreducible polynomials: Gauss Lemma and Eisenstein criterion. Section 23. New homework.
• Friday, January 20: Vector spaces over arbitrary fields. Curtis, Section I.A.
• Monday, January 23: Linear maps. Curtis, Section I.B.
• Wednesday, January 25: Algebra End(V). Linear independence and bases. Curtis, Sections I.B and I.C. New homework.
• Friday, January 27: Existence of a basis. Dimension of vector space. The rank theorem. Curtis, Section I.C.
• Monday, January 30: External and internal direct sums. Exact sequences of vector spaces. Curtis, Section I.D. We will have MIDTERM on Friday!!! Please find practice problems!
• Wednesday, February 1: Quotients of vector spaces. Curtis, Section I.D. Please find solutions for the practice problems. New homework.
• Friday, February 3: MITERM. The solutions are here.
• Monday, February 6: Eigenvectors and eigenvalues. Curtis I.E.
• Wednesday, February 8: Dual vector space. Curtis I.F New homework.
• Friday, February 10: Linear maps and matrices. Curtis II.A.
• Monday, February 13: Matrices of operators and change of basis. Algebras. Curtis II.A-II.B.
• Wednesday, February 15: Exterior algebra. Curtis II.C. New homework.
• Friday, February 17: Determinants. Curtis II.C.
• Monday, February 20: Complements on determinates; inverse matrices; linear systems. Curtis II.C-II.D.
• Wednesday, February 22: Eigenvalues and characteristic polynomial. Generalized eigenspaces. Curtis II.E-III.A. New homework.
• Friday, February 24: Caley-Hamilton Theorem. Curtis III.C.
• Monday, February 27: Spectral decomposition. Curtis III.D. We will have MIDTERM on Friday!!! Please find practice problems!
• Wednesday, February 29: Jordan theorem. Curtis III.E. Please find solutions for the practice problems. New homework.
• Friday, March 2: MIDTERM. The solutions are here.
• Monday, March 5: Applications of Jordan normal form. Curtis III.E.
• Wednesday, March 7: Bilinear forms. Curtis IV.A. Last homework.
• Friday, March 9: Symmetric bilinear forms over the real numbers. Gram-Schmidt orthonormalization. Curtis IV.B.
• Monday, March 12: Hermitean forms and inner products over the complex numbers. Curtis IV.C.
• Wednesday, March 14: Symmetric real matrices are diagonalizable. Curtis IV.E. Please find (updated version of) practice problems for the final!
• Friday, March 16: Linear algebra and group theory. Curtis IV.D. Please find solutions for the practice problems.
• END