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Math 445/545 WINTER 2012, 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 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