## Schedule for Math 310     Spring 2005

Week Topics Reading Homework
Linear Equations: fields, complex numbers, systems of linear equations, matrices, row-reduced echelon form.
1.1, 1.2, 1.3, 1.4 1.2: 1, 3, 5, 7.   1.3: 2, 3, 8.   1.4: 3, 7, 10.
Solutions
1/31 Matrix multiplication, invertible matrices.
Fri, Feb 4: last day to add or drop without a W
1.5, 1.6 1.5: 2, 3, 4, 7.   1.6: 2, 8, 9, 10.   2.1: 4, 5, 6.
Solutions
2/7 Vector Spaces: definition, examples, subspaces, bases and dimension. 2.1, 2.2, 2.3. 2.2: 1, 2, 4, 7, 8.   2.3: 2, 3, 6, 7, 12.
Solutions
2/14 Coordinates, row equivalence and computations.
2.4, 2.5, 2.6. 2.3: 8. Bonus: 14.   2.4: 1, 2, 4, 7.   2.6: 2, 3, 6.
Solutions
2/21 Linear Transformations: linear transformations, linear transformations as a vector space. 3.1, 3.2, 3.3 3.1: 1, 3, 7, 8, 9.   3.2: 2, 5, 7.   3.3: 2, 4. Bonus: 7.
Solutions
2/28 invertible and nonsingular linear transformations, isomorphisms, representation by matrices. 3.3, 3.4 3.4: 1, 4, 8, 9. Bonus: 12.
Solutions
3/7 change of basis and similarity, linear functionals.
First midterm, on 3/9. Covers thru section 3.4 (more info is here)
3.4, 3.5 Extra Credit: rewrite problem 5 of the exam completely. More details here.
due in class by 3/30
3/14 Duality, annihilators, and the double dual. 3.5, 3.6 3.5: 2, 3, 4, 8, 9.   3.6: 1.
Solutions
3/21
 Spring Break
3/28 Transpose of a linear transformations, overview of determinants.
Class cancelled on 3/28.
Friday, Apr 1: last day to withdraw or change to P/NC
3.7, Skim 5.1-5.4 3.7: 2, 3, 6, 7.   5.2: 5. 5.4: 3, 4, 5.
Solutions
4/4 Canonical Forms: eigenvalues, eigenvectors, and diagonalization 6.1, 6.2, 6.3 6.2: 1, 4, 5, 8, 9, 13.
Solutions
4/11 Minimal polynomials, invariant subspaces 6.3, 6.4 6.3: 1, 3, 4, 5, 6.   6.4: 3, 4, 7, 9.
Solutions
4/18 diagonalization and the Cayley-Hamilton Theorem, Nilpotent matrices and generalized eigenvectors, Jordan form; 6.4, 7.1, 7.2, 7.3; Down with Determinants
4/25 no class on 4/25 (passover)
Recap and Review.
second midterm on 4/29 (covers through 6.4; more info is here)
8.1 7.3: 1, 3, 4, 5.   8.1: 2, 3, 5.   8.2: 1, 2, 9.
Solutions
5/2 Inner Product Spaces: inner products, inner product spaces, orthogonality, Gram-Schmidt 8.1, 8.2, 8.3; Axler's Chapter 6.
5/9 orthogonal complements, minimization.
Last class on Monday, 5/9

 Friday, May 13 8:00-10:30am Final exam Physics P113
Last change: Wednesday, 11 May 2005 at 04:46 PM EDT.