# Math 545 Course Info

**Course Meets:** TTh 11:15-12:30 in the Engineering Laboratory, room
306.

**Instructor**

Michael Sullivan, LGRT 1544, 545-1909

Office Hours: Tues 1:30-2:30, Weds 10:00-11:00 and by appt Tues and Weds.
I will also stick around after class Tues and Thurs in the classroom
if anybody is there.

**Prerequisites: ** Math 233, 235 and 300 (or equivalent).

**Credit:** 3 credit hours

**Required Text: **
Linear Algebra and Its Applications, 4th ed., By Gilbert Strang

The 4th edition (2006) is available at the UMass DuBois library reserves

** Overview: **
This is a course in Advanced Linear Algebra and Applications. We will
cover LU decomposition, Vector and Inner Product Spaces, Orthogonality
and Least Squares, Determinants and Eigenvalues.
Other decompositions such as SVD and QR, and, time permitting,
numerical issues and/or basic linear programming.
There will be elements of proof and computation in the course.

** Syllabus (may be adjusted) **

Chapter 1 (about 2 weeks): Review of basic concepts about matrix.

Chapter 2 (about 2 weeks): Vector space, and the theory of single linear transformation

Chapter 3 (about 2 weeks): Orthogonality, Gram-Schmidt, the Fast Fourier Transform.

Chapter 4 (about 1 week) Determinant: Definition, properties, and application.

Chapter 5 (about 2 weeks): Eigenvalues and eigenvectors, exponential power of matrix,
similarity transformations.

Chapter 6 (about 2 weeks): Positive definite matrices, singular value decomposition.

Chapter 7 (about 1 week) Computations with matrices: Computation of eigen-pairs, iterative
algorithm for linear system.

Appendices (about 1 week): Jordan form of the matrices

**Grading: **
The grade will be based on 30% (almost weekly) HWs and class attendance,
30% midterm, and 40% final. Not all HW problems will be graded.
See the exam link
for details on both the midterm and final,
including make-up policy and material covered.
With an acceptable excuse, the lowest HW score will be
dropped. Otherwise, HW must be turned in on time in class.
Moreover, if you miss half or more of the HWs
(drop won't help you here), you'll be penalized by 2/3 of a letter grade;
e.g., B+ to B- or C- to D. (I do not assign A+, D+, or D- as a grade.)
There will be no make-up or extra-credit work.