Mathematics 173 -- Advanced Linear Algebra

Spring Semester 2015

Prof. Weiqing Gu

Office: Shan3420 and Lecture room: Shan3465

 

TEXT

Peter Lax, Linear Algebra, Wiley-Interscience

   

TOPICS

  • A quick review of basic principles of linear independence, spanning sets, bases, and dimension.
  • Quotient and dual spaces
  • A quick review of the algebra of linear transformations, matrix representations of linear transformations, and determinants.
  • Spectral Theory of Square Matrices leading to the Jordan Canonical Form
  • Euclidean Structure; the Spectral Theory of Self-Adjoint Matrices
  • Calculus of Vector and Matrix Valued Functions
  • Normed Linear Spaces
  • Perron-Frobenius results on positive matrices. Applications to asymptotics of Markov chains.
  • Applications to large data analysis.
   

ASSIGNMENTS

Weekly problem sets due on Tuesdays (usually) before lectures at 7:00 pm. Work on these assignments will account for 35% of your grade. Except in cases of illness or other extenuating circumstances, no late homework papers will be accepted after the time on the day due. Assignments may be found bellow.

   

PROBLEM SESSIONS

Weekly tutoring sessions will be on Mondays from 6:00--7:30 p.m. (Tutor and grader: Paul David. Location: TBA. paul.david@cgu.edu) Please feel free to come to the tutoring sessions if you have any questions.

HOMEWORK KEYS

We will hand out homework keys for all assignments for the purpose of reviewing for exams.

   

EXAMS

Midterm Exam will account for 30% of the course grade. Probable dates: Thursday, March 10. Take-home final will account for 35% of the course grade.

   

COMPUTER SOFTWARE

Rather than do tedious hand calculations, we will rely on mathematical applications software (MATLAB, etc.) in some of our work. You may use your favorite mathematical package, but I will take MATLAB as the class standard.

   

OFFICE HOURS

Mondays 5:00--6:00 p.m., Wednesdays 4:00--5:00 p.m., Shan342.
Office phone: Ext.18929;

E-mail: gu@g.hmc.edu.