Advanced Linear Algebra. Math 5651. Fall 2011

TuTh 2-3:15 pm, Clark 102.

Text: Linear Algebra, Friedberg, Insel and Spence, fourth edition.

Course outline

This course is aimed at students with some prior exposure to linear algebra. The goal of the course is to provide a thorough and comprehensive treatment of the main concepts and theorems of linear algebra. Approximately the first 6 weeks of the course will be spent on the material discussed in 3351 (elementary linear algebra), inlcuding vector spaces, bases, linear transformations, solving linear matrix equations and determinats (Chapters 1-4 of the book). Compared to 3351, these concepts will be investigated in more depth and the emphasis will be made on theoretical rather than computational aspects. During weeks 7-12 we will study more advanced topics: diagonalization, Jordan Canonical Form and bilinear forms (Chapters 5-7 of the book). In the last 2 weeks I plan to discuss some applications of linear algebra to other areas of mathematics and possibly applications outside of mathematics.


There are two main prerequisites for the course: There is also some overlap in the material between MATH 3354 and MATH 5651, so it is recommended that you take MATH 3354 (which is more elementary than MATH 5651) prior to or concurrently with MATH 5651.


The course grade will be based on homework and three exams. Homework will count for 30% and exams will count for 70% of your grade. The distribution of weights between exams will depend on their format (in class, take home or combined), which has not been determined yet, but will be finalized no later than the end of September.


The tentative dates of the exams are as follows: According to the current plan, the first and third exams will be take-home, while the second exam will have both in-class and take-home parts. Third midterm exam may be replaced by an IN-CLASS final on SAT, Dec 10th, 9-12am.

Make-up policy


The homework format is NON-STANDARD, so read this paragrpah carefully.


Major announcements will be made in class and also posted on the course webpage. Some other announcements may only be made by e-mail, so check your e-mail account regularly.

Add/drop/withdrawal dates:

Office hours

During the first week of classes office hours are by appointment only. The proposed times for regular office hours (starting the second week) are

     Tue 4:15-5:45 and Wed 1:15-2:45