Linear Algebra Syllabus
Course Description: Linear algebra is a fundamental branch of
mathematics dealing with the
solution of linear equations. We will consider systems of linear equations,
properties of matrices and
determinants, vector spaces, linear transformations, inner products,
orthogonality, eigenvectors and
eigenvalues, and the canonical representation of linear transformations.
Text Book: Elementary Linear Algebra, 9th Edition, 2005, by Anton and
Rorres
Prerequisite: Calculus III, Math 335.
Office Hours: 10am MTWF, 2pm MTW. Other times by appointment. My
schedule and office
hours are also listed on the webpage.
Practice Problems: Once material has been covered in class it is
expected that you will work
through problems in the relevant section of the text. This daily homework is the
absolute minimum
work required to succeed in the course.
Homework: Regular assignments and their due date will be announced in
class. These assignments
will be graded, and are due at the beginning of the relevant class.
Exams: Exams will be held in class on Monday February 2nd, Monday
March 2nd, and Monday
April 6th. The Final Exam will be held on Monday May 4th, 9:00am - 11:00am.
Attendance: Students are expected to be present at every class.
Success in this course requires
regular attendance.
Grading: Grades will be based on 3 one-hour exams (a total of 300
points), homework assignments
(equally weighted and scaled to a total of 100 points), a final project (100
points) and a final
comprehensive exam (150 points). A total of 650 points are available, and the
cut-o s for the final
letter grade are as follows:
| A |
85% |
B |
70% |
C |
60% |
D |
50% |
| B+ |
80% |
C+ |
67% |
D+ |
57% |
F |
Below 50% |
Makeup Exams: Departmental policy dictates that make-up exams are to
be given under extenuating circumstances only. No make-up quizzes will be given.
Course Outline and Tentative Schedule
Linear Algebra - Spring 2006
| Week |
Date |
Section |
Topic |
| 1 |
Jan 12 |
§1.1 |
Systems of Linear Equations |
| |
|
§1.2 |
Gaussian Elimination |
| |
|
§1.3 |
Matrices and Matrix Operations |
| 2 |
Jan 19 |
§1.4 |
Inverses; Matrix Arithmetic |
| |
|
§1.5 |
Elementary Matrices and the Inverse |
| 3 |
Jan 26 |
§1.6 |
Systems of Equations and Invertibility |
| |
|
§1.7 |
Diagonal, Triangular, Symmetric Matrices |
| 4 |
Feb 2 |
§2.1 |
Determinants by Cofactor Expansion |
| |
|
§2.2 |
Determinants by Row Reduction |
| 5 |
Feb 9 |
§2.3 |
The Determinant Function |
| |
|
§2.4 |
Combinatorial Approach to Determinants |
| 6 |
Feb 16 |
Ch 3 |
Vectors in 2-Space and 3-Space |
| |
|
§4.1 |
Euclidean n-Space |
| 7 |
Feb 23 |
§4.2 |
Linear Transformations from Rn to Rm |
| |
|
§4.3 |
Properties of Linear Transformations |
| 8 |
Mar 2 |
§4.4 |
Linear Transformations and Polynomials |
| |
Mar 9 |
- |
Spring Break |
| 9 |
Mar 16 |
§5.1 |
Real Vector Spaces |
| |
|
§5.2 |
Subspaces |
| 10 |
Mar 23 |
§5.3 |
Linear Independence |
| |
|
§5.4 |
Basis and Dimension |
| 11 |
Mar 30 |
§5.5 |
Row Space, Column Space and Nullspace |
| |
|
§5.6 |
Rank and Nullity |
| 12 |
Apr 6 |
§6.1 |
Inner Product Spaces |
| |
|
§6.2 |
Angles and Orthogonality in Inner Product Spaces |
| 13 |
Apr 13 |
§6.3 |
Orthogonal Bases; Gram-Schmidt Process |
| |
|
§7.1 |
Eigenvalues and Eigenvectors |
| 14 |
Apr 20 |
§7.2 |
Diagonalization |
| |
|
§8.1 |
General Linear Transformations |
| 15 |
Apr 27 |
§8.2 |
Kernel and Range |
| |
|
- |
Review |
| |
May 4 |
|
Final Exam: Monday May 4th, 9-11am. |
Sections may be skipped or other sections added as time
allows.
