Spring 2005

Title of the Course: Linear Algebra

Instructor: Ali Mostafazadeh

Textbook: ‘Linear Algebra Done Right,’ S. Axler Second Edition (Springer, New York, 2002)

Topics to be covered:            

1. Vector spaces, subspaces, their sums and direct sums (Chapter 1)

2. Finite-dimensional real and complex vector spaces (Chapter 2)

3. Linear maps between vector spaces (Chapter 3)

4. Eigenvalue problem (Chapter 5)

5. Inner product spaces (Chapter 6)

6. Linear operators between inner product spaces, self-adjoint, normal, and positive operators, the spectral theorem (Chapter 7)

7. Generalized eigenvectors, minimal polynomials, and Jordan decomposition       (Chapter 8)

9.* Tensors

* These topics will or will not be covered depending on the progress of the class.

Evaluation method: The students’ progress will be evaluated according to their performance in quizzes, midterm exams, and a term paper. There will be five quizzes which will take place during the PS hours and will count as 20% of the total grade. There will be three midterm exams contributing a total of 60%. The term paper will contribute as %20.

Make-ups: If you miss a quiz or either of first two exams and have a valid excuse, your grade in the next exam will be substituted for the grade in the missed quiz or exam. If you also miss the exam following a missed quiz or exam, you will be given zero in the latter regardless of whether you have a valid excuse or not. If you miss the last exam, you will be given a written or an oral make-up exam.

Attendance: The students are required to attend the classes. If a student misses 6 or more classes, 2 points will be deduced from his or her total grade for each missing lecture (including the first 6 lectures that are missed). This will apply to all the students regardless of whether they have a valid medical report or any other excuse. The students that miss less than 6 PSs will receive 5 bonus points to be added to their total grade.

Requirements from the students auditing this course: In order to get an AU in this course, you must attend at least 20 lectures.

Suggested Method of Study: The students are advised to study the material covered in class immediately after the lectures. Reading the lecture notes and the book is necessary for grasping the subject, but it is by no means sufficient. The students must try to reproduce the results derived in class and solve the related problems on their own. They are expected to spend an average of six hours per week on studying the material covered in class in addition to the time they need to spend on the term paper.