Math 341: Linear Algebra

Syllabus and Course info

Syllabus: Fields, vector spaces, subspaces, linear independence, basis and dimension, matrices and linear equations, linear transformations, determinants, rank and nullity theorem, change of basis, inner product spaces, eigenvalues, singular values, spectral decomposition.

A brief list of topics covered in each lecture can be found here. This list will be updated as the semester progresses.

Schedule info.

Class email list

I will use the mailing list math-341 to for announcements regarding this course. (I WILL NOT USE BLACKBOARD).

Any student who is registered for this course on 2009-08-24 (first day of class) will be automatically subscribed this mailing list. If you register for the course at a later time, you should join this mailing list yourself, by visiting the above link. Similarly, if you chose to drop this course, you can un-subscribe yourself from this list using the above link. Emails requesting me to add/remove you from this list will be ignored.

Contacting me by email

For mathematical email queries other than minor clarifications or typos on the homework, I request you come speak to me in person instead of sending me an email. Mathematics is not easily expressed via email, and a physical in person conversation will be a lot more productive.

For minor clarifications, typos on the homework, and logistical queries, my email address is . (Please get the numbers and the plus sign correct, as that will ensure that your email goes to my course folder.) I don't always check email in the evenings, so if you send me a desperate question about the homework at the 11th hour, then you're on your own.

Grading

Homework 30%, the "better" of your two midterms 30% and final 40%.

Note: When I choose the "better" of your two midterms when computing your final grade, I will chose the midterm for which you have a higher percentile ranking (and consequently the midterm for which you have a higher grade). I will then use statistical methods to correct this score so that it can be compared with your scores on the homework/final, and then average it. Bottom line -- you can safely "bomb" one midterm with no consequence to your grade, and let me worry about how the numbers work.

Homework

Homework will be assigned every week on Wednesday, and posted here. Your homework is due the following Wednesday in class, at the beginning of class. During midterm weeks, your homework is due on Friday instead (as your midterm's are all on Wednesdays).

Late homework policy: Late homework will never be accepted. If your homework is not turned in at the beginning of class, it is considered late. To accommodate special and extreme circumstances, your bottom two homework assignments will not count towards your grade. Keep in mind, that this policy is to accommodate special and extreme circumstances. If you use it frivolously early in the semester, then please ensure you and your extended family remain in good health for the remainder of the semester.

Note: Homework is probably the most important part of this course. Trying such problems on your own is the only way to get a good conceptual understanding of this material. You're encouraged to work in groups, however you must write up the solution on your own. Photo-copying or blindly plagiarising solutions from members of your study group (or anyone else for that matter) will be treated as cheating, and dealt with severely.

Optional problems: Your assignments will frequently contain optional problems. These problems are helpful to think about, but you should not turn them in with your regular homework. Problems are made optional for a variety of reasons: Some problems are optional because they are (easy?) standard facts which I did not have time to do in class. Others are optional because they are interesting `challenge' problems, which may or may not have a tractable solution in the scope of this course. You're welcome to discuss any optional problem with me or your classmates, but don't turn it in with your homework. Optional problems won't be graded, and won't count towards your grade.

1. Assignment 1
2. Assignment 2
3. Assignments 3 and 4
4. Assignments 5 and 6
5. Assignments 7 and 8
6. Assignments 9 and 10
7. Assignment 11
8. Assignment 12
9. Assignment 13
10. Assignment 14 (optional)

Solutions

I will sometimes write up solutions to a couple of problems on each homework. For the remaining problems, perfect, or nearly perfect student solutions will be scanned in (with identifying information removed) and hosted here. (If you would not like your homework assignments scanned in and hosted, then please let me know.)

1. Hw1 #5 & 6, and perfect/nearly perfect scanned student solutions to the remaining.
2. Hw2 #5(b) & 6, and perfect/nearly perfect scanned student solutions to the remaining.
3. Hw3 #3 & 4, and perfect/nearly perfect scanned student solutions to the remaining.
4. Perfect/nearly perfect scanned student solutions to all HW4 problems.
5. Hw5 #6, and perfect/nearly perfect scanned student solutions to the remaining.
6. Hw6 #3 & 4, and perfect/nearly perfect scanned student solutions to the remaining.
7. Hw 7 #5 & 6 and perfect/nearly perfect scanned student solutions to the remaining.
8. Hw 8 #5 & 6 and perfect/nearly perfect scanned student solutions to the remaining.
9. Hw 9 #5 and perfect/nearly perfect scanned student solutions to the remaining.
10. Hw 10 #3 & 4, and perfect/nearly perfect scanned student solutions to the remaining.
11. Hw 11 #3, 4 & 5. (Unfortunately scanned student solutions were irrecoverably corrupted)
12. Hw 12 #3, 4 & 5, and perfect/nearly perfect scanned student solutions to the remaining.
13. Hw 13.
14. Optional hw 14.

Handouts

1. Last years midterm with solutions. (The course last year had only ONE midterm, which took place later in the semester. Thus you will see a couple of questions on this midterm which are beyond the scope of your midterm.)
2. Your first midterm and solutions.
3. Some notes on studying for exams.
4. Your second midterm and solutions.
5. A note on the existence of determinants.
6. Last years final. Note that last years final was a take home final. Your final will be in class, closed book.

Textbook/References

1. Linear Algebra. An Introductory Approach, by Charles W. Curtis. (This will be your text book, and the course will roughly follow it).
2. Linear Algebra done right Sheldon Axler
3. Linear Algebra by Hoffman and Kunze

Feedback

Feedback at any time (either anonymous or signed) is always appreciated. You can use this form to send me (or your course assistant) anonymous (or signed) feedback. [Note: Evil spammers have been using this form to clutter my INBOX. Thus I have restricted access to this form to within cmu.edu domain.]