SYLLABUS: LINEAR ALGEBRA, Section 4 (Fall 2007, Tuesday/Thursday@6:10pm in Math 203; Elliott Stein)

The final grade is based on the two midterms (20% each), the final (40%) and the weekly homework (20%).

Office hours: Tuesday and Thursday, 5pm-6pm, Math 424

Class Schedule and Homework Assignments (subject to change; all references are to Elementary Linear Algebra: A Matrix Approach (2^nd edition) by Spence, Insel and Friedberg):

DATE	TOPICS	SECTION OF TEXT	HOMEWORK PROBLEMS
September 4,6	Matrices and vectors; systems of linear equations	1.1, 1.2, 1.3	1.1: 13, 15, 16, 18, 19, 21, 22, 24, 25, 26, 27, 28 1.2: 1, 2, 13, 14, 15, 16, 19, 26, 29, 35, 40, 44 Due Sept. 11
September 11, 13	Row echelon form; rank and nullity; the span of a set of vectors	1.3, 1.4, 1.6	1.3: 6, 20, 21, 22, 37, 38, 45, 52 1.4: 7, 8, 17, 24, 35, 40, 47, 48 1.6: 3, 16, 17, 18 Due Sept. 18
September 18, 20	Linear dependence and independence; matrix multiplication	1.7, 2.1	1.6: 23, 28, 36, 42 1.7: 11, 12, 19, 20, 23, 30, 31, 38, 48, 56 2.1: 4, 13, 14, 19, 20, 27, 32, 59* (* = optional problem) Due Sept. 25
September 25, 27	Inverse of a matrix; elementary matrices; linear transformations	2.3, 2.4, 2.7	2.3: 3, 6, 12, 22, 23, 32, 67, 68 2.4: 9, 16, 27, 28, 56, 84*, 85* 2.7 25, 32, 59, 62, 67, 70, 75, 101* Due Oct. 2
October 2	Linear transformations (continued)	2.7, 2.8	2.8: 5, 6, 15, 18, 27, 30, 33, 40, 56, 68, 84, 92* Due Oct. 9
October 4	MIDTERM 1
October 9, 11	Determinants; vector subspaces	3.1, 3.2, 4.1	3.1: 11, 12, 13, 20, 28, 44, 80* 3.2: 9, 10, 15, 16, 24, 32, 72*, 74* 4.1: 5, 10, 18, 23, 24, 37, 40, 84 Due Oct. 16
October 16, 18	Dimension; bases; coordinate systems	4.2, 4.3, 4.4	4.2: 5, 8, 11, 14, 21, 30, 70, 74* 4.3: 1, 10, 16, 19, 22, 40, 68, 80* 4.4: 9, 11, 22, 28, 71, 74 Due Oct. 23
October 23, 25	Linear transformations as matrices; eigenvectors and eigenvalues	4.5, 5.1, 5.2	4.5: 3, 8, 13, 18, 47, 54, 96* 5.1: 7, 17, 26, 30, 34, 38, 72* 5.2: 3, 15, 22, 27, 30, 40, 44, 86* Due Oct. 30
October 30, November 1	Diagonalization; geometry of vectors	5.3, 6.1, 6.2	5.3: 5, 6, 20, 57, 62, 76, 77 6.1: 7, 8, 15, 16, 32, 40, 47, 48, 96* 6.2: 15, 16, 23, 24, 58* Due Nov. 8
November 8	MIDTERM 2
November 13, 15	Orthogonality and orthogonal projections	6.2, 6.3	6.2: 14, 22 6.3: 5, 8, 13, 14, 19, 20, 24, 32, 66* Due Nov. 20
November 20	Orthogonal matrices	6.5	6.5: 5, 6, 7, 8, 37, 38, 49, 54*, 62, 63 Due Nov. 27
November 27, 29	Symmetric matrices; abstract vector spaces	6.6, 7.1	6.6: 17, 18, 20 7.1: 1, 8, 11, 14, 28, 32, 60, 61, 74 7.2: 1, 2, 7, 8, 33, 34, 35, 36 Due Dec. 6 (no extension)
December 4, 6	Abstract vector spaces and linear transformations	7.2 – 7.?
Thursday, Dec. 13 Math 507, 6:15pm	Review session
Tuesday, Dec. 18 Math 417, 7:10pm	FINAL EXAM

• This syllabus will be updated weekly, usually on Sunday night, to post the assigned problems that relate to the material that will be covered in class in the upcoming week. Those problems are due on Tuesday of the following week, i.e. about nine days after they are posted. Homework can be handed in to me directly in class or can be left in my mailbox. Faculty mailboxes are located on a landing just downstairs from the main entrance to the Mathematics Building.
• Before attempting the homework problems, you should read the corresponding section(s) of the text, as indicated on the syllabus.
• Your homework papers do not have to follow any prescribed format, but you should (1) write legibly, (2) show how you get your answer and (3) staple the pages if you’re handing in more than one page. I keep a stapler in my office that you can use for this purpose. You can submit homework electronically by e-mail to the address below or by fax to 212-403-2228, but make sure that what I get will be legible.
• I will circulate solutions to the assigned problems by e-mail promptly after the assignment is due. If you hand in your paper late, but before I circulate the solutions, you will not be penalized for lateness. Homework that is turned in after the solutions are circulated will not be graded and will not receive credit.
• Each student has one “free pass” on the homework during the semester, meaning that you can not turn it in and there will be no penalty. If you turn in all the homework, I will discard your lowest grade before computing your overall homework grade.
• You will get the most out of the homework if you do it on your own, but there is nothing wrong with discussing a problem with another student or getting an idea from another student, so long as you do not literally copy someone else’s work.
• You do not need a calculator in this course, and they are not permitted on the exams.
• The latest version of this syllabus can always be found at math.columbia.edu/~stein/Syllabus5.html. You might want to bookmark the site on your browser. It’s a good idea to hit the “refresh” button on your browser after logging onto this site to make sure that you’re not looking at an earlier version of the page that your computer has cached.
• You can reach me by e-mail at stein@math.columbia.edu. My office telephone is 854-8746, but I’m rarely there except during office hours.