18.700 (Linear Algebra) Home Page

Subject evaluations are open from now until 9:00 a.m. Monday December 16. These evaluations are taken very seriously both by your fellow students and by the math department; comments can have an important effect on how subjects will be taught in the future. Please participate!

Instructor: David Vogan, 2-355, dav@math.mit.edu, 617-253-4991

Office hours: Thursday 3-4:00, Friday 4-5 in 2-355, including 12/5-6.

Office hours for final exam: Thursday December 12 3-5, Friday December 13 4-5:30, Monday-Wednesday December 16-18 2-4 p.m.

I was asked to advertise a concert that's raising funds for the Dana Farber Cancer Institute in Boston, orginally scheduled for Monday, December 9. The event is POSTPONED to spring 2020. I'll leave the other info up, because why not. Here's a link to the musician. I can certainly attest that Dana Farber is a great institution to support, and I've verified that Dana Farber thinks this is a fundraising event for them. I listened to some video of the singer; she sounded very talented, but not too much to my taste. Probably you should take that as a strong recommendation. (I loved the guitarist; but probably you should take that as a negative.)

Problem sets will be posted at least a week before they are due. Solutions will be posted the afternoon after the problem sets are due.

pdf file for Problem Set 1
pdf file for solutions to Problem Set 1 (Partly in fairness to others using this text, I will not post solutions to the problems assigned from the text.)
pdf file for Problem Set 2
pdf file for solutions to Problem Set 2
pdf file for Problem Set 3
pdf file for solutions to Probl em Set 3
pdf file for Problem Set 4
pdf file for solutions to Problem Set 4
pdf file for Problem Set 5
pdf file for solutions to Problem Set 5
pdf file for Problem Set 6
pdf file for solutions to Problem Set 6. CORRECTED 11/7/19: in 2(b), the fourth entry in Vc was calculated incorrectly.
pdf file for Problem Set 7
pdf file for solutions to Problem Set 7
pdf file for Problem Set 8
pdf file for solutions to Problem Set 8 CORRECTED 12/3/19 thanks to Quinn Brodsky. (Wrote A instead of A^{1/2} several times; wrote lambda instead of lambda^{1/2}.)
pdf file for Problem Set 9.
pdf file for solutions to Problem Set 9

Here's a distribution of scores on the final, and what letter grade each range corresponds to. (Of course getting an X on the final does not guarantee getting an X for the class.)
A 185-200: 26
B 170-184: 12
C 150-169: 13
D 140-149: 2
below 140: 3

Parallel for semester totals:
A 600-707: 33
B 500-599: 17
C 400-499:: 6

As I've explained in class, the grade you received is not taken directly from your point total for the semester. The list shows the number of As in the class, not the (smaller) number of people with the indicated point totals.

After I posted a score distribution on Exam 3 to help you understand what happened in a situation where a great many people should be disturbed about their scores, several people asked for score distributions on all three exams.

range Exam 1 Exam 2 Exam 3
90-100 26 20 6
80-89 13 15 3
70-79 10 13 13
60-69 5 6 11
50-59 6 6 9
40-49 1 2 13
0-39 0 0 5
average 83.5 81.8 61.7
std dev 15 15 18

Here's how Exam 3 looked to me. There was a good bit of content covered in class and in the notes but not so much in the text. Many people had a lot of difficulty with that material. There were some questions asking you to reproduce proofs of simple facts about self-adjoint operators. Those also caused a lot of grief, perhaps in part because I have not often asked such questions in the past.

Despite these "dangerous bends," the exam was entirely material that I (still) think it's reasonable for you to understand. On the other exams, I've said that the class average might be thought of as approximately a low B. On this exam I don't say that: I think that a reasonable lower bound for a B-level understanding is more like 75.

I've also said that I'm interested more in where your understanding ends up than in how you get there. If your work on the final shows a good understanding of the material you didn't get on this exam, I'll be happy.