[12 Dec 2019] Two practice finals are available:
practiceA (fall 2015)
. Some notes about these:
These exams give an idea of the time, length, but our material will differ in content somewhat (ours will have more SVD, Jordan canonical form, symmetric matrices).
2015 exam: For problems (1), (5), assume that the field is the complexes. Modify problem:
(1) to assume that T^4 = 0, but T^3 not equal to 0, not T^2 = 0
(2) do not do this problem (it isn’t so relevant for us), instead modify (5) as suggested below.
(4) (b) V = R^n, T = matrix, T^* is its transpose.
(5) do the problem as written, but as another problem, do not assume that T is diagonalizable. Find all possible
JCF’s of T, and then answer (a),(b),(c) for each of these.
problem 2: do not consider tensor product (times, with circle around it). Instead with the S, T as given, define a linear transformation
U : L(V,W) —> L(V,W) by U(f) = SfT. Now use this U instead of the S \otimes T mentioned in the problem.
(d) Assume that the field is the complexes.
(ignore part e)
- Any problem that references a determinant: do not do those. Also not on the exam: inner products over the complexes, normal operators.
- On the final, in contract to the first 2 prelims's: the T/F and short answer questions will require/allow a short (i.e. at most 2-3 sentences) explanation.
The SVD problems that I have found in the previous finals are not so good, so review our HW too! This goes with the other material we have done since the last prelim too.
Whenever the adjoint T^* is mentioned, replace A with a matrix, and T^* is its transpose.
[12 Dec 2019] Office hours next week are as usual. I also have office hours today (Thursday) 3:30 - 5.
[8 Dec 2019] As mentioned in class, we will make up the cancelled class on Wednesday, Dec 11, at the usual time and place. It will
be a review for the final exam. HW11's due date has been extended to that date,
and HW11part2 (3 problems on Jordan canonical form) is also due that day.
[18 Nov 2019] Second prelim stats: median: 83, median 81.9, stddev 13.7, range: 32 - 100, rough letter grades: >= 90 A, >= 78 B, >= 65 C.
[18 Nov 2019] HW10 has been posted. Caution: the due date is not the usual: it is Monday, Nov 25 in class. Office hours this week have also been
changed accordingly: Beihui Yuan: Thursday 1:30 - 3:30, Mike Stillman: Friday, 3 - 5 pm. Usual places!
[10 Nov 2019] Here are some previous prelim's for practice for prelim2.
practiceA (fall 2015)
practiceB (spring 2017)
and practiceC (2012)
. We will discuss the
answers on Wednesday in class. Some problems are not relevant for us
Fall 2015 prelim2, ignore: TF(a,c,e), Question 1. Spring 2017 prelim2: all problems are OK.
2012 problems: ignore Question 2, Question 4. Also, the notation here is not our standard:
N(T) means the kernel of T, S(v1, ...) means the span of the given vectors. Renni product: is a made up term!
Note that this was a take home exam, so is longer
and more involved than what we will have. Still, any specific problem would be reasonable on
our exam. As usual, these practice problems do not cover everything that we have done. You might also look at all the T/F questions in
Friendberg, Insel and Spence (1st problem of each section, usually).
[10 Nov 2019] Problems 3(c) on HW9 has a typo! The first integral should be squared: HW9 has
been updated to fix this typo.
[23 Oct 2019] Prelim 2 date has been set. It is in class on Friday, Nov 15. If you have any conflict, please
tell Prof. Stillman about it by Wed, Oct 30.
[23 Oct 2019] Prelim 1 stats: mean 77, median 79, std dev 15.
[10 Oct 2019] Here are some basic answers (not all proofs are done out
in full, T/F don't have explanations, but hopefully it will still be
useful. practice prelim solutions A,B,C
[4 Oct 2019] Here are some previous prelim's to try.
. We will discuss the answers on Wednesday in class.
Some problems are
not relevant for us (i.e. ignore practiceB: TF(b,c,d), question 3 (in
question 2, they assume you know the def of the dual vector space, which we will not assume).
practiceC: short answer(d), short answer (e, part iv, v), and question 3).
[2 Oct 2019] HW5 has been posted. It is due Wednesday, Oct 9.
[24 Sep 2019] HW4 has been posted. It is due Wednesday, Oct 2.
[17 Sep 2019] HW3 has been posted. It is due Wednesday, Sep 25.
[16 Sep 2019] Beihui will cover Stillman's office hours for Tuesday, Sep 17 and Tuesday, Sep 24.
These office hours will be the same time 3 - 5 pm, but in Malott 218 (Beihui's usual office hours location).
Prof. Stillman will be back for the Sep 30 class, and office hours that week.
[11 Sep 2019] HW2 has been posted. It is due Wednesday, Sep 18.
[9 Sep 2019] Prof. Stillman's office hours are on Tuesday, 3 - 5 pm, in Malott 503.
[6 Sep 2019] HW1 is now due Wednesday, Sep 11 in class, not the Monday.
[6 Sep 2019] Office hours for our TA/grader Beihui Yuan have now been posted. Prof. Stillman's office hours will likely be on Tuesday's most weeks, the exact time will hopefully be set this weekend. We will discuss this in class today (Sep 6). See the info page.
[29 July 2019] Welcome! The first class meeting is Friday, August 30, at 9:05 am, in room: Malott 406.