Math 115AH: Announcements and Corrections

Wednesday 4:00 meeting 30 March 16

We shall discuss motivation for the course from 33A Questions PDF Version and some algebra.

Remarks on HW 1

In Problem 4 we have C{-1,1] = { f : [-1,1] --> R | f is continuous on [-1,1]}.

You may use the Subspace Theorem (H-K (Book): Theorem 1 p. 35) even if we do not get to it.

Friday 29 April 16: First Midterm

The test will cover material through that covered in class through Monday 18 April 16,
the Classification of fdvs ( material through the fourth homework).
The exam will ask for definitions, examples, statements of theorems, consequences of theorems,
main ideas of proofs of theorems, and one full proof of a result that you may not have seen.

Homework 4 Problem 4: should read S: U --> V -- correction on problem made.

Homework 4 Problem 4: was still wrong and the third line should have said suppose that both T and S (not U) ...
and in parts ii) and iii) im(T) should have read im(S). i have corrected the problem on the homework 4 sheet that is now posted.

Homework 6 Problem 2 is not true. I have corrected the problem on the homework 6 sheet that is now posted.

On the exam, problem 2 was suppose to be worth six points for each part, but I only gave five points for a correct answer. I have corrected this.
In each part in Problem 2, if you had a positive score I raised your grade by one point (to a maximum of six).

Homework/Mideterm 7 has been posted. You should be able to do at least the first five problems this week, the week of May 9.

On the HW 7, you cannot use the Cayley-Hamilton Theorem unless you prove it.

On the HW 7, Problem 2. Comment should have said see Problem 8 (not nine). Now corrected

On the HW 7, Problem 7a. < v_i, T(v_j)> should have read < v_i, S(v_j)>. Now corrected.

Thursday 26 May 16: Second Midterm

The second midterm will cover material from the first midterm through the Approximation Theorem,
i.e., matrix representations, dual spaces, eigenvectors, inner product spaces.
No questions on spectral theory on this exam.
The midterm will be similar to the first midterm, except it will have some computation.

Handout Page: I had forgotten to put the handout page on the web.
It had a summary of matrix representations.
Since today's extra lecture was not as clear as it should have been, I rewrote my notes and have posted it -- sorry I do not have time to tex it.