## Honors Linear Algebra, Math 2270-3, Fall 2014

Syllabus

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Announcements:
• (12/1) The last midterm exam will take place on Friday, 5 Dec, covering Chapters 8-11.
• (11/24) Comments on HW8: graded 6 of them at 6 points each and the remaining 14 at 1 point each. The 6 problems to receive 6 points each were 8.1.4, 8.2.12, 8.4.3, 8.4.5, 8.4.21, and 8.5.1. Again, the main reason that students lost points was that they did not finish the problems for a particular chapter and section; they would do the first few and leave off the last few problems for a section.
• (11/19) A computational strategy for the Jordan normal form by Tabrizian.
• (10/27) Third midterm will be Friday, 7th Nov. It will cover Chapters VI and VII. HW7 is due on Wednesday, 29th Oct instead of the usual Monday.
• (10/20) Comments on HW6: graded problems 5.3.6, 5.4.1, 5.4.2, 5.5.2, 5.6.5, and 5.6.6 at 5 points each, then 2 points each for the other 10 problems. It is graded somewhat more strictly than prior homeworks. For instance, if the student indicated that it would be trivial to prove some point, but does not actually prove the point, then the student lost some points. Also on problems 5.4.1 and 5.4.2, many students took short cuts in their proofs such as "\sum_{i=1}^n \sum_{j=1}^m Y_i a_{i,j} X_{j} = \sum_{i=1}^n \sum_{j=1}^m X_i a_{i,j} Y_{j}" means that "a_{i,j} = a_{j,i}". What I was looking for was more detailed steps in the proof which would show why that statement is true in this case. That is one of the more telling issues on the last few homeworks, the students do not take the time to prove all points, instead they just make (possibly correct) assumptions without any proof to back the statement up. Another issue which lost a lot of points comes from questions with two parts, such as problem 5.4.1 which had a second part which was "show that this is a scalar product" - many students did not include that part of the answer.
• (10/5) Comments on HW5: scored 4.3.2, 5.1.2, 5.1.3, 5.2.6, and 5.2.9 at 8 points each and the other problems all at 1 point each.
• The last problem, 5.2.9, was difficult to grade. What I was looking for was for the student to show why their new vector "'w" was equal to "v". Many just skipped over showing why that is true and just stated it without proof. This makes their proofs just a lot of assumptions. On problem 5.2.8, many students had issues trying to find the magnitude of vectors which had complex components. On problem 5.1.3, many students failed to do the second part of the problem which was to provide a matrix "M" which was positive definite for this operation (in their partial defense, the way the book defines positive definite and the way that this problem is stated do not make use of the term in the same manner).
• (9/29) Some comments on HW4: Scored problems: 3.3.4, 3.3.9, 3.3.10, and 3.4.7 at 8 points each and the remainder at 2 points each for a total of 50 points. The biggest problems that students seemed to have was that they leave out entire problems or leave out part (b) of a problem. Other than that, the solutions for linear operators on the space of infinitely differentiable functions caused some issues for a few students because they would set up that the kernel is the set of functions such that an ODE (some function of the derivative, etc...) is equal to zero, but they did not solve for the kernel any further.
• (9/28) Comments on HW3: Most everyone did well. The biggest problems were that a few students did not do all of the problems, they may have run out of time at the end. A mistake that keeps coming up is that students attack a proof in the wrong way. For instance, to prove that if A has an inverse and B has an inverse, then AB has an inverse, some students started with the statement that the inverse of AB is the inverse of B times the inverse of A. But that assumes existence, which is something that needs to be proven here.
• (9/28) Comments on HW2: The issue on 1.4.3 was that the one student who lost points was that the student used "A - cB = 0" to show that A, and B form a basis, for the student who lost points on 1.4.4 simply mis-stated the formation of the basis formed by U and W.
• (9/28) Comments on HW1: For one problem, 1.2.8, a re-occurring issue was that students could not get the derivative of sin t to be +cos t. Other errors came from having to solve a 3 x 3 set of equations to prove linear dependence, there were many arithmetic errors there. So a mostly easy problem got included in my set of 5 point problems. Some of the proofs involved in the 1 point problems were difficult for some of the students. The most common error was that they would start with the line to be proven such as "c O = O" and then prove something given that fact. Some students use a proof of the contra-positive to complete some of the proofs required here and that type of proof works very well.
• (9/26) HW for V.3 is moved to the next. On the other hand, I add #6 to V.2.
• (9/8) The scanned pdf of Gaussian elimination.
• (9/8) If you are interested in mathematics, you might consider going to undergraduate colloquia on Wednesdays 12:55-13:45. Free pizzas after each talk. For more details, consult the link above.
• (7/31) This is an honors, PhD-track class and requires permission code, which can be requested easily at mathematics department homepage.
• (7/27) Please email me or see me in my office if you have any question about the class.

HW:
• Always read the textbook and lecture notes!
• (Due 9/3) Sect 1.1: 1-5, 9-13. Sect 1.2: 1(a,c,e,g), 3-4, 5(a,c,e,g,i), 7-10.
• (Due 9/8) Sect 1.4: 1-4. (Review Chapter 1. Midterm is a week away!)
• (Due 9/15) Sect 2.1: (matrices) 2, 4, 5, 8, 10; (dimensions) 1-2. Sect 2.2: 1-2 + additional 2 problems #15, 16 in the scanned PDF. Sect 2.3: 1, 3(c), 4, 8, 11, 17-19, 21, 35.
• (Due 9/22) Sect 3.2: 1(a-d), 2, 4. Sect 3.3: 3-10. Sect 3.4: 2, 7.
• (Due 9/29) Sect 4.2: 1, 2(a,b,c), 6. Sect 4.3: 1, 2. Sect 5.1: 2, 3. Sect 5.2: 0-6, 9.
• (Due 10/8) Sect 5.3: 1(a,c,e,g), 2, 4(b,d), 5(b,d), 6. Sect 5.4: 1-4. Sect 5.5: 1(a), 2. Sect 5.6: 2-6.
• (Due 10/29) Sect 6.2: 1, 2. Sect 6.3: 2(a,i), 3, 5. Sect 6.4: 1(a,c). Sect 6.8: 1(a,c,e), 2-4. Sect 6.7: 1-3. Sect 6.9: 1, 3, 5.
• (Due 11/3) Sect 7.1: 1, 2, 6, 7. Sect 7.2: 2, 5, 9. Sect 7.3: 1, 2, 3(b), 4(c), 6, 7.
• (Due 11/17) Sect 8.1: 1-4, 7. Sect 8.2: 2, 4(a,c), 8 (d,f), 9-13. Sect 8.4: 1, 3, 5, 6, 9(a,c,e), 21. Sect 8.5: 1.
• (Due 11/24) Sect 10.1: 1, 2, 4, 6. Sect 10.3: 1, 2. Sect 11.1: 1(a,b), 2, 3. Sect 11.2: 1, 3, 4.
• (Due 12/5) Sect 11.3: 1, 2, 4, 5, 6, 15. Sect 11.4: 1, 2, 3. Sect 11.5: 1, 2, 5. Sect 11.6: 1-4.

Coordinating Page