Dec-19, YS
The final exam will be graded by Thursday evening / Friday morning and I will post final grades on Friday (probably morning). Happy Holidays!

Dec-06, YS
Here are the FIVE questions you need to answer for HW6: 1   2,   4,   8,   and   10.

Dec-05, YS
Questions related to HW6.

• 1. For question 8, do you want us to show how we can reduce a matrix into Hessenberg form using only Givens rotations? Or do we make it Hessenberg form with Householder transformations and then use Givens rotations to make it triangular? Should the final matrix be Hessenberg or triangular?
  Answer It is the former: you have a full matrix and want to find a matrix G which is a product of rotation matrices so that G A G' has a Hessenberg form.. All you need to show is the sequence of rotations and the progress of the algorithm on a small (say) 6x6 matrix.

Dec-05, YS
Because HW6 is due on a Monday - I will have an (unofficial) extra office hour Friday at 1:00pm.. By then the questions to answer for HW6 will be announced. [See this page on Thursday afternoon/evening or Friday morning]. Also if there are recurring questions about HW6 I will make sure to post those here as well.

Dec-04, YS
Someone pointed out that Canvas does not scale the grades by their maximum (which is dumb) -- so Hw5 was weighed differently from the others because its max was 75, vs. 100 for the others. Each of the 6 homeworks will count 5% [see syllabus]. A temporary fix has been to create a different group specifically for HW5. Once HW6 will be graded the totals you will see will be accurate [I will check them with my own script before making them public]. This is now fixed.. HW5 has been adjusted to reflect a 100 point basis - so you may fractions in the corresponding column.

Dec-03, YS
Here are the stats for Exam 3. The base was 100 pts with 5pts of extra credit.

 mean       77.94   * mean   without zeros   87.68 
 median     88.00   * median without zeros   91.00 
 max       105.00   * min    without zeros   51.00 

Nov. 28, 2018. YS
I added the `grading scheme' in Canvas so you can see your `current' letter grade (based on the total you have so far and the table in the syllabus). This is in preparation for deciding on the final grade. After HW6 is graded you can determine whether or not you want to take the final exam. The letter grade posted on Canvas at that time would become your actual grade if you do not take the exam. It is very important to check your grades as they are posted in Canvas and report any discrepancy to us asap.

Nov. 14, 2018. SH
Here are the grade distribution of HW4. The full score of HW4 is 100 pts.

Question	Grade (pts)
Q1	10
Q2	10+5=15
Q3	5*3=15
Q4	3*5=15
Q5	6+10+4=20
Q6	15 (10 for code and results, 5 for comments)
Q7	3+4+3=10

Nov. 17, 2018. YS
The grade settings for the totals on Canvas were not taking into account the exams [Canvas was totalling only the homeworks.] This has been corrected [I have my own system and now my totals agree with those on Canvas]. It is important to take this into account because the total you get after the last homework will determine the final (letter) grade you will get in this course if you elect not to take the final exam [see syllabus].

Nov. 3, 2018. YS
HW4 related:

• There were questions about what is asked in question 5.b. Here is an additional hint. You write the orthogonality condition : b-Ax should be orthogonal to e (and to the other columns but we ignore those). This gives you *one* equation (e^T(b - Ax) = 0).. From this equation you extract xi_0 as a function of the other unknowns. You substitute this into the whole system -- and this now gives you a new system where xi_0 is no longer present (you have 'eliminated' xi_0).. You then need to solve this system by the normal equations.
• There were some issues with the notation in Question 5 of HW4 - because the matrix was called $X$ and the variable $x$ and also later $\alpha$. I reposted the HW with many changes for better clarity. The matrix is now called A [the Hald.m script has been changed accordingly] and the unknowns (proportions of the 4 chemical compounds) are called xi_1, ...., xi_4 - they form a vector called x. The same symbol A is used for the matrix after it is modified. It is OK if you have already written your answers with the old notation (the questions are the same).

Oct 30, YS
Here are the stats for Exam 2. The base was 100 pts with 5pts of extra credit.

 mean       74.40   * mean   without zeros   83.70 
 median     86.00   * median without zeros   87.00 
 max       103.00   * min    without zeros   43.00 
 Number of As and A-s: 31 

Oct 30, YS
Please make sure to see the latest HW statement.. Those who have printed an older version will see a small error in Question~7. Also note that the due date has been pushed back to Wednesday..

Oct. 18, 2018. SH
Here are the grade distribution of HW1, HW2 and HW3.

• HW3: (a) and (b) in Q4 will not be graded. The full score of HW3 is 100 pts with 5 bonus pts.
  

  Question	Grade (pts)
  Q1	5+4+8+8=25
  Q2	5x3+5=20
  Q3	8
  Q4	8
  Q5	20
  Q6	10
  Q7	4+3+3+4=14

• HW2
  

  Question	Grade (pts)
  Q1	6+10+4=20
  Q2	4+3+4+4=15
  Q3	15
  Q4	5x3=15
  Q5	8+12=20
  Q6	3x5=15

• HW1: Q11 (e) is not graded.
  

  Question	Grade (pts)
  Q1	6x2=12
  Q2	2+8=10
  Q3	1+2+2+1+2+2=10
  Q4	10
  Q5	8
  Q6	10
  Q7	8
  Q8	4+4=8
  Q9	6+2=8
  Q10	2+3+3=8
  Q11	4x2=8

Oct. 3, 2018. YS
Here are all the notes/corrections on HW2:

• The last part of question 6 (c) on condition numbers should be ignored since we have not covered this yet. [ignore the last 2 subquestions that come after ``Prove your result''. If in doubt see the reposted HW]
• Question 5 had a small typo [absolute values missing for l_ij]. I reposted the HW with the correction.
• No need to answer Question 7 of HW2. It is post-poned to HW3.
• Someone asked about the term `pivoting'. The terminology that is widely used is a little ambiguous. A pivot is often just the term a_kk encountered at step k of the elimination or even the multipliers a_ik/a_kk. Sometimes it refers to just the row being used for the elimination at that step. `Pivoting' refers to the process of intechanging rows during the process. Thus, row k is interchanged with a row i>k and becomes the `pivot row'. `Partial pivoting' refers to the process seen in class where you always swap row k with the row i that has the largest | a_ik |. Often one uses the term 'pivoting' as opposed to `partial pivoting' for this (because it is the most common pivoting strategy). I hope this clarifies the terminology. If you want to learn more about this look for `complete pivoting', `rook pivoting' for other strategies used.

Oct. 1, 2018. YS
Re: HW2. No need to answer Question 7 of HW2. It is post-poned to HW3.

Sep. 30, 2018. YS
I have to move the office hour of Monday Oct. 1, to earlier in the day, namely 10:00am to 11:00am. Drop me an e-mail if you need to meet with me on Monday at a different time.

Sep. 26, 2018. YS
The solution of HW1 has been posted in the homeworks page .. You will need the login and password to access this.. refer to an earlier e-mail I sent.

Sep. 26, 2018. YS
Regarding Homework submissions: A number of you asked if they could add a page or two to their homework after the due time, i.e., after you submitted it -[ and one student dropped a page to be added to his/her homework.] This is OK if you accept the 25% penalty For the whole homework . Submitting different pieces at different times is actually more disruptive than submitting the whole thing late so I will be very strict about this in the future.

Sep. 17, 2018. YS
Note: for HW1 questions 6, you need botn m <= p and n <= p. The statement has been corrected accordingly.

Sep. 14, 2018. SH
On TA office hours for next week:
The TA office hours on Sep. 19 and 21 will be canceled. An extra TA office hour will be given on Sep. 17 (Monday) 10-11am at Keller H. 2-209.

Sept. 14, 2018. YS
On Homework 1:
There are a couple of small (but important) corrections in Questions 6 and 9 (these are marked in red in the reposted version).

Aug. 22, 2018. YS
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