Assignment 1

                        Marking Scheme and TA Comments


Question 1:

Most students did very well. A few typical errors include 

  - not using the round-to-nearest rounding rule (I deducted by 0.5), 
    and 

  - completely incorrect digits (I deducted 1)


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Question 2:

1. Few students left three decimals for floating numbers which is incorrect. 
   But I only took 1 mark off in total if this is the only mistake.

2. Lots of students did question (i) incorrectly. They think the solution 
   will be rounded to 0 but actually not.
 

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Question 3:

Overall the students did very well. Some common errors: 

1. no explanation for part b, students just turned in the code 

2. program doesn't calculate the condition number OR discuss the ratios of
   the relative input/output error

3. missing parts such as x=1 or x=10 or didn't turn in code. 


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Question 4:

The following are my comments and the general marking scheme :

  * The students did extremely poorly on this question and did not 
    understand floating point analysis at all
  * A good number of students did not even attempt to do Q4
  * Most students only got 1 pt for point A and 1 pt for point B
  * 90% of students did not think to Taylor expand the given function to
    see its behaviour
  * Most of the students did not answer the question in that 99% of the
    analysis given tried to explain why f(x) diverged in terms of k;
    their analysis did not explain the seeming convergence for k=1-8 and
    then the divergence for k >= 8
  * The majority of students did not follow through the arithmetic of
    the floating point analysis correctly even if they did arrive at the
    correct initial expression for the floating point analysis
  * I tried to give as many marks for part (a) as possible:
      o I gave 1 pt for a correct initial expression of the floating pt
        analysis
      o 1 mark for correct arithmetic
      o 1 mark if they attempted to align the analysis with the regimes
        seen in the data
      o 1 mark if the main idea was correct
  * Many students tried to show that g(x) was a good approximation for
    f(x)....not sure why they did that
  * Many students tried to back some errors out of the ratio f(x) /
    g(x), again I did not understand their rationale
  * Again, I tried to give as many marks for part (b) as possible:
      o 1 mark for a correct starting formula
      o 1 pt if they mention the delta_x is the same in the numerator as
        it is the denominator
      o 1 pt if they mention that (1 x delta_1)(1 x delta_2)/(1 x
        delta_u) does not affect the result
      o tried to give marks if the general idea was correct

In general I found it very difficult to justify giving marks out. The
students universally did poorly on this question.