Average : 73.4% (It was very nice for the first assignment)



I have a few remarks concerning the homework :

Imported general remark : There is a LOT of red on their assignments, students shouldn't be afraid of it. I made a lot of comments to help out, but not every red writing took points away.

=== Personal Comfort === ***I would appreciate some space from people so I can write comments, people write whole assignments on a sheet and there is no space left for grading. ***Some HW have 0 (ZERO) word, some even start at the middle of the exercise without even writing what they are trying to prove. Example : For exercise 3 (e) one goes : "(f(x)+f(-x))/2=(f(-x)+f(x))/2" that's all. I gave the points but it is frustrating when I make more efforts than them to understand what they thought.


===Homework related remarks=== *** Exercise 1 : People need to learn how to deal with absolute values, I saw several |a+b|= |a|+|b| and (a+b)^2=a^2+b^2. Lots only did the cases where everything was positive, then everything negative, but didn't take into account that some can be positive and some negative.

*** Exercise 1 : A big amount of people multiplied the inequality by x on the first without checking the sign of x.

*** Exercise 1 : They need to understand that we can only square an inequality or inverse it if we have a monotonous function on the interval we consider (and reverse the inequality if the function in decreasing).


*** Exercise 1 : Lots of people did not understand that there were no solutions for the (e), with |x-4|+|x-10|=5, I would emphasize the geometrical aspect of it, the LHS is the distance of x to (4,0) + the distance of x to (10,0) which cannot be smaller than the distance between (4,0) and (10,0). Since x, (4,0), (10,0) make a triangle, by the triangular inequality 6 = |10-4| = |10-x+x-4| <= |x-4|+|x-10| so it has to be at least 6, and it is 6 when x is in the closed interval [4,10].

*** Exercise 2 : Almost everyone gave answers with no justification whatsoever.

***Exercise 3 : Very few to no people understood how to prove uniqueness (both for the decomposition in even+odd and to prove that 0 is the only function both even and odd).

*** Exercise 3 : To prove that the product of 2 even / odd functions is odd, lots of people took examples (like x^2 and 1/(x^2+1)) but didn't do the general case.

*** Exercise 3 : Important one, a LOT of people treated some question like this : "if f is even ... if f is odd ... so we proved for all function f", they need to understand that a function needn't be even or odd.


That was a lot of remarks, I hope this will help out.