Hey,
I consider studying maths at uni, and I have few questions about the courses. Basically, I heard that in maths, at uni, you did not demonstrate anything or prove anything in particular during your course. Here, I mean specific demonstrations, not just calculations or reasoning. I'll try to make myself clearer by giving you an example in a second.
I also have a French friend at Imperial, and he says the same. I wonder how do strangers in general feel about it, or at least people who, during their pre-uni teaching, used to be very rigorous in maths.
I do not mean that A-levels students are not rigorous, but look at this example.
Q1: Differentiate f(x)=(3x)/[ln(x)]
So, according to what I saw, and what I've been told, here is the A-levels method;
f'(x)=[3.ln(x)-3x/x]/(ln(x)²)
= 3(ln(x)-1)/(lnx)²
Now, here is how we have to do it in France (and other countries)
f(x) is a quotient of two functions u(x)=3x and v(x)=ln(x)
u(x)=3x, Du=R and v(x)=ln(x), Dv=R+* (Du is the domain of u)
Now, we need v(x)=/=0 because it is the denominator, therefore ln(x)=/=0 so x=/=1
Therefore, Df=R+*/{1}
Now, u(x) is derivable on R as linear function, and v(x) is derivable for all x of Dv, that is for all x>0
By quotient, f(x) is derivable for all x>0 and x different of 1
Now, for all x of ]0,11,+inf[, f is derivable, and we have
f'(x)=[3ln(x)-3x/x]/(lnx)²
=3(lnx-1)/(lnx)²
Of course, I exagerated a bit, but still in France we have to solve it this way. therefore, I wondered how uni was in terms of maths demonstrations.
Another example would be the demonstration that e^(X+Y)=(e^X)(e^Y) that I could post the French way if you wanted...