- Joined
- 18 Mar 2008
- Posts
- 12,751
I went to a mate's house today, and together we managed to teach each other the whole of FP1. All the stuff I was unsure about were his strengths, and my strengths were the things he was unsure about
I agree. I did maths at A level and I don't remember any of it, which goes to show just how important further education in maths is.Maths threads need to be BANNED from these forums for making me feel like a stupid
Burn him!!!I agree. I did maths at A level and I don't remember any of it, which goes to show just how important further education in maths is.
Now if you'll excuse me, I need to find a place to hide from the hoards of angry maths fanatics who will no doubt be infuriated by the above statement
I didn't say you did. I was referring to how it would be beneficial if more people have a better basic ground in science so that they are a bit more informed in discussions of a scientific ilk. The knee jerk ignorant reactions which are all too common when it comes to discussions of new technologies illustrate what sort of problems can arise when you have a group who know nothing about a subject but who want to voice an opinion none-the-less. Of course people shouldn't have their opinion silenced, it'd just be better for all if their opinion were informed a little.I don't think you need to have an in-depth knowledge of something to have an appreciation of its benefits.
True. The issues I refer to are more in regards to when there's a public debate on whether something should be funded or something should be allowed to be researched or further developed. People appreciate the applications after the research has been done and the thing in question understood better. The issue of whether a line of research or whether a particular technology should be used is not so clear cut because often the applications are not immediately apparent. Many of the things we now take for granted and are endemic in our lives started out as very blue sky research which didn't immediately seem to have applications.I can understand the need for a basic maths and basic science because they are applicable to everyday life, but other than that I feel that unless you need or hold an interest in more advanced maths and to a lesser extent science, you need not have an understanding of it to accept and appreciate its value.
A good example is medicine, I have no idea how the doctors fixed me up many years ago....but I appreciate that they did and I equally value the knowledge they had to do so.
I went to a mate's house today, and together we managed to teach each other the whole of FP1. All the stuff I was unsure about were his strengths, and my strengths were the things he was unsure about
I didn't say you did. I was referring to how it would be beneficial if more people have a better basic ground in science so that they are a bit more informed in discussions of a scientific ilk. The knee jerk ignorant reactions which are all too common when it comes to discussions of new technologies illustrate what sort of problems can arise when you have a group who know nothing about a subject but who want to voice an opinion none-the-less. Of course people shouldn't have their opinion silenced, it'd just be better for all if their opinion were informed a little.
True. The issues I refer to are more in regards to when there's a public debate on whether something should be funded or something should be allowed to be researched or further developed. People appreciate the applications after the research has been done and the thing in question understood better. The issue of whether a line of research or whether a particular technology should be used is not so clear cut because often the applications are not immediately apparent. Many of the things we now take for granted and are endemic in our lives started out as very blue sky research which didn't immediately seem to have applications.
Just this week there's been a thread on the forum about whether space technology is worth the money. What about other areas of science? Would the debate be better if everyone were familiar, even to just A Level standards, with science? Of course. For instance, someone said "What has the space race given us?" and then someone provided a list on the NASA website of the sorts of technology we take for granted now but which came from the space race and its legacy. That's the sort of 'ignorance' I think a bit of education would help to address.
Scientists are ultimately answerable to the public, since its the public who determine the law and, indirectly, the funding of projects. If there's a big enough outcry from the public then the course of science is changed. For instance, Germany shut down all of its nuclear reactors after the problems in Japan, due to public outcry. Does Germany suffer level 9 earthquakes? Was there any danger? No, but the public suddenly went "OMG!! Nuclear power is dangerous!!". Things like stem cell research has also been mired in problems and the less said about the entire MMR farce the better. All of those situations could have been improved (not solved, but at least improved) if the general public's level of science understanding were a bit higher. Heck, I said A Levels a moment ago but I wonder how many could pass even a GCSE exam now, despite everyone having sat something akin to that when they were in school.
Anyway, this is a little off topic for the original post.
If it's any consolation FP2 + FP3 are way easier than FP1, that makes little sense but it's way easier. If you do C3 + C4 along with them, then FP2 + FP3 is basically advanced C3 and advanced C4, A2 I'm finding way easier than AS.
It's trivial to prove. In fact you can prove the general result in precisely the same manner but due to lack of LaTeX support I'll do the cubic case.
f(x) = ax^3 + bx^2 + cx + d. Let the three roots be A, B, C, ie f(A) = f(B) = f(C) = 0. By factorisation theorems if f(A) = 0 then f(x) is exactly divisible by x-A and likewise for B and C. Thus f(x) is exactly divisible by (x-A)(x-B)(x-C). The coefficient of x^3 in that is 1 so we overall scale by a to get f(x) = a(x-A)(x-B)(x-C). This has all been done without doing actual expansions and factorisations. We expand this form of f(x) and equate the two formulae, f(x) = a(x-A)(x-B)(x-C) = ax^3 + a(A+B+C)x^2 + a(AB+BC+CA)x + a(ABC) = ax^3 + bx^2 + cx + d. Therefore b = a(A+B+C), c = a(AB+BC+CA), d = a(ABC). QED.