As an ex-physicist I wholly second the quote below, which I consider the most important part of your mail:
> You can't see the connections between engineering problems > if you haven't first been exposed to the problems. In my personal > experience early exposure to really valuable mathematics is somewhat > wasted--I did not have the engineering experience to see where that > mathematics would apply. I did not really appreciate higher math until > after I had practiced for a while--a situation you find yourself now.
I have seen numerous times similar situations. Personally I think that learning much math is a 'leap of faith' - you have to _trust_ your lecturers that it really will be necessary one day. Plus - you do not really know what of they tell you is important and _how_ it is important. During my course I was initially exposed to 'too much' mathematics. Then we went into physics - which required _different_ mathematics than taught in the 'pure maths course'. Later then I had to _relearn_ parts of maths from the pure maths course - because it was necessary. I wasn't alone in this - at least 80% of my friends had exactly the same opinion. The only good thing about all these was that we learnt very quickly that you can pick up any maths you need - if you have to.
So there is a delicate balance between what and _when_ to study. As one of my lecturers - a pure mathematician, strangely enough - said: this (series of lectures) is not to make you into mathematicians, but to give you mathematical _culture_, so later you can go on your own.
Perry Stout <email@example.com> wrote in article <346E6F3C.6AEE@pacbell.net>... > kdieudonX@spacey.net wrote: > > > > As an electrical engineer with a BS, I'm frustrated by not knowing all the > > math I need to fully grasp the theories involved in many areas of my job. > > [snip] My question is basically this: I have > > heard it said from the engineering side that mathematicians are not worthy > > of as much respect as engineers because what they learn is far afield--even > > the applied math being somewhat suspect. Still, isn't it better to learn > > the math first and apply it later? [snip] I ask because I am considering > > leaning more toward math and less toward engineering in my future education. > > Engineering education is a balance between a large number of competing > interests. Degreed engineers are a "product" that universities and > colleges produce and engineering firms "purchase". Therefore engineering > education is structured mainly to prepare you to function successfully > in the engineering workplace. To that end, you are exposed to courses in > the natural sciences (chemistry, physics), pure mathematics (calculus, > differential equations, vector analysis), applied mathematics (circuits, > statics, dynamics) and direct practice (programming, drawing, design). > For the most part, everyone is relatively happy with the formula. > > Obviously there are deep connections between various topics in > engineering, and the fundamental language used to explore those > connections is mathematics. In my experience the more mathematics you > know the more connections you see, which leads to a greater capability > to solve engineering problems. > > So you should study more mathematics first, right? > > Probably not! You can't see the connections between engineering problems > if you haven't first been exposed to the problems. In my personal > experience early exposure to really valuable mathematics is somewhat > wasted--I did not have the engineering experience to see where that > mathematics would apply. I did not really appreciate higher math until > after I had practiced for a while--a situation you find yourself now. > > You sound like a candidate for an advanced degree. Good luck! > > Perry Stout > firstname.lastname@example.org >