tangsiuje

02-10-2008, 12:53 PM

Excuse the slightly imbecile title of this thread. I'm not wondering what calculus is, but rather about the level of sophistication of the typical US Calc I-III sequence.

This year, I'm trying very hard to improve my maths profile, so I've joined some courses in the maths department (I have to do this outside of my degree, and I'm probably the only person doing a non-maths degree who has done these classes, ever: English universities are kind of inflexible compared to their American counterparts. ;))

As you might be aware, kids here tend to get introduced to the techniques of differentiation and integration at high school, and everyone admitted to an economics degree will have done these things already. Consequently, very little maths is taught in the typical economics degree. Essentially, we just do a first-year one-semester course about multivariable calculus and matrix algebra with economics applications (called "mathematical techniques"), and the rest is taught as it comes along, e.g., we had to do quite a bit on sets and hyperplanes for my micro class last term.

I'm currently doing (ehrm... struggling with) a course called "Analysis". It is given to first-year year maths students, actually as part of a 1.5 year sequence. The first term is about sequences, series and completeness, the second term about continuity and differentiability (only at this point have I learnt the formal derivation of the calculus!), and the third term (which I obviously won't be doing since I will have graduated from university by then) about integration and some other bits and pieces. These classes are entirely proof-based and deal with deriving all the calculus stuff we've already been using for years in a nitpicky (but beautiful) mathematical fashion.

Now, I'm thinking that "Analysis" here must be something quite different from "Real Analysis" in most US colleges (since that's usually offered as third-year course), and I've got increasingly concerned that what I'm doing now actually corresponds more to the Calc I-II sequence. But in that case, I wouldn't even have finished the level of Calc III before I graduate, and then I'd be quite screwed with regard to most economics admissions. :eek:

So essentially, my question is what is taught in the typical Calc I-III sequence: are these courses generally concerned with proofs/derivation or application/computation?

I've tried to google for syllabi, but it's kind of difficult to determine the level of sophistication if the topic is just "chain rule" or "integration". If you'd happen to know of some more detailed syllabi (which you would consider typical for a Calc I-III sequence) lying around, a link would be highly appreciated. If this question has been answered before (and it's just my search skills that are poor), a friendly pointer in the right direction would be equally appreciated.

This year, I'm trying very hard to improve my maths profile, so I've joined some courses in the maths department (I have to do this outside of my degree, and I'm probably the only person doing a non-maths degree who has done these classes, ever: English universities are kind of inflexible compared to their American counterparts. ;))

As you might be aware, kids here tend to get introduced to the techniques of differentiation and integration at high school, and everyone admitted to an economics degree will have done these things already. Consequently, very little maths is taught in the typical economics degree. Essentially, we just do a first-year one-semester course about multivariable calculus and matrix algebra with economics applications (called "mathematical techniques"), and the rest is taught as it comes along, e.g., we had to do quite a bit on sets and hyperplanes for my micro class last term.

I'm currently doing (ehrm... struggling with) a course called "Analysis". It is given to first-year year maths students, actually as part of a 1.5 year sequence. The first term is about sequences, series and completeness, the second term about continuity and differentiability (only at this point have I learnt the formal derivation of the calculus!), and the third term (which I obviously won't be doing since I will have graduated from university by then) about integration and some other bits and pieces. These classes are entirely proof-based and deal with deriving all the calculus stuff we've already been using for years in a nitpicky (but beautiful) mathematical fashion.

Now, I'm thinking that "Analysis" here must be something quite different from "Real Analysis" in most US colleges (since that's usually offered as third-year course), and I've got increasingly concerned that what I'm doing now actually corresponds more to the Calc I-II sequence. But in that case, I wouldn't even have finished the level of Calc III before I graduate, and then I'd be quite screwed with regard to most economics admissions. :eek:

So essentially, my question is what is taught in the typical Calc I-III sequence: are these courses generally concerned with proofs/derivation or application/computation?

I've tried to google for syllabi, but it's kind of difficult to determine the level of sophistication if the topic is just "chain rule" or "integration". If you'd happen to know of some more detailed syllabi (which you would consider typical for a Calc I-III sequence) lying around, a link would be highly appreciated. If this question has been answered before (and it's just my search skills that are poor), a friendly pointer in the right direction would be equally appreciated.