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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.

Andronicus
02-10-2008, 01:07 PM
Don't worry, you are on the right track. Your analysis course sounds comparable to a US undergrad course in real analysis or advanced calculus. Calc I-III usually skip proofs and derivations, focusing on application and computation.

08Applicant
02-10-2008, 04:31 PM
What do you do in Calculus class?

The campus newspaper's crossword puzzle.

So that I contribute, Andronicus is right.

Olm
02-10-2008, 08:52 PM
All I have is Cal 1 lol :(

Luckykid
02-10-2008, 09:37 PM
For me:

Calc I:
Limits, derivatives, and graphs of algebraic, trigonometric, exponential, and logarithmic functions; antiderivatives, the definite integral, and the fundamental theorem of calculus, with applications.

Calc II:
Applications of integration, techniques of integration; infinite sequences and series; parametric equations, conic sections, and polar coordinates.

Calc III:
Three-dimensional analytic geometry and vectors; partial derivatives; multiple integrals; vector calculus, with applications.

Linear Algebra:
Elementary differential equations. Vectors; matrices; linear transformations; quadratic forms; eigenvalues; applications.

Roy

signal08
02-10-2008, 10:29 PM
The two-year math sequence i took as an undergrad at Berkeley--

Math 1A (corresponds to "Calc I"): This sequence is intended for majors in engineering and the physical sciences. An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions.

Math 1B (corresponds to "Calc II"): Techniques of integration; applications of integration. Infinite sequences and series. First-order ordinary differential equations. Second-order ordinary differential equations; oscillation and damping; series solutions of ordinary differential equations.

Math 53 (corresponds to "Calc III): Parametric equations and polar coordinates. Vectors in 2- and 3-dimensional Euclidean spaces. Partial derivatives. Multiple integrals. Vector calculus. Theorems of Green, Gauss, and Stokes

Math 54 (corresponds to "Linear Algebra and Diff Eq"): Basic linear algebra; matrix arithmetic and determinants. Vector spaces; inner product as spaces. Eigenvalues and eigenvectors; linear transformations. Homogeneous ordinary differential equations; first-order differential equations with constant coefficients. Fourier series and partial differential equations.


... at least at Berkeley, the courses *do* emphasize proofs (nothing too hardcore, mostly baby proofs compared to the stuff you see in Real analysis...) the applications come mostly from computer science and engineering, and theres nothing really "economic-y" about it. berkeley also has a one-year calculus sequence for business/econ majors. that sequence is ok for a major requirement but is definitely NOT formal or rigorous enough for grad school. (i'm glad i took the the engineering sequence :D!)

Ibn Abbas
02-11-2008, 01:10 AM
the applications come mostly from computer science and engineering, and theres nothing really "economic-y" about it.

The Math world in general, from what I have seen, doesn't have a clue how mathematical Economics have become in the last 6 decades. The typical Math prof thinks Economics and Sociology/Political Science use the same level of math.

For examples of applications to Economics to filter into mainstream Mathematics is going to take some more time.

Having said that, my Calc prof makes fun of engineers and physicists all the time (because they only use the math and not develop the theory behind it). Wonder what he would say if he discovered that I came from the Econ dept.:hmm:

buckykatt
02-11-2008, 02:46 AM
In our calculus classes the professor presented proofs in class, and of course those of us who actually read the textbook saw more there, but we weren't expected to be able to reproduce them on an exam. Calc II included lots of work with sequences, but not in the more formal way (e.g. using open sets, the Cauchy criterion, etc.) that we dealt with them in real analysis.

Math majors at my school take an "intro to proofs" type class (discrete math) at the start of their studies and finish with a two-semester sequence in real analysis in their senior year. Many students have seen calculus in high school, and either earn college credit for it directly or via the advanced placement exam, allowing them to start the sequence with Calc II or sometimes Calc III.

asianeconomist
02-11-2008, 05:17 PM
The Calculus I-IV sequence is entirely covered by this book:

Anton, Bivens, Davis: Calculus: Early Transcendentals Combined, 8th Edition - Student Companion Site (http://bcs.wiley.com/he-bcs/Books?action=index&itemId=0471472441&bcsId=2257)

In each course, we did four chapters, thus finishing the entire text after four semesters.

Ancalagon The Black
02-11-2008, 06:23 PM
Err, I was going to start a similar thread but I will post my doubts here.

My course is titled Real Analysis and it is a year long course. It includes the obvious topics in RA as mentioned above as well as Topology Analysis and Measure Theory.

Is this Real Analysis II? I didn't give the syllabus in my applications though as I didn't know. :(

And I thought that Calculus II was Multivariate Calculus. We had a course called Calculus but it included both differentiation and integration (we already know the topics in high school in India) In a course called Advanced calculus we did what is multivariate and differential equations was a separate course.

I am such a fool. If I had known then I would have placed my applications directly as a math oriented student rather than a student who knows a bit of maths.

I will not get admission anywhere. :(

buckykatt
02-11-2008, 06:46 PM
My course is titled Real Analysis and it is a year long course. It includes the obvious topics in RA as mentioned above as well as Topology Analysis and Measure Theory.

Is this Real Analysis II? I didn't give the syllabus in my applications though as I didn't know. :(

And I thought that Calculus II was Multivariate Calculus. We had a course called Calculus but it included both differentiation and integration (we already know the topics in high school in India) In a course called Advanced calculus we did what is multivariate and differential equations was a separate course.

I am such a fool. If I had known then I would have placed my applications directly as a math oriented student rather than a student who knows a bit of maths.

I will not get admission anywhere. :(

Let's see..

1. The topics covered in a second semester of analysis seem to vary between schools much more than than those in the first, but I'm guessing that your year-long course was roughly equivalent to two semesters of analysis here.

2. Again, the sequence of topics varies between schools, but AFAIK it's typical that the first two semesters of the calculus sequence covers the single variable case while the third covers multivariate. At my school, Calc I covers differentiation in depth with a basic introduction to integration and then Calc II piles on the integration techniques and applications (with lots of volumes rotating around various axes and such) while also doing a lot with sequences. The standard calc sequence includes lots of trig stuff that's not terribly useful for economics, whereas courses labeled "calc for economics and business" or something similar might leave that stuff out in favor of emphasizing more log stuff and optimization applications. (But I gather that these courses are not as rigorous as the standard sequence.) I'd guess that many if not most schools include at least a brief introduction to ODE in their Calc II class, as well. As I said above, many US students skip the first calc class or two after having covered the topics in high school, so their experience is probably similar to what I've heard from students outside the US.

3. Don't despair. Have a little faith that adcoms know something about the general level of math preparation in India and have a good idea how you compare to US students. They see *lots* of applications and students from India and similar countries.

Ancalagon The Black
02-12-2008, 04:29 AM
Thank you buckykatt for the kind words !!

Right now though, I am ready to despair because its Feb 12 and I have no offers, no rejections and no waitlists at all. Judging from the present data and me having applied to B-schools primarily and NOT having received any interview offer, I think that I am out of reckoning in them schools.

I am hoping that my MS admissions in some other state schools work out so I can get a 4.0 graduate GPA, 8 publications in 2 years and then apply again. :D

On another note, 4 years ago, when I thought that I would be doing undergrads in the US, I had given the AP examinations in 9 subjects along with my sister (AP is only available, thankfully, in my city of Calcutta in India). Both of us got 5 in all of them. I remember giving 2 calculus examinations. Since, the AP examinations are in April or May and my Class 12 examinations were over in March, we had not studied for them at all. I remember finding it very easy to give the examinations as the syllabus was very broad in scope but the level of difficulty was pretty average.

I know that AP is used to get exemption from introductory courses. How would you rate the level of AP to the actual typical courses exempted?? This is a question of mine which I have been thinking about for a long time but never got a chance to ask anyone.

AstralTraveller
02-13-2008, 12:49 AM
Right now though, I am ready to despair because its Feb 12 and I have no offers, no rejections and no waitlists at all.

Brother Ancalagon. I'm in the same ground as you are. No nothing from any schools :(

God knows I trust him. We will succeed! ;)

Ancalagon The Black
02-13-2008, 04:03 AM
AT:

May your words ring true and loud. However, you will definitely get into good places as your profile is stronger than mine. Methinks, I should have applied to some top 100 places as well instead of just restricting myself to the top 30. :(

AstralTraveller
02-13-2008, 04:12 AM
May your words ring true and loud. However, you will definitely get into good places as your profile is stronger than mine. Methinks, I should have applied to some top 100 places as well instead of just restricting myself to the top 30. :(

Believe me, I have you in my prayers. It breaks my heart to see your profile (which is not bad at all...it's very good indeed) and your messages regarding your passion for research, and thinking you won't get in. I think you will, sincerely.

Wish you the best. Gee, I wish the best for everyone, but specially for you and all of us passionate researchers who want to become professors just because that's what we were born for ;)

Ancalagon The Black
02-13-2008, 05:58 PM
AT:

Thank you so much for the kind words. I need to get into a top ranked institution. That means a lot to parents here in India. :(