View Full Version : Clarification about nomenclature of mathematics courses

Ancalagon The Black

02-16-2008, 05:06 AM

I learn new things every day here in TM. The other day I learnt that Calculus I was primarily differential calculus, Calculus II was integral calculus and Calculus III was multivariate.

So, now I had another question. What is Calculus IV?

Another question is, I applied to a program which said that you must have a year of undergraduate probability and statistics. Now, what would comprise the syllabus of such 2 courses (or 1 year long course)

Any appropriate link would be more than welcome.

Thanks.

polkaparty

02-16-2008, 05:15 AM

I learn new things every day here in TM. The other day I learnt that Calculus I was primarily differential calculus, Calculus II was integral calculus and Calculus III was multivariate.

I think you got the wrong impression in general. Calc 1 is differential and integral calculus in a univariate setting. Calc 2 is a hodgepodge of techniques and topics. Calc 3 is multivariate.

So, now I had another question. What is Calculus IV?

My school doesn't have a calc 4. There might be trimester programs that do have a calc 4 where the calc 1-3 material is split into 4 courses, but that's just a guess. For semester system schools, I don't know what a calc 4 course would entail, perhaps a mixture of linear algebra and diff eqs?

Another question is, I applied to a program which said that you must have a year of undergraduate probability and statistics. Now, what would comprise the syllabus of such 2 courses (or 1 year long course)

Definitions and basic probability theory (Bayes rule, whatever), distributions, expected values, moments, convergence, sample data, estimators, biasedness, inference, etc.

For example, almost all of the material in this textbook (http://www.amazon.com/Mathematical-Statistics-Analysis-Duxbury-Advanced/dp/0534399428/ref=ed_oe_h).

takemoremath

02-16-2008, 05:16 AM

At many schools Calculus IV is a first course in ordinary differential equations.

AstralTraveller

02-16-2008, 05:30 AM

Definitions and basic probability theory (Bayes rule, whatever), distributions, expected values, moments, convergence, sample data, estimators, biasedness, inference, etc.

I lectured the undergraduate sequence of Probability and Stats at my alma mater. The first course was mainly random variables, distributions and moments of first and higher order, and the second course was statistical inference (point estimation, asymptotic theory, confidence intervals, hypotheses testing). I find it weird to learn all these subjects without basic notions of measure theory, because otherwise the students feel they are fed a bunch of un-understandable formulas and loads of stuff they have to memorize. It's so frustrating, both for the teacher and as for the students! With Probability and Measure theory, it all suddenly makes sense!

OK, enough rambling....sorry for (somewhat) derailing the main point of the thread.

Ancalagon The Black

02-16-2008, 05:31 AM

Thanks a lot guys!!

I have done 1 course in Calculus which is both differential and integral calculus combined (we all know calculus very very thoroughly in high school). One course in Multivariate Calculus and 1 course in Differential Equations (ODE and PDE). I suppose that covers Calc I - IV if there.

I have also done 1 course in Probability and Statistics which covers all the material which you mention (and more besides)

polka: I think buckykatt told me that Calc I was diff and Calc II integral. I used to think that Calc II was multivariate and Calc III was tougher and more advanced versions but thank you for the clarifications. It seems to me that even in the US different schools have very different nomenclatures for their courses, especially in mathematics.

I actually did 2 prob/stats courses - 1 from the business department and 1 from the mathematics department. Both were similar but the mathematics department course covered more material as I mentioned above. That should suffice no? I didn't include any syllabus with my application packet. I hope it is enough. Otherwise.... :(

canecon

02-16-2008, 07:48 AM

You basically described the calc 1-3 we have at UBC. For us Calc 4 is:

Textbook Multivariable Calculus, J. Stewart, edition 5e.

Course outline

Chapter 14. Curves, vector functions, velocity, acceleration, length.

Chapter 17, 3. Vector fields and line integrals

Chpater 17, 4. Green's theorem

Chapter 17, 5. Curl, Divergence.

Chapter 17, 6{7. Surfaces and surface integrals.

Chapter 17, 8{9. Stokes and divergence theorems.

asianeconomist

02-16-2008, 08:35 AM

You basically described the calc 1-3 we have at UBC. For us Calc 4 is:

Textbook Multivariable Calculus, J. Stewart, edition 5e.

Course outline

Chapter 14. Curves, vector functions, velocity, acceleration, length.

Chapter 17, 3. Vector fields and line integrals

Chpater 17, 4. Green's theorem

Chapter 17, 5. Curl, Divergence.

Chapter 17, 6{7. Surfaces and surface integrals.

Chapter 17, 8{9. Stokes and divergence theorems.

I studied identical topics, only the textbook (Anton, Bivens,Davis: Early Transcendentals) was different. Oh, and I also did a bit of ODE's

Ancalagon The Black

02-16-2008, 11:32 AM

canecon:

The syllabus you mentioned is part of my course called Advanced Calculus though we use Indian author books.

AT:

The 2 courses which you mention in probability is very helpful. All the topics are present in one of the courses which I did in the mathematics department named Probability and Statistics. We did not do measure theory there. Topology and measure theory was covered in our Real Analysis course.

Does this make it a rigorous mathematics preparation for me? Consider also the following taken: Linear Algebra, Diff Eq (PDE/ODE), Real Analysis(includes topics from both RAI and RAII which I gathered in another course), Numerical Analysis and Discrete Mathematics.

AstralTraveller

02-16-2008, 11:52 AM

Does this make it a rigorous mathematics preparation for me? Consider also the following taken: Linear Algebra, Diff Eq (PDE/ODE), Real Analysis(includes topics from both RAI and RAII which I gathered in another course), Numerical Analysis and Discrete Mathematics.

I strongly believe it does. Now, it would be great to find a way to shove it on the face of the adcoms...although they should be aware of your background coming from India. If they don't know something, they might ask you.

All my best, AT

buckykatt

02-16-2008, 04:43 PM

polka: I think buckykatt told me that Calc I was diff and Calc II integral.

I said that at my school we covered both in Calc I but Calc II covered integration in much more depth (both in terms of techniques and applications, e.g. finding the volumes and surfaces of various geometric objects) plus lots of stuff with sequences. Calc III is multivariate with lots of vector stuff.

One of the things that accounts for the variation in how the material is broken up is that some schools cover "two years" of calculus in four semesters (4 classes of 3 credits each) while others do so in three semesters (3 classes of 4 credit each). (And, of course, some schools use a quarter system--I'm not sure how they break things up there.) So one school's Calc I - IV could be the same as another's Calc I - IV, in terms of contact hours, while a different school's could actually cover more material. The trend has been schools switching from three credit to four credit classes.

The bottom line is that if you've completed whatever part of your school's sequence gets you through multivariate calculus with vectors, you should be all set with the "two years of calculus" part of the requirement. At many schools, this sequence also includes at least some introduction to differential equations, but usually an in-depth study is part of a separate course. Ditto for the topics that come under the heading of "real analysis".

buckykatt

02-16-2008, 04:47 PM

Now, it would be great to find a way to shove it on the face of the adcoms

If it were me, I'd prepare a one-page list of the math & stats courses I'd taken, with short descriptions from the catalog or syllabus and the textbook used, and include it with all my applications. If you make it easy for folks to understand your transcript, they probably will. :)

Ancalagon The Black

02-16-2008, 04:50 PM

Aaah, thanks for the clarification bucky. I have a pretty poor memory. As I said before, we did a separate course on Differential Equations in great detail.

AT: I did shove it in the face of the adcoms but I didn't include the syllabus. The funny thing is, even after the application process is over, I am discovering ways in which I could have made my SOP better or my packet more streamlined or even more clarification about my educational system. :( :D

Ancalagon The Black

02-16-2008, 04:55 PM

bucky: I read your post moments after I submitted mine. Thats exactly the kind of idea I am getting NOW after the applications process is over... :(

buckykatt

02-16-2008, 05:00 PM

bucky: I read your post moments after I submitted mine. Thats exactly the kind of idea I am getting NOW after the applications process is over... :(

I got the idea from one of the master's programs I applied to this year, which asked for exactly this (minus the course descriptions). I went ahead and included it with my other master's apps, figuring better too much info than not enough...

But I wouldn't worry. If your letters of recommendation, grades, scores, etc. are good and the adcom thinks they should be admitting you, they'll probably seek out clarification if there's any doubt about your prerequisites. Hang in there!

doubtful

02-16-2008, 05:08 PM

for Minnesota I prepared 8 pages of math-stats exams with detailed syllabus.. maybe I exagerated.. the fact is that CalcI-->CalcIV--->Real Analysis. are spread trough 6 years..

polkaparty

02-16-2008, 05:12 PM

I don't understand all these people sending extra stuff. I thought schools specifically ask for applicants to not send anything which is not requested.

Thesus

02-16-2008, 05:13 PM

Calc IV over here is pretty much identical to what canecon described as Calc IV at UBC.

As for statistics, that's a bit more complicated. At least here, we have two statistics streams: statistics, and mathematical statistics. The former is basically just running through techniques, while the second is proof-based and relies on Hogg/McKean/Craig, Casella/Berger.

doubtful

02-16-2008, 05:17 PM

I don't understand all these people sending extra stuff. I thought schools specifically ask for applicants to not send anything which is not requested.

do you believe them?

my guess is that if they don't want it they trash it... I don't think they are gonna disqualify people because of extra paper.

anyway.. I mean I sent stuff that thought to be useful, UMN asked for something like that and the graduate coordinator told me it was ok to send an extended version of the syllabi to explain the difference in the classes I have taken in Europe with respect to the American system.

buckykatt

02-16-2008, 05:38 PM

I don't understand all these people sending extra stuff. I thought schools specifically ask for applicants to not send anything which is not requested.

I've seen some programs say that, and to those I wouldn't send anything extra. Maybe I'd make the file available via the web and reference the URL in my SOP "for further information" though.

The programs I applied to basically said "send us anything you think will help us", though. They also required that I assemble everything--letters, transcripts, etc.--and send it together in one big package, which I imagine saved them some work. :)

Ancalagon The Black

02-17-2008, 05:10 AM

doubtful:

Did you get into UMN with all that info? I also believe in the fact that too much information is better than too little info. After all, we have to distinguish ourselves from everybody else. The adcoms want a story - they don't want automatons. I believe that this is a reason why perfect 4.0, 800qs are rejected in favor of research/work experience and say, relevant hardships faced.

After all, nobody has the same opportunities.

bucky:

I did exactly that. I built an e-portfolio and included the link in every application I could get. Maybe they will see it, maybe they won't, but I am sure (from poking around in my webstats), that most of the schools (and the professors whom I emailed) have looked around in my e-portfolio.

Praise Web 2.0 !! :D

econofrosh!

02-20-2008, 11:14 AM

Hello fellow TM-ers! I've been lurking for some time now and this is my first post! :D Bear with me. haha

I realize that the term 'Advanced Calculus' and 'Real Analysis' are used interchangeably; however, there are two different courses in our math department that are named so. Which would be the equivalent of RA among these:

Math 123.1. ADVANCE CALCULUS I. The real number system; point set topology sequence of real numbers; limits and continuity; metric spaces; the derivative; the Riemann integral; series of real numbers; sequence and series of functions; uniform convergence; power series. 3 units. Prerequisite: Math 65 or equivalent

Math 123.2. ADVANCE CALCULUS II. Topology of Rn; continuity and derivative; Taylor's formula; implicit and inverse function theorems; analytic geometry of curves and surfaces; Serret-Frenet formula; multiple integration; improper integrals; transformation; metric and normed spaces. 3 units.

Prerequisite: Math 123.1

Math 126. REAL ANALYSIS. Properties of real numbers; integrals of step functions; Lecesque integral; convergence theorems; measurable functions; measurable sets; introduction to the Hahn-Banach theorem, Riesz representation theorem, fixed-point theorems. 3 units.

Prerequisite: 123.1

If I were to take only two from the abovementioned (I would definitely have to take Advanced Calc I), which would be more advisable to take?

Thanks in advance! :) And good luck to those whose application results are about to come! ;)

asianecon

02-20-2008, 01:08 PM

Hi econofrosh. I'm guessing you're form UP. I'm not, but there are several here. I can think of one person that might help you regarding course choices.

(in case you're wondering how I found out: Lecesque integral)

zappa24

02-20-2008, 04:21 PM

At my undergrad, Calculus I was differentiation. Calculus II was devoted to integration. Calculus III was the before mentioned hodge podge of techniques. Multivariate Calculus didn't come until Calculus IV. The Math department has since condensed the entire sequence to three courses.

fp3690

02-20-2008, 06:32 PM

econofrosh, advanced calc 1 and 2 look like analysis 1 and 2 respectively. Real analysis looks like a grad course in analysis, and also a bit like measure theory, based on my limited contact with the latter. I think even advanced calc 1 is sufficient.

Mr.Keen

02-20-2008, 06:41 PM

I would say Adv Calc 1 is like an introduction to analysis. If you can take that course, then learn on your own topology on Rn and metric and normed spaces you can enroll in real analysis

buckykatt

02-20-2008, 10:02 PM

econofrosh, advanced calc 1 and 2 look like analysis 1 and 2 respectively. Real analysis looks like a grad course in analysis, and also a bit like measure theory, based on my limited contact with the latter. I think even advanced calc 1 is sufficient.

That's my sense, as well.

asianecon

02-20-2008, 10:13 PM

econofrosh, advanced calc 1 and 2 look like analysis 1 and 2 respectively. Real analysis looks like a grad course in analysis, and also a bit like measure theory, based on my limited contact with the latter. I think even advanced calc 1 is sufficient.

I agree. Econofrosh and I have a similar educational system. Adv Calc 1 and 2"are actually first courses in Calculus in my local university and these are aptly labeled as Math Analysis 1 and 2.

mysherona

02-20-2008, 10:47 PM

(in case you're wondering how I found out: Lecesque integral)

I'm still wondering how you found out... How does "Lecesque" tell you this?

C152dude

02-21-2008, 01:30 AM

I'm still wondering how you found out... How does "Lecesque" tell you this?

Google.

Ancalagon The Black

02-21-2008, 05:21 AM

I had a single course in Real Analysis where we did the usual suspects in RAI and topology and measure theory and some other assorted topics. Since I had no idea of what it was, I checked MIT's website and found that my single Real Analysis course comprised topics from both RAI and RAII.

My course named Advanced Calculus is actually a course in Multivariate Calculus - the first part and the second part is tougher problems in Multivariate Calculus.

econofrosh!

02-21-2008, 10:35 AM

thanks for the replies everyone. :)

@asianecon

yup I'm from UP ;)