Math Test Struggles Abroad: Common Knowledge for Non-Uni Students?

[Anden]

Hello!
A few months ago I applied to a university abroad (in Switzerland to be exact), I myself come from Sweden. As I have not finished upper secondary school I was required to pass a test, all tests went well except for mathematics where I failed completely.
The math tests had elements from three-dimensional vectors (Calculating closest point between two vectors in 3-D space), Plane Geometry, Construction and Applied mathematics (Gaussian Elimination, etc.). None of these I am familiar with, in fact I have never seen these things before and I've completed every single math course in the curriculum.

Are these subjects common knowledge for people abroad, not having begun university yet?

I'm not trying to complain or anything, but it has bothered me quite a bit, so that's why I'd like some opinions. I've taken steps to plug the holes in my knowledge until next year, so hopefully it will go better then

 

[rubrix]

what subject are you trying to study? (i.e. if you have declared your major/minor yet)

i'm from a different country and hence the curriculum is bound to be different. But tell you what, we were required to do a college entrance test on English, mathematics, chemistry (and foreign language optional). I remember the mathematics test had stuff from Calculus I and Calculus II (and perhaps even higher courses). Those questions were there to test those who were familiar with the subject. Say if you could answer Calculus I based questions then you could jump right into Calc II.

That might be the case here, although I'm not so sure since you say "I failed completely". If by that you mean to say you got relatively low score then you'll most likely be placed in a suitable math course based on the test, perhaps precalc or something.

 

[Anden]

I applied to the Physics program on the Technical University in Zürich, and you were required to pass all the tests in order to be permitted to attend the university. I don't know what you mean by "being placed", in Switzerland everyone follows a fixed curriculum, ie everyone reads the same courses at the same time.

Calculus I, II and III are they university courses or upper secondary school? I haven't heard of the names before, so I don't know exactly what they mean.

 

[f95toli]

The math you say you weren't familiar with sounds like topics that would normally be covered in the first math courses at a Swedish technical university (as far as I remember during that first 3-4 weeks, although that might have changed over the past few years). My guess is that the curriculum is just somewhat different in Switzerland.

That said, ETH is one of the best technical universities in the world and I am not at all surprised that the entrance exam is hard, it is entirely possible that they on purpose have included materials that you were supposed to have studied on you own.

 

[rubrix]

Calculus I, II and III are they university courses or upper secondary school? I haven't heard of the names before, so I don't know exactly what they mean.

Yes they are university courses, at least here. Calc III is usually where you kick-off with 3D vectors. Gaussian Elimination usually comes in Linear Algebra which is even a higher Mathematics course.

BUT, these stuff are not that hard. I imagine one could do those with basic high school mathematics knowledge. If you could possibly list more topics that you were tested on (perhaps there is a list of those topics in their website or catalog), we could help you out :)

 

[sokrates]

Plane geometry, Simple analytical geometry ( calculating closest points of vectors in 3D), and Linear algebra are all in high school curricula these days... At least in the US.

If that's all they expect you to know. These are not terribly difficult... You are probably close, just study more.

 

[emyt]

there's no way gaussian elimination is something done in high school..

 

[sokrates]

Haven't you solved 2 equations in 2 unknowns in high school? Maybe you haven't...Gaussian elimination is just the standardized way of doing that.
But it's almost common these days, and what country are you referring? Even within a country, it depends on the type of school we are talking about here.

Nothing very difficult, and yes, it's part of the high school curriculum, linear algebra

 

[CharmedQuark]

Nothing very difficult, and yes, it's part of the high school curriculum, linear algebra

You must have went to an amazing school, for many of us- especially in the U.S. where I'm from- linear algebra is completely foreign to high school. Hell, many of us are lucky enough to get into a calc class at all, mine was almost canceled because of lack of students. I find it amazing that a university anywhere would require knowledge of calc 4(typically known as vector/multivariable) and linear algebra as an entrance prerequisite.

 

[Anden]

From what I've read here, I get the feeling that I'm not so hopelessly behind after all. ;)

I was tested on the subjects German, Chemistry, Applied Mathematics, Mathematics and Physics. I received my result and succeded in all the subjects except Mathematics(Score: 3,7), I needed a 4 to pass and 6 was max. So it wasn't such a complete failure as I thought, Applied Mathematics I succeded with 0,1 extra :). I've contacted the university again and they've said I might be allowed to attend some math courses next term so I'm well prepared for the next year.

I have now invested in Calculus by Gilbert Strang(I think), a book on Applied Mathematics by the same author, a swedish book about Linear Algebra with Vectorgeometry, and the book University Physics by Young. Are there any other books that covers this stuff that you'd recommend?

 

[Etenim]

You must have went to an amazing school, for many of us- especially in the U.S. where I'm from- linear algebra is completely foreign to high school

In most of Europe, basic linear algebra and differential/integral calculus of functions of a single real variable are part of the high-school curriculum. Gaussian elimination is the very first thing we learned, and then continued with determinants and Cramer's method. We studied the foundations of Analytical Geometry in R^2 and R^3 in quite some detail. Of course, the coverage wasn't mathematically rigorous.

Actually, the topics the university expected from the OP all seem to fit perfectly into a high-school curriculum.

 

[sokrates]

Actually, the topics the university expected from the OP all seem to fit perfectly into a high-school curriculum.

Exactly.

Including single variable calc., basic linear algebra, relativity type easy physics etc...

high school

 

[vociferous]

Some high schools might cover certain topics of linear algebra and Calculus III in Algebra II or Precalculus like vectors and matrices, though not in the same detail or manner, since students would obviously lack the proper background.

I suspect though that at most schools, if the subjects are offered at all, they are offered as part of an "advanced" class. In the US, I do not think it is common for universities to assume that students coming from High School were exposed to these topics.

 

[Bourbaki1123]

I think that the U.S. 'Algebra II' course seems to cover Gaussian elimination as standard material. I know that we did matrix manipulation and inversion as well as Gaussian elimination at my relatively high school (which was relatively average).

 

[Nick M]

I had a horrible high school preparation...

9th: Geometry, 10th: Algebra II, 11th: Pre-Calculus, 12th: Graduated early.

In pre-calculus the teacher taught us statistics... determining chances of winning the lottery, opening a pad-lock, etc. Some basic use of sin/cos/tan was covered towards the end.

My first round into a University setting I was placed in Calculus I and passed with a B-.
Calculus II was like flying IFR with a pocket-compass into cumulogranite (failed it).

I was 24 when I went back to school and insisted upon starting in Pre-Calculus, which I placed out of and was advised not to take. After arguing with the advisor, I took Pre-Calculus, Calculus I, Calculus II, Multivariate Calculus, Differential Equations, and Linear Algebra (all standard engineering basics). It made a huge difference, and I got all A's and one B. More importantly, I finally understood everything - and even finished the remainder of the textbooks during summer/winter breaks.

Coming from someone who has learned the importance of having a solid foundation in the fundamentals, I advise you to start off at a level you are comfortable with. To hell with being pressured into something with no footing - take your time to learn it well.

 

[symbolipoint]

Nick M knows what he is talking about. He is smart, not just in the courses he studied, but in his ability to self-judge.

I had a horrible high school preparation...

9th: Geometry, 10th: Algebra II, 11th: Pre-Calculus, 12th: Graduated early.

In pre-calculus the teacher taught us statistics... determining chances of winning the lottery, opening a pad-lock, etc. Some basic use of sin/cos/tan was covered towards the end.

My first round into a University setting I was placed in Calculus I and passed with a B-.
Calculus II was like flying IFR with a pocket-compass into cumulogranite (failed it).

I was 24 when I went back to school and insisted upon starting in Pre-Calculus, which I placed out of and was advised not to take. After arguing with the advisor, I took Pre-Calculus, Calculus I, Calculus II, Multivariate Calculus, Differential Equations, and Linear Algebra (all standard engineering basics). It made a huge difference, and I got all A's and one B. More importantly, I finally understood everything - and even finished the remainder of the textbooks during summer/winter breaks.

Coming from someone who has learned the importance of having a solid foundation in the fundamentals, I advise you to start off at a level you are comfortable with. To hell with being pressured into something with no footing - take your time to learn it well.

So many people need to learn that course credit by itself is meaningless; it tells nothing about the quality of the courses passed and tells nothing of the persons current knowledge of those courses.