The Math(s) Thread

[Luca]

This was on the old board, so it might as well be revived.

I'm generally a person with very, very few regrets, but one of my most sincere ones is opting to do a commerce degree in undergrad and not a maths degree. It's a subject that has always deeply appealed to me, and I've been making efforts to learn it on my own. If anyone else feels this way, here are a few resources to get you started (the material overlaps with, and then picks up from, the end of high school/college):

Single Variable Calculus (MIT OCW) (http://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/)
Multivariable Calculus (MIT OCW) (http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/)
Linear Algebra (MIT OCW) (http://ocw.mit.edu/courses/mathematics/18-06sc-linear-algebra-fall-2011/)
Intro to Analysis (MIT OCW) (http://ocw.mit.edu/courses/mathematics/18-100a-introduction-to-analysis-fall-2012/)

Hi, Ital.

[ItalAussie]

I am more than happy to answer any questions that may pop up, particularly if anyone is working through coursework on their own and runs into trouble. :nodd:

[hfswjyr]

Ital, have you read the story in the news recently about the aussie 50 cent coin question?

The state of Australian/Western math education...

[niko_cee]

That is fairly poor.

Compare that to that Singaporean question that went viral.

[mugbull]

The singaporean question was pretty easy, I was surprised there was that much of a fuss about it

[ItalAussie]

Ital, have you read the story in the news recently about the aussie 50 cent coin question?

The state of Australian/Western math education...

It's crazy that the question is even news. It's basically trivial, and you could even eyeball it.

The thing is, all maths questions look hard when you're out of practice, which is why it's a subject that newspapers can milk for as long as they need. Find the hardest question. Write an article about how hard it is. Rinse. Repeat every year.

[simon]

I've just googled the Australian 50 cent question out of intrigue.

Honestly, how has that question made a Year 12 Maths Test, let alone the news for being too hard!?

[DC]

Because it's a bit random. Not many people would know offhand the several ways to get to the result. My solution to that shape one was 360/12 = 30. 30*2 = 60 but there are a few other ways to get to it.

I have a big issue with diagram type questions like that - particularly when underneath the diagram it used to say things like "drawing not accurate". I think it was the 1994 AQA Maths Exam that actually had one such diagram that proposed an impossible shape in the text as the angles added up to greater than 360, I also recall an equally infuriating 50p question involving a similar scenario (but I think it was to do with working out the circumference).

[SvN]

I think it's a very clever question to test student's genuine understanding of interior angles. It's actually very straight forward if you do.

[niko_cee]

The singaporean question was pretty easy, I was surprised there was that much of a fuss about it

It was a bit tougher than basic geometry.

[mugbull]

Eh, it didn't even involve math really, it was just a reading problem.

[niko_cee]

I think I'm just remembering it wrong (sic).

[Toby]

The Singaporean one was just a logic puzzle.

[mugbull]

I have one.

Suppose U is the subspace of R4 defined by U = span( (1, 2, 3, -4), (-5, 4, 3, 2) ).

They want me to find an orthonormal basis of U and an orthonormal basis of U perp. Find an ortho basis of U is trivial if you use Gram-Schmidt, and finding an ortho basis of U perp would be fairly simple if U was 1-dimensional (because you could then just find two linearly independent vectors orthogonal to a line). But since U is spanned by two vectors, you have to find 2 lin independent vectors for which any linear combination thereof is orthogonal to any linear combination of the two spanning vectors of U. I've found vectors that are linearly independent and orthogonal to (1, 2, 3, -4) and (-5, 4, 3, 2), but not to an arbitrary linear combination of them, and although it makes sense in theory (a 2D plane intersecting another 2D plane orthogonally in 4D space), I can't compute it. Any thoughts?

[ItalAussie]

I've found vectors that are linearly independent and orthogonal to (1, 2, 3, -4) and (-5, 4, 3, 2), but not to an arbitrary linear combination of them
This seems a bit weird/impossible. What are the vectors?