MM4B Quadratic Functions. This video re-visits Quadratic Functions, presents a summary of the features of Quadratic Functions, shows the various ways of solving quadratic equations, talks about the use of the discriminant and then show how completing the square can be used to describe the transformation steps from the basic function of a quadratic to a new variant in turning point form. The video was made for students studying Mathematical Methods (CAS) in Year 12, a course fully prescribed by the Victorian Curriculum and Assessment Authority in the State of Victoria, Australia

All currency coins or notes are issued in these 4 denominations: {1, 2, 5, 10} but not {3, 4, 6, 7, 8, 9}.

Reason: These 4 numbers {1, 2, 5, 10} just need at most  2 operations (+ or -) to generate any number from 1 to 10.

(1 = 1)
(2 = 2)
3 = 1 + 2
4 = 2 +2
(5 = 5)
6 = 1 + 5
7 = 2 + 5
8 = 10 – 2 = 1 + 2 + 5
9 = 10 – 1 = 2 + 2 + 5
(10 = 10)

As I’ve already described, I’m worried about the oncoming MOOC revolution and its effect on math research. To say it plainly, I think there will be major cuts in professional math jobs starting very soon, and I’ve even started to discourage young people from their plans to become math professors.

I’d like to start up a conversation – with the public, but starting in the mathematical community – about mathematics research funding and why it’s important.

I’d like to argue for math research as a public good which deserves to be publicly funded. But although I’m sure that we need to make that case, the more I think about it the less sure I am how to make that case. I’d like your help.

So remember, we’re making the case that continuing math research is a good idea for our society, and we should put up some money towards it…

SM3C Inverse Circular Functions. Inverse Circular Functions of Cosecant, Secant and Cotangent are introduced and then transformations of the their graphs are explored and implied domains and ranges are calculated. The video was produced for students undertaking Specialist Mathematics in Year 12 in the State of Victoria, Australia.

Hello reader,

I am an applicant to Oxford/Cambridge, and sometime after I was informed about whether I was accepted/rejected, I decided to write up on the application process for new applicants who may not know too much about Oxford and Cambridge. I have recently done some research, whipped up some numbers which I hope can help you in your application. Most people start off thinking about applying to Oxford and Cambridge (and other famous universities) without anything except their ambition to start with, and I hope this guide can provide you with useful information for your university applications.

This is written mostly from a Singaporean student’s perspective, although some information is applicable to applicants from other countries as well.

Overview of Oxford and Cambridge

Oxford and Cambridge are the oldest and 2nd oldest universities in the English speaking world respectively, and 2^nd and 3^rd oldest in the world…

Draw a circle and an equilateral triangle inside it, with the three vertices of the triangle touching the circle.

Since we know that the circle has a finite area, the triangle inside must have finite area as well. At this point, we still have finite perimeter on the triangle as well.

Now, divide each edge of the triangle into thirds; draw an equilateral triangle using the middle piece of the divided edges as the base, as follows:

With careful observation, you can see that the perimeter has increased. Specifically, the perimeter increased by a third: instead of one…

There are countless situations in mathematics where it helps to expand a function as a power series. Therefore, Taylor’s theorem, which gives us circumstances under which this can be done, is an important result of the course. It is also the one result that I was dreading lecturing, at least with the Lagrange form of the remainder, because in the past I have always found that the proof is one that I have not been able to understand properly. I don’t mean by that that I couldn’t follow the arguments I read. What I mean is that I couldn’t reproduce the proof without committing a couple of things to memory, which I would then forget again once I had presented them. Briefly, an argument that appears in a lot of textbooks uses a result called the Cauchy mean value theorem, and applies it to a cleverly chosen function. Whereas I…

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