New South Wales Higher School Certificate Mathematics Extension 2

(Online since January 1, 2001)

Theme song - Spem in alium

(October 27, 2008)

How NOT to find the surface area of revolution, by Derek Buchanan

(October 5, 2008)

Timothy Gowers from Cambridge University has just finished his gargantuan project, the Princeton Companion to Mathematics.

He speaks about it in the following mp3 (18.3 MB, 19min 58sec):

http://www.press.princeton.edu/podcasts/Gowers/gowers.mp3

John Watkins from Colorado College calls it THE reference work in mathematics.

It's already available as a free torrent download on the internet - and looks great on the iphone (and also much lighter to carry than the huge book!). I will attempt to finish reading it by the end of the holidays - when I'm not trying to get past Level 5D on Space Invaders Extreme for the Nintendo DS, which I am finding very difficult (even with the Paddle Controller)

(September 12, 2008)

15 trial papers added to http://au.geocities.com/ext2papers

(August 23, 2008)

A new Mersenne prime, 2^43,112,609-1 has been found on August 23, 2008 on Edson Smith's computer and is the largest known prime to date and has 12,978,189 digits 316,470,269,...,511 which you can download at http://prime.isthe.com/no.index/chongo/merdigit/long-m43112609/prime-c.html It is the first discovery of a prime with more than 10,000,000 digits and hence the $100,000 prize can thus be claimed. There is another prize for the first discovery of a prime with more than 100,000,000 digits for $150,000. More info on these prizes are at http://www.eff.org/awards/coop More info on this discovery is at http://www.mersenne.org

(July 18, 2008)

YouTube of Australian Team for the 2008 IMO

(July 17, 2008)

2008 IMO

(June 11, 2008)

Submission for Draft Syllabus

(May 22, 2008)

It seems that despite all the international condemnation of USQ's original plan to decimate its maths department and good advice to reverse the decision, the USQ administration have nevertheless decided to go ahead with the original plan (albeit with some minor changes). Adam Walsh has responded with the following comments in the Toowoomba Chronicle, Thursday, May 22, 2008 (page 5):

"I am extremely disappointed that opportunities will be taken away from young people in our region. I feel very annoyed at the primary school teacher who, so many years ago, instilled such a hatred of mathematics in the current dean. I am ashamed that some of the smartest maths and science minds in the world came together behind Dr Tao’s petition for our little uni in Toowoomba and yet these third-rate bureaucrats kept their ears closed. If that many first-class minds told me I was doing the wrong thing, I would certainly be thinking very hard about changing direction! I would like to thank Dr Tao for everything he did and apologise for how pathetic and short-sighted we can be in this country."

(May 12, 2008)

Sample HSC Questions for the Draft Syllabus

(May 5, 2008)

New draft syllabus

(April 17, 2008)

The following has been presented to the Queensland Parliament

from page 1196 in

http://www.parliament.qld.gov.au/view/legislativeAssembly/hansard/documents/2008.pdf/2008_04_17_WEEKLY.pdf

(April 14, 2008)

The petition has been submitted to the USQ administration supported by well over 800 signatories.

(April 5, 2008)

Over the last 10 or so years, university maths departments have been decimated in Australia. Now, as indicated in Adam Walsh's email, USQ has decided to decimate it's maths department, so Terry Tao has started a petition at

http://terrytao.wordpress.com/about/petition-to-support-maths-statistics-and-computing-at-usq

I signed it with the following comment:

I support this petition. Service teaching is indeed inadequate. Putting philistines in charge of schools and universities has never been such a great idea, but this sort of thing is inevitable if they are put in charge.

You might like to also sign it.

(March 31, 2008)

Adam Walsh sends Terry Tao the following email thereby causing an avalanche of criticism both within Australia and overseas against the USQ administration

(February 21, 2008)

Induction (again)

The concluding statements for inductions provided by many candidates show that they incorrectly think that a proof by induction is actually an iterative proof, in which you imagine that the recipe should be repeated as many times as necessary in order to verify the statement for whichever positive integer is of interest. In fact, the Principle of Mathematical Induction is that every set with the property that, for each integer n in the set, n+1 is also in the set and which also contains 1 contains all positive integers. So, having established that the statement is true for 1 and, if true for some integer, is also true for the next integer, the correct conclusion is to simply state that, by induction, the statement is true for all positive integers. - 2007 HSC Examiners' Report.

I was told by a member of the exam committee that at least 75% of teachers disagree with the exam committee. This is because most maths teachers blindly teach from textbooks written by amateurs without thinking about what they are teaching. Not only is this a very boring way to teach, it also will lead to errors such as the one indicated by the 2007 HSC Examiners' report.

Although this has been corrected in recent years in published solutions to 4 Unit papers, the published solutions to 3 unit papers are still bedevilled by the dreaded mantra, true for n=1, so true for n=2, so true for n=3, etc, therefore true for all positive integers - whereas in 4 unit solutions, we now see by induction, the statement is true for all positive integers.

So we now have another problem of confused 4 unit students (who have to sit both papers) with conflicting conclusions to published induction proofs. The only thing teachers can do is to tell them that the published 3 unit solutions are wrong.

(February 7, 2008)

Terry Tao's Powerpoint presentation at Sydney University, February 7, 2008

(January 16, 2008)

Here's an alternative solution to the 2007 exam question 3b. I bet you thought the answer was x³-20x+24. That's too boring.

Of course, a better question would be that if two distinct points on E: y²=x³-5x+3 are A(x₁, y₁), B(x₂, y₂) with x₁≠x₂ show that if λ=(y₂-y₁)/(x₂-x₁) then there is a third point C on E through AB given by (λ²-x₁-x₂, λ(λ²-2x₁-x₂)+y₁).

Such a shame they don't ask better questions in HSC exams thesedays!

For pdf documents

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Practice papers

31 papers

113 papers

70 papers

Teaching Resources

Hard Problems on youtube. This is a trailer of a new movie to be released on January 8, 2008 about the 2006 IMO.

Johan Wastlund's Elementary Proof of the Wallis Product Formula for pi

Yet another proof of the irrationality of e

DON'T BAN YOUTUBE!

Three Unit Notes 1

Three Unit Notes 2

Professional mathematics versus amateur mathematics

Syllabus (from boredofstudies server)

Submission for Stage 6 Syllabus Review

New Topics for the Draft Writing Brief and Writing Brief

Extract of Response to the Draft Writing Brief

Sixty 4 unit lectures