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Jean-Pierre Serre did a lecture on Nov. 10, 2003 on writing mathematics at Harvard. Here's the video: http://modular.fas.harvard.edu/edu/basic/serre/serre.avi (459 Mb)

Papers: http://www.boardofstudies.nsw.edu.au/schoolcertificate/2007/mathematics-sc-test-07.pdf (SC) http://www.boardofstudies.nsw.edu.au/hsc_exams/exam-papers-2007/pdf_doc/gen-maths-07.pdf (Gen) http://www.boardofstudies.nsw.edu.au/hsc_exams/exam-papers-2007/pdf_doc/maths-07.pdf (2U)...

Here's something which might help for ii http://www.geocities.com/threeunitnotes/pisquaredoversix.pdf

Another alternative is to view the files in an online pdf viewer (one not requiring anything to be installed) called <a href="http://view.samurajdata.se">view.samurajdata.se</a> Copy and paste the pdf url into the WEB view and click View! Then click View All and click on the page to enlarge...

Here's heaps: http://www.angelfire.com/ab7/fourunit and heaps http://au.geocities.com/ext2papers and heaps http://www.geocities.com/fourunitmaths

In 2002, Bill Pender said it's too hard for High School students in the following document: http://members.optusnet.com.au/limkw/SGS_harder3U_2002.zip (on page 8) Clearly that is wrong. That same year the exam committee put it in the HSC! Furthermore, the examiner's report for 2002 indicated...

I've attached a solution to the 2002 HSC question 8a (i)-(iii) with this extension.

Here's another lecture by Tao given at UCLA in 2007, similar to the one he gave at Sydney uni. in 2008: http://video.google.com/videoplay?docid=7691494040933085582 (note however that this one is a bit out-of-sync)

No. But there are other videos of Tao. Here are some from 2006 (the year he won the Fields Medal). Check out the youtube ones: http://www.youtube.com/watch?v=zO7m7LS8dyg http://www.youtube.com/watch?v=p6ZUeQv2yFQ And here is a full length lecture by Tao...

Right. ..........................

The HSC material will go onto the Board of Studies website, and the SC material might go up onto MANSW's website.

Are you interested in how the 2007 HSC and SC were marked? If so, you can go to the examiners day on Saturday 23rd February 2008 at Macquarie University – Mason Theatre - 9am. Free for MANSW members, $35 for non-members.

The lecture notes are now available: From Sydney Uni: http://terrytao.files.wordpress.com/2008/02/structure-and-randomness-in-the-prime-numbers.ppt From Katoomba: http://terrytao.files.wordpress.com/2008/02/anziam1.pdf and http://terrytao.files.wordpress.com/2008/02/anziam_pics.pdf...

yorkstanham's school motto says, De virtute in virtutem. How very apt! So why concern yourself with such pedestrian rubbish? See if you can do this one instead. If two distinct points on E: y²=x³+x²-2x-3 are A(x₁, y₁), B(x₂...

Nope. It only has 1 real root. The other 2 are complex. See http://www.angelfire.com/ab7/fourunit/Image-5.jpg for the roots a,b,c See http://www.angelfire.com/ab7/fourunit/Image-7.jpg for a solution to questions a) and b) See http://www.angelfire.com/ab7/fourunit/Image-8.jpg for an...

It's on the Board of Studies website on the bottom of page 40 in the document http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths-st6-calculus-dwb.pdf (from 2007) "Euler’s formula (e^i&theta;=cos&theta;+isin&theta;) has been included in the revised Mathematics Extension 2...

I don't think <a href="http://www.itute.com">itute</a> have solutions to the AMC anymore. They've still got solutions to HSC exams though. Also, it said for a while on the <a href="http://www.amtt.com.au">AMT website</a> that the 2007 AMC solutions aren't available yet. Well that must have been...

No way. It's much better with Euler's identity. It's almost right. But you are assuming the answer is only one number. It isn't. It's an infinite set of numbers. iⁱ={(e^{&pi;i/2+2&pi;ik})ⁱ}_k&epsilon;Z={e^{-2&pi;k-&pi;/2}}_k&epsilon;Z.

So why is it a better question? Because this happy fact is used extensively in the arithmetic of elliptic curves and you can read more about it in Silverman, J. H. and Tate, J., Rational Points on Elliptic Curves, Springer, 1992.

Solution Then let a=0.