What math level is required?
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From: victor_meldrew_666 on 16 Jan 2010 06:54 On 16 Jan, 07:44, "Ostap S. B. M. Bender Jr." <ostap_bender_1...(a)hotmail.com> wrote: > I have to say that as a student at the best math school in Russia and > a winner of math Olympiads in both Russia and USA, I never studied > much analytic geometry in high school, nor even as a math major at > Harvard U. > In solving this problem, I myself would never even think of using > analytic geometry, Too bad, since such problems are easily demolished with a modicum of vector algebra, still taught at A-level in the UK. Still, at least it's reassuring for those of us who didn't attend "the best math school in Russia", never was a winner of a "math" Olympiad and never was a "math major at Harvard U", that someone who was all these can be a bit of a duffer on occasion :-)
From: Ostap S. B. M. Bender Jr. on 16 Jan 2010 07:46 On Jan 16, 3:54 am, "victor_meldrew_...(a)yahoo.co.uk" <victor_meldrew_...(a)yahoo.co.uk> wrote: > On 16 Jan, 07:44, "Ostap S. B. M. Bender Jr." > > <ostap_bender_1...(a)hotmail.com> wrote: > > I have to say that as a student at the best math school in Russia and > > a winner of math Olympiads in both Russia and USA, I never studied > > much analytic geometry in high school, nor even as a math major at > > Harvard U. > > In solving this problem, I myself would never even think of using > > analytic geometry, > > Too bad, since such problems are easily demolished with a modicum > of vector algebra, still taught at A-level in the UK. > What is "A-level"? Is that part of high school or college? When I was in high school in Russia, we didn't study much linear linear algebra in math beyond what is required for simple partial derivatives, although we did 3D vector products in physics classes. I remember spending much time in 9th grade learning useless tricks to evaluate complicated indefinite integrals and 10th - on equally useless stereometry, and on volumes. You have to remember that you, Brits, are mathematically (and in all other ways) superior to Russians and Americans like myself. A look at the list of Fields Medal winners will surely confirm that. And your record at the International Mathematical Olympiad is also quite... well, unexpected: http://www.imo-official.org/results.aspx Ranking of countries Cumulative results by year Cumulative results by country The following table shows the positions of each country each year in the unofficial mark ordering. The year of the IMO is represented by its last two digits. Year 09 08 07 06 05 04 03 02 01 00 99 UK 19 23 28 19 13 20 10 27 31 22 20 RUS 3 2 1 2 3 3 5 2 2 2 1 USA 6 3 5 5 2 2 3 3 2 3 10 Since year 2009 was a relatively good year for you Brits, let's look at it: People's Republic of China Japan Russian Federation Republic of Korea Democratic People's Republic of Korea United States of America Thailand Turkey Germany Belarus Taiwan Italy Romania Ukraine Vietnam Islamic Republic of Iran Brazil Canada United Kingdom Belarus, Vietnam, Islamic Republic of Iran, Brazil, eh? According to the proud you, all of your high school students are supposed to be able to "demolish" the above Chinese high school problem "with vector algebra", and yet your Royal Chemistry Society offers 500 quid to anybody in the country who can solve this very problem in unlimited amount of time, and your "well known and respected" English universities test the incoming science undergraduates by asking them to figure our the hypotenuse if the cathetii are 3 and 4. > > Still, at least it's reassuring for those of us who didn't attend > "the best math school in Russia", never was a winner of a "math" > Olympiad and never was a "math major at Harvard U", that someone > who was all these can be a bit of a duffer on occasion :-) > Well, I guess I asked for it when I volunteered that I am very bad at solving high school geometric problems using analytic geometry. I should have known that there is always some bigshot lurking around waiting to assert his intellectual superiority over those who freely confess their shortcomings. Congratulations: you are a better and smarter man than I, and better at applying analytic geometry to college entrance exam problems, especially now that I haven't taken such tests in more than 30 years and my mind and memory aren't nearly as sharp as they once were.
From: The Qurqirish Dragon on 16 Jan 2010 08:29 On Jan 15, 1:36 pm, Ask me about System Design <grpad...(a)gmail.com> wrote: > On Jan 15, 2:17 am, "Ostap S. B. M. Bender Jr." > Finally, the angle between AD and BC1 will be the most > challenging, primarily because of coordinatizing B > algebraically. B has coordinates (s3t,t,0) for some > positive t (because B is not D) and is distance 2 away > from (2,0,0). Thus t^2 + 3t^2 -4s3t +4 = 4, so t = s3. > Then B = (3, s3,0), BC1 has direction (-3,s3,s3), and > AD has direction (-2,0,0). Their cosine is their dot > product divided by the product of their lengths, or > 6/(2 * sqrt(15)), or sqrt(3/5). The angle is then > inverse cosine of sqrt(.6), which I am told is > 39 degrees and some number of minutes. Just a side note on finding the location of B: since AD = 2, DC=2s3, and angle ADC is a right angle, triangle ADC is a 30-60-90 triangle. Since the diagonals of the base are perpendicular, it is easy to show ABC is congruent to ADC. (one way: AB = AD, AE = AE makes ADE congruent to ABE, so BE = DE, and CE = CE gives BCE congruent to DCE. ABC is congruent to ADC by SSS theorem)
From: victor_meldrew_666 on 16 Jan 2010 11:35 On 16 Jan, 12:46, "Ostap S. B. M. Bender Jr." <ostap_bender_1...(a)hotmail.com> wrote: > What is "A-level"? http://en.wikipedia.org/wiki/A-level > Is that part of high school or college? What is "high school"? > You have to remember that you, Brits, are mathematically (and in all > other ways) superior to Russians and Americans like myself. The opinion of a pupil of the best "math" school in Russia, a winner of "math Olympiads" and a "math major" at Harvard is clearly definitive. > According to the proud you, all of your high school students are > supposed to be able to "demolish" the above Chinese high school > problem "with vector algebra", I didn't say that. I don't even know what a "high school" is :-( > and yet your Royal Chemistry Society > offers 500 quid to anybody in the country who can solve this very > problem in unlimited amount of time, and your "well known and > respected" English universities test the incoming science > undergraduates by asking them to figure our the hypotenuse if the > cathetii are 3 and 4. "catheti". > > Still, at least it's reassuring for those of us who didn't attend > > "the best math school in Russia", never was a winner of a "math" > > Olympiad and never was a "math major at Harvard U", that someone > > who was all these can be a bit of a duffer on occasion :-) > > Well, I guess I asked for it when I volunteered that I am very bad at > solving high school geometric problems using analytic geometry. I > should have known that there is always some bigshot lurking around > waiting to assert his intellectual superiority over those who freely > confess their shortcomings. So attending "the best math school in Russia", winning "math" Olympiads and being a "math major at Harvard U" are shortcomings? Just as I suspected! > Congratulations: you are a better and smarter man than I After listening to your impassioned discourse, I find I haven't the heart to disagree with you there.
From: victor_meldrew_666 on 18 Jan 2010 10:14
On 17 Jan, 12:09, "Ostap S. B. M. Bender Jr." <ostap_bender_1...(a)hotmail.com> wrote: > > I don't. What are "grades 1 through 12"? > > I will let you take more time to figure out what "grades 1 through 12" > here in USA are, I'm afraid I cannot see the utility of cluttering my mind with the minutiae of the educational system of a far-away country of which we know little. > When and if you ever manage to figure out this challenging for you > puzzle, we can continue discussing your intellectual prowess and > superiority over me. I have no interest in doing that. What has been baffling me is your obsession with discussing your moral and intellectual inferiority to me. |