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Everything posted by epi

  1. It is unfortunate the score distribution is so compressed. He surely has a good chance next year.
  2. (1) No need to worry about what "level" one is at. You're really "competing" against the questions (i.e. trying to solve them). If you're >4 SD above average, and some others are >5 SD above average, just do your best, and not worry too much about what others can do. Getting a medal can help affirm feelings of belonging there (but don't say that, to avoid pressure). Also, he is still somewhat younger than many, and has another year, right? (2) This is interesting - I wonder what kind of university this is (you needn't say the exact one). I thought the "elite" U.S. ones had a strict purely needs-based financial aid policy (while admission is highly merit-based). Is there any exception to the needs-based financial aid policy, or is this a university that doesn't strictly have such a policy.
  3. I just looked at the ANU prices - Yikes! - I had no idea. I played with a few US college Net Price Calculators a while ago, and I found that if you have modest income, then the Ivies, MIT etc were a small fraction of sticker price, and actually cheaper than most other options. The calculators are simplified and may not handle non-standard situations well.
  4. lewelma, I'm curious what you found about the net cost of good Australian and British universities compared to NZ and USA. My regrets about going to the local "average" university, instead of a much better one in a distant place, was not the social aspect, but the academics. You'll be much more academically challenged and learn a lot more at an elite university. The local one may give a "solid" education but it really is less, and you can end up isolated and complacent. I now believe one should go to the best place possible. But costs really do matter.
  5. I agree it's a good idea to go to the academically best universities possible, rather than something local, for undergraduate. (I didn't do this and it was a mistake.) I'm curious about the issue of costs. Some of the elite American universities have very good financial age aid packages, if applicable, (though that could still leave a residual cost that is still "big bucks"). (Edit: typo.)
  6. Now results are (publicly) up on the website. http://www.mathkangaroo.org/mk/results.html https://www.mathkangaroo.org/MKR/faces/Results.xhtml
  7. Now results are (publicly) up on the website. http://www.mathkangaroo.org/mk/results.html https://www.mathkangaroo.org/MKR/faces/Results.xhtml
  8. Any suggestions for this, in particular, for a kid who's finishing up the AoPS Intro level, and good at math, but not necessarily ready for higher level abstraction. (We've got several Graduate Text in Math books on our shelf. -- They're definitely not suitable.)
  9. Results are now up on the website (if you log in).
  10. From AMC stats, about 1000 kids "grade 4 or lower" take AMC 8. (The stats don't separate the lower grades.) You can take AMC 8 any number of times (until grade 8). Since pre-algebra is typically taken in grade 8 or 7, that is surely "enough" to take AMC 8, in the sense that the topics are covered (but of course the questions are trickier than typical school course questions).
  11. What is "college algebra" (in this context)?
  12. It looks like the same links are good for 2017 (Monday, May 15 at 10:00 am ET).
  13. Good question! I like to here about this too (and the corresponding question about any overlap in courses, as well as the books). Even for very advanced students, some review doesn't hurt, especially if it then goes to a higher level. But I don't know if there's any actual redundancy, and I'd like to hear. Here's some links for anyone wanting a quick look. Introduction to Algebra book https://artofproblemsolving.com/store/item/intro-algebra Table of Contents (pdf) https://s3.amazonaws.com/aops-cdn.artofproblemsolving.com/products/intro-algebra/toc.pdf Intermediate Algebra book https://artofproblemsolving.com/store/item/intermediate-algebra Table of Contents (pdf) https://s3.amazonaws.com/aops-cdn.artofproblemsolving.com/products/intermediate-algebra/toc.pdf Courses Introduction to Algebra A https://artofproblemsolving.com/school/course/catalog/algebra-a Introduction to Algebra B https://artofproblemsolving.com/school/course/catalog/algebra-b Intermediate Algebra https://artofproblemsolving.com/school/course/catalog/intermediate-algebra
  14. Sorry, I wasn't doing it on purpose. :rolleyes: Nah, just kidding. I really was doing it on purpose. :)
  15. Actually, since Gödel in the 1930s, mathematicians have come to terms with the fact that you can have different versions of mathematics based on different axioms. For example you could include the the Axiom of Choice https://en.wikipedia.org/wiki/Axiom_of_choice or you could include its negation. Earlier I mentioned Inverse function https://en.wikipedia.org/wiki/Inverse_function Example: squaring and square root functions https://en.wikipedia.org/wiki/Inverse_function#Example:_squaring_and_square_root_functions Indeed a square root function is a right inverse or section https://en.wikipedia.org/wiki/Section_(category_theory) of a squaring function. In general, the existence of a right inverses or sections is equivalent to the axiom of choice (which, recall, is an optional axiom). For real numbers, it's easy to define a square root function (just choose the positive square root). But what about in general. In general, for the squaring function in a field or ring or group or semigroup, can we be sure that a square root function (i.e. a right inverse or section of the squaring function) even exists. Or does it depend on which version of based on which axioms. Is the statement that "a square root function (i.e. a right inverse or section of the squaring function) always exists", equivalent to the axiom of choice? Something to think about.
  16. It does matter. You should try and sort it out now.
  17. Also look at this Inverse function https://en.wikipedia.org/wiki/Inverse_function Example: squaring and square root functions https://en.wikipedia.org/wiki/Inverse_function#Example:_squaring_and_square_root_functions
  18. Also see https://en.wikipedia.org/wiki/Square_root and generally search for "square root" on the internet. But I think I explained the distinction between a square root and the square root.
  19. Given a number a, in a lot of cases there are 2 solutions for x in the equation x^2=a So sometimes you would like to say that all the solutions are square roots of a. But sometimes you want to canonically* choose one particular solution from among the others, e.g. within real numbers x^2=4 has two solutions +2 and -2, but in this case it is easy to choose a convention that we'll choose the solution +2 to be the square root of 4. In this case there's an easy rule for choosing. If a is a positive real number, then there are exactly two solutions to x^2=a with exactly one positive and one negative, so we set up a convention where the positive solution is the one that is chosen to be called the square root of a. For other types of numbers, it's not so easy. For example with complex numbers, the equation x^2=-1 has exactly two solutions +i and -i. This time, there's no clear way to choose one of them to be designated to be called the square root of -1. One option is to just let them both be called square roots. Another is to make a choice of which one, but to also make such a choice for picking one of the two solutions for all equations x^2=a for complex a (except there's just one solution when a=0). There is unavoidably some arbitrariness in the choice, and no matter how you do it, you can't get the square root function to be continuous, which you may have wanted (or you can have a continuous multi-function if you keep both solutions). Note that sometimes there can be lots of solutions to x^2=a For example within the quaternions, every negative real number has infinitely many square roots. * https://en.wikipedia.org/wiki/Canonical_form http://mathworld.wolfram.com/Canonical.html
  20. I don't think the percentage used is really an issue. You can just say students in the top X% are in the top X%. It's a bit like the other thread about how terms like "<prefix>-gifted" have no standard meaning. The real point is that there is a continuum of intellectual abilities, and education systems would be vastly improved if they catered to ALL levels. This is the way it should be done. Group students by ability and have separate classrooms moving at different paces as appropriate.
  21. When I first saw that chart, I came to the conclusion that these adjectives simply don't have a standard meaning, and probably never will. One can legitimately make statements about scores and results obtained and about abilities and achievements, but it's better to do so without using terms that have such inconsistent usage.
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