Jump to content

Menu
Giving You and Your Child a Road Map to the Best Possible Education
The Well-Trained Mind Community

epi

Members
 View Profile  See their activity

  • Posts

    126

  • Joined

  • Last visited

 Content Type 

Posts posted by epi

    The big day has come - Rio!

    in Accelerated Learner Board

    Posted

    (1) DS is very aware that he is small fries and will be competing with "the smartest kids in the world" as he puts it.  I think this year it is feeling more intimidating than last year, because last year at age 15 he was not actually competing with those kids (his level was too low), but this year he will be. ...

     

    (2)I also did not remind him that one of the universities he is interested in will give him a full ride if he medals. Didn't think he needed that extra pressure.

     

    (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.

     

    • Like 1

    Accelerated Learner forums question

    in Accelerated Learner Board

    Posted

    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.
     

    Accelerated Learner forums question

    in Accelerated Learner Board

    Posted

    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.
     

    • Like 1

    Accelerated Learner forums question

    in Accelerated Learner Board

    Posted · Edited by epi

    I am so grateful that my older ds has one true peer. They are currently at the library studying math together for 6 hours.  :thumbup1:  Unfortunately, his friend goes to Cambridge in August, so ds's last year of high school will be solitary again. We are willing to spend the big bucks to find peers for him at university.  It is just that important.

     

    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.)

     

    AMC registration is open

    in Accelerated Learner Board

    Posted

    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).

     

    • Like 1

    National MATHCOUNTS Webcast

    in Accelerated Learner Board

    Posted

    For anyone interested, there is a webcast of the National MATHCOUNTS Countdown Round tomorrow (Mon 9 May 2016) at 10am ET which can be found here

    https://www.mathcounts.org/national-competition

    https://www.mathcounts.org/national-competition-webcast

    If you miss it, it will probably be archived here

    https://www.mathcounts.org/programs/competition-series/competition-videos

     

    It's pretty interesting to watch, though I wish they displayed the questions to the viewers better, to see what the contestants are seeing. The contestants see the whole written question appear on a screen, and an announcer starts reading it out, but sometimes they only get to read a few words before someone buzzes in with an answer.

     

    It looks like the same links are good for 2017 (Monday, May 15 at 10:00 am ET).

    • Like 3

    AOPS algebra book overlaps

    in Accelerated Learner Board

    Posted

    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

     

    • Like 1

    Maths whizzes, please help :)

    in Accelerated Learner Board

    Posted

    I can't remember the context, but I remember my professor in a course on Aristotle telling us that the only necessary rule of any system of mathematics is that it be internally consistent. I don't know why, but it's the only thing I recall from the whole class LOL. Many mathematicians would probably revolt at such a relativistic view of "the purest science". :-)

     

    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.

     

     

     

    • Like 1

    Maths whizzes, please help :)

    in Accelerated Learner Board

    Posted · Edited by epi

    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

     

    • Like 1

    News (Australia) Are we leaving our brightest children behind?

    in Accelerated Learner Board

    Posted

    "Approximately 10 per cent, or close to 400,000, Australian students are intellectually gifted. ....â€

     

    Why is it that the percentage of gifted kids in Australia is five times as high as everywhere else?

    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.

    I remember receiving differentiated instruction way back in the 70's.

    This is the way it should be done. Group students by ability and have separate classrooms moving at different paces as appropriate.

×
×
  • Create New...