20150927, 16:01  #12  
Bamboozled!
"ð’‰ºð’ŒŒð’‡·ð’†·ð’€"
May 2003
Down not across
2^{5}×3×113 Posts 
Quote:
"Not haven taken calculus" might be interpreted as a statement which suggests the general level of mathematical education which may be assumed for further discussion. 

20150927, 20:47  #13  
Nov 2003
16444_{8} Posts 
Quote:
tends to indicate something else. 

20151003, 05:41  #14  
Sep 2015
3 Posts 
Quote:
Now I'm curious if you're one of those people who have a hard time putting yourself in another persons shoes. Quote:
By the way, you are telling me calculus can be complex, and then also telling me elementary problems in math can be complex. See the issue there? Quote:
Cool thanks. 

20151003, 22:02  #15  
∂^{2}ω=0
Sep 2002
RepÃºblica de California
11,657 Posts 
Quote:
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(F29 has a known small factor; I intend to use the Pe'pin residue for future fast cofactorPRP tests.) To the OP: You still haven't commented on whether your number has any kind of special algebraic form. If so, what is it? If not, in what context does the number arise? Last fiddled with by ewmayer on 20151003 at 22:04 

20151004, 08:08  #17  
Jun 2003
1010000000001_{2} Posts 
Quote:
For 33,219,000, it gives. 37.7. For 332,190,000, it gives 4,941. About 131x. Sounds rightish. For 3,321,900,000, it gives 91,629. At the very least it should be 100x the previous, so about 500,000. In practice, it might be 150200x? 

20151004, 13:06  #18 
Romulan Interpreter
Jun 2011
Thailand
2×3×5^{3}×13 Posts 
Indeed it is an order of magnitude off there. It should be ~900k, not ~90k. If you double the exponent, your time more than quadruples, because you will have a (roughly, more than) double time for each iteration and a double number of iterations to do. In practice, it is more that that, and the FFT won't scale linearly for so big range. Tripling the exponent you have about 1012 times longer the time (and not 9 times, as for squaring) and it sounds reasonable that if the exponent grows 10 times you may have 100x for small expos, but you will have 150x for average expos, and 200x for big expos. I think ~4.5k*~200x is the right number here, giving about 900k. And that assuming we have already the soft and hardware able to do it.

20151004, 20:37  #19 
∂^{2}ω=0
Sep 2002
RepÃºblica de California
26611_{8} Posts 
That was the reason for my doubletake: While my code is still slower than George's, it's not *that* much slower, and O(n^2 * lg(n) * lg lg(n))  extrapolating my current F29 timings to Gdigit (I was away from home, thus not able to simply do a timing run at the needed length) gave a runtime estimate much higher than the one Uncwilly posted.

20151005, 00:07  #20  
Nov 2003
2^{2}×5×373 Posts 
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BTW, in my experience classes "below" calculus are NOT properly college level subjects, except perhaps at local community colleges (which are usually just overblown high schools for people who struggled in high school] Most colleges start with calculus, and precalculus level math is assumed as an admisison criteria. It is true that remedial classes can be and are offered, but they are not usually taken for credit. Quote:
know enough to whether it will or won't be advanced. It is merely something that YOU HAVE NOT STUDIED. We are discussing the philosophy of mathematical study here. 'Advanced' is not well defined. Singlevariable calculus is not generally considered an advanced subject. You personally may consider it advanced, but it really isn't. One does need to approach its study with a POSITIVE ATTITUDE rather than "it's going to be too complicated for me". I have seen too many people fail at mathematical study because they view it with fear and apprehension. Math is not unique in this regard; the same is true in any technical subject. Basic Number theory, as a subject certainly can be studied before taking calculus. It can even be taken prior to studying modern algebra, although number theory and algebra are very much intertwined. Quote:
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mathematics. Quote:
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'complicated' by the general technical community. 

20151005, 02:36  #21  
"Curtis"
Feb 2005
Riverside, CA
2·2,473 Posts 
Quote:
At colleges that admit students below the top 15% of their HS graduating class, precalc is not even an admission requirement. It amazes and disappoints me how many high school counselors advise mediocre students to take statistics instead of precalc to "help their GPA". Regional level private colleges and stateschools have little choice but to work around this lack of preparation. 

20151005, 03:11  #22 
Romulan Interpreter
Jun 2011
Thailand
2·3·5^{3}·13 Posts 
At my time, we did precalculus (mainly differentials, limits, series) in grade 11, and calculus (Riemann integrals, etc, what is called "ap calc" over the big pond) in grade 12. At the university we repeated that all in the first year, at higher level (included Lebesgue integrals, etc), and moved to partial derivatives and more complicated stuff in the second year (which subject I failed two times, and passed the third time with mark 7 (of 10), haha). We also did elementary probabilities theory in grade 12, and much high level statistics during the 2nd and 3rd (of 5) college years.
Related to your last paragraph, my girl (who goes to an international school here) did precalculus in grade 11, but to a much lower level that I used to, and she didn't like it (in spite of getting the highest mark, for which the reason was mainly endless crying evenings when we did the homework together) so she took statistics this year (grade 12) exactly as you said, to avoid calculus. Up to now, they are doing very elementary stuff, like graphing data and interpreting graphs. I don't think this can "survive" a "test" for a possible admission, at any university. But my wife tells me I am too exaggerate, and I am thinking "well, maybe there are different times now..." My girl took SAT by the way, the day before yesterday. We are waiting for the results... Last fiddled with by LaurV on 20151005 at 03:15 
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