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#11
11-04-2007, 02:37 PM
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Re: maths problem for DS
there is a simple way of doing this, its called a series. any series of all whole numbers from 1 to n can be represented as (n+1)n/2. simply you add the first and last number of a set of all whole numbers, and multiply by half the total number of integers in the set.
think about it like this, you have 1+2+3+4+5+6+7+8+9+10. you have 5 sets of number, 1+10, 2+9, 3+8, 4+7, 6+5, each equaling 11, or n+1. since there are half as many sets of numbers as there are number, you multiply n+1 by the number of sets, which is n/2. 
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#13
11-04-2007, 03:26 PM
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Re: maths problem for DS
[ QUOTE ]
First off I think you misunderstood my original comment about math and logic. I didn't mean that advanced problems can be easily solved without recourse to advanced math. I meant that they could in theory be solved that way. After all advanced math is just a logical progression from less advanced math. (Which is why it is ridiculous to postulate someone who is extremely adept at everything through calculus could have more trouble with higher math than someone who wasn't.) Meanwhile unless you have some trick up your sleeve your problem is a perfect example of my point. Add them up two at a time from the outside inwards. n/2 pairs of n+1 totals. [/ QUOTE ] David, The thing about math is that it's like a integrated circuit or branching tree, only many times more complex and interlinked:  Each node is an area of mathematics, or a distinct mathematical concept. But the thing is, the human brain can only see this much at a time:  And can only learn a portion of the circuit in their lifetime. When you're trying to find complex interrelationships, or prove the closed nature of link that branches in multiple directions or extends to infinity, or juggle multiple inputs to produce a useful output, it becomes much more than a simple game. There is actual genius and significant creativity required to achieve such things because the topic is so massively complex and abstract that you're operating on a different level of thought. Simple iterative logic doesn't get you anywhere past a certain point.
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#14
11-04-2007, 03:58 PM
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Re: maths problem for DS
[ QUOTE ]
[ QUOTE ] Meanwhile unless you have some trick up your sleeve your problem is a perfect example of my point. Add them up two at a time from the outside inwards. n/2 pairs of n+1 totals. [/ QUOTE ] That requires an idea. Once you've had the idea the rest is simple logic. Many people would never have that idea but can grasp it if its pointed out because integers are simple and its a simple idea. To the point, the idea and understanding are not reducible to simple logic and its the inability to grasp the concepts and ideas that prevents people from doing advanced maths. All of us are limitation in this respect and its why although anyone of moderate intelligence can do maths methods (differential equations etc) most struggle with advanced abstract algebra or number theory - these require very high intelligence to graps the concepts and ideas. chez [/ QUOTE ] As usual we have a communication problem. Because I agree with everything above. Which is why David Steele and myself called madnak's Fred and Ginger impossibilities. Fred wouldn't be able to perfectly answer all elemetary problems unless he had very high intelligence. And if he did he would have little trouble with tougher stuff. (Even though most people like to pooh pooh the SAT and GRE math aptitude tests, I would guess that 80% of those who could get a perfect score on those tests at age 16 could go on to get a Phd in math if a gun was held to their heads while only perhaps 20% of those scoring 700 at age 18 could do that Phd. 700 still being in the top 3% or so. If I'm right it proves that there is an very high correlation between ability at simple math and higher math.)
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#15
11-04-2007, 04:35 PM
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Re: maths problem for DS
[ QUOTE ]
Even though most people like to pooh pooh the SAT and GRE math aptitude tests, I would guess that 80% of those who could get a perfect score on those tests at age 16 could go on to get a Phd in math if a gun was held to their heads [/ QUOTE ] I have perfect scores on the aforementioned tests, a couple of top 200s on the putnam, a 98th percentile score on the GRE math subject test, am a math graduate student, and think that you are very, very wrong with this assertion. I think that most people who could do this could probably get a degree in math from an average school and possibly a masters from a mediocre school, but a Ph.D is too ambitious.
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#16
11-04-2007, 04:55 PM
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Re: maths problem for DS
[ QUOTE ]
[ QUOTE ] Even though most people like to pooh pooh the SAT and GRE math aptitude tests, I would guess that 80% of those who could get a perfect score on those tests at age 16 could go on to get a Phd in math if a gun was held to their heads [/ QUOTE ] I have perfect scores on the aforementioned tests, a couple of top 200s on the putnam, a 98th percentile score on the GRE math subject test, am a math graduate student, and think that you are very, very wrong with this assertion. I think that most people who could do this could probably get a degree in math from an average school and possibly a masters from a mediocre school, but a Ph.D is too ambitious. [/ QUOTE ] Well firstly I said that they could get their perfect score at age 16. And I stipulated a gun to their head. Secondly even if you are right, you have merely raise the bar, rather than disputed my point. Maybe it is 15% vs 1% rather than 80% vs 20%.
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#19
11-04-2007, 08:58 PM
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Re: maths problem for DS
[ QUOTE ]
is it just me or does every thread in this forum get derailed within 20 posts of the OP? [/ QUOTE ] is it just me or is every post you make in math related threads horrible (stellar example: your first post in the thread)
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#20
11-04-2007, 09:02 PM
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Re: maths problem for DS
[ QUOTE ]
Well firstly I said that they could get their perfect score at age 16. And I stipulated a gun to their head. [/ QUOTE ] maybe I am reading your post wrong. If you mean the GRE subject math test, then getting it perfect at 16 is virtually impossible and such a person would probably be able to get a Ph.D easily, even by 20 if you 'held a gun to their head'. conversely the GRE quantitative section is just as easy as the SAT math portion is, and getting it perfect at 16 is not really all that rare. there are tens of thousands of people who could get both perfect at the age of 16 if they wanted to prepare enough, but the vast majority of them are not Ph.D material.
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