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Suggestions for learning Mathematics?

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Samarda
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20 Oct 2011, 7:51 am

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I feel like all of it boils down to "monkey see, monkey do" and that doesn't interest me at all. I want to learn Maths in all of its elegance, not just as "Here are 15 indefinite integrals. Evaluate them with integrating by substitution where the substitution is either really obvious or given, and even then it wouldn't of been hard". Any suggestions for reading?


It looks like these guys just gave you more exercises.. Uh oh

( Highly Relevant )Read this: A mathematicians Lament - on education

or this: A mathematician's apology for elegance , How mathematicians Think - to see through thier lens and Letters to a young mathematician - light read , it's an update of A mathematician's apology , The Unreasonable Effectiveness of Mathematics in the Natural Sciences - befuddled author.

Hope that helps..



Ancalagon
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20 Oct 2011, 8:57 am

MDM wrote:
can only occur if the number + 1 divided by 4 has a remainder of 0, there is an approximately 25% chance that the number will rise, and a 75% chance that it will lower. Given an infinite amount of possible turns, the 75% will always be triumphant.

I think what is hard about this for the mathematicians is that there could be a cycle, where it goes through several numbers and then returns to its starting point. There are an infinite number of integers out there that could form a cycle, and there isn't a limit on the length of the cycle either, so this is actually a harder problem than it seems. They have run it on a computer for the first hundred million numbers (or something like that) and haven't found anything, but that just shows us a small section of numbers doesn't have a cycle.


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