My math term paper is due soon and i originally picked mathematical inductions as my topic and its too late to change it now...but i am freaking out b/c i don't know what to do in relation to math inductions!!
If anyone has any specific topic ideas, how i could get started (it has to be original)
Thank you I'd appreciate it
Inductions!!!
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Re: Inductions!!!
You could do something like other applications of induction outside of purely abstract math proofs. Nothing so obscene as "Induction in Everyday Life" but more along the lines of how it has been used in other disciplines...
Re: Inductions!!!
Some topic ideas:
 "Regular" induction versus strong induction.
 Proving something by induction and by a "traditional" proof; one example in which each is easier than the other.
 A few inductive "proofs" that are subtly false; and the reason they're false. (There are some nonmathematical "proofs" like this).
 The history of induction.
 Induction on more than one parameter, and for the reals instead of the naturals.
 Rigorous, logical basis of induction (wellordering principle, etc.)
 Modern significant research that uses induction.
 Induction as used in logic and computer science (structural induction). Compare and contrast to numerical induction.
This is presumably in addition to an intro on the basics of what induction is.
I don't know the specifics of your paper, so maybe one or some or none of these is good. Anyway, good luck!
 "Regular" induction versus strong induction.
 Proving something by induction and by a "traditional" proof; one example in which each is easier than the other.
 A few inductive "proofs" that are subtly false; and the reason they're false. (There are some nonmathematical "proofs" like this).
 The history of induction.
 Induction on more than one parameter, and for the reals instead of the naturals.
 Rigorous, logical basis of induction (wellordering principle, etc.)
 Modern significant research that uses induction.
 Induction as used in logic and computer science (structural induction). Compare and contrast to numerical induction.
This is presumably in addition to an intro on the basics of what induction is.
I don't know the specifics of your paper, so maybe one or some or none of these is good. Anyway, good luck!

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Re: Inductions!!!
what original work could i do in relation to "weak" and "strong" induction?? it's due this week so i'm desperate
Re: Inductions!!!
You could also compare strong induction to transfinite induction, but I'm not sure what you mean by "original work".
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Re: Inductions!!!
Another topic is relating induction to recursion. Also you could spend some time discussing the Peano axioms.
Some of us exist to find out what can and can't be done.
Others exist to hold the beer.
Re: Inductions!!!
reverse induction
flawed induction argument
flawed induction argument
while moronic idle do something (stupid).
Re: Inductions!!!
god, i hate induction. i just dont get it  and i know i need to cause it seems to be important in my study (computers). it seems simple when i get it explained but if i try to do it myself i fail every time..hehe. oh well, good luck on your paper:)
Re: Inductions!!!
I wish I could remember the problem, but my favorite induction ever involved first showing the statement for n = 2^{m} by induction, and then showing that the nth case implied the n1th case. Anyone know of a problem that needs to be proved as such?
It has occurred to me in the occasionally that we should teach Well Ordering instead of Induction, since Well Ordering is more 'obvious', and induction proofs easily become well ordering proofs. Plus we get to use contradiction.
Cheers,
Mike
It has occurred to me in the occasionally that we should teach Well Ordering instead of Induction, since Well Ordering is more 'obvious', and induction proofs easily become well ordering proofs. Plus we get to use contradiction.
Cheers,
Mike
addams wrote:This forum has some very well educated people typing away in loops with Sourmilk. He is a lucky Sourmilk.
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Re: Inductions!!!
mikel wrote:I wish I could remember the problem, but my favorite induction ever involved first showing the statement for n = 2^{m} by induction, and then showing that the nth case implied the n1th case. Anyone know of a problem that needs to be proved as such?
That's how my book proved the AMGM inequality.
Re: Inductions!!!
Torn Apart By Dingos wrote:mikel wrote:I wish I could remember the problem, but my favorite induction ever involved first showing the statement for n = 2^{m} by induction, and then showing that the nth case implied the n1th case. Anyone know of a problem that needs to be proved as such?
That's how my book proved the AMGM inequality.
Sweet, thanks!
Mike
addams wrote:This forum has some very well educated people typing away in loops with Sourmilk. He is a lucky Sourmilk.
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