We, the Mathies of North America, find that the use of math in the world is at a disgustingly low level. We call for a robust cleaning and higher standards of mathematics per the Church of Mathematics
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They will squeal in delight at finite fields of prime power order.
As opposed to what other kind of finite field?
Never shall a student say "When will I use this?"
Heh, working in applied maths has finally given me a million answer to that annoying question, "what is all of this good for?"
functions exist in higher degrees than 2
By degree, you mean its degree when expressed as a (Taylor) polynomial, whenever possible?
Vive La Revolucion!
Heh, pick a spelling already! "Vive la Revolution!" in French and "¡Viva la Revolución!" in Spanish! Sorry, pet peeve, because I speak both of those languages, and despite similarities, they're not the same!
The rest, is just to exhibit mathematical points. I love saying finite fields of prime power order. It just rolls off the tongue.
And as a pure mathematician, I couldn't stand not having my abstractions. And I know what it's all good for, I just would prefer to develop those things that make it applicable.
And degrees, was in a very linearly, high school mentality, where all you deal with is trig functions, and power functions. So I guess you're partially right.
Since I was being picky with the French, I might as well correct my own typo (oops): "Vive la Révolution!" Forgot the acute accent.
And oh, don't rally against CASes (but if you were rallying against that one in particular for being non-libre, then I'm with you). They're not the ones at fault, and they're an essential tool of modern mathematicians.
Rally against the kids who think that a CAS can solve their maths assignments for them, because it can't. You need to learn how to use a CAS, how to feed it information, how to extract output from it, and to know its limitations, and most importantly, its possible bugs. Mathematicians are the Pythia of the CAS Oracles, and the Oracle used to get high on fumes and spew out nonsense anwyays. :-)
Trust me, I love my CAS. I don't rely on them, because they're just that: computer programs. But it's a very helpful tool, and saves you from having to do everything by a ridiculously large amount of work. Who wants to solve some ugly DE's by hand that will take them 20 minutes, when it will take less than a minute with a CAS.
But I completely agree with the last part. A CAS doesn't teach you anything. If you can't remember how to do it from the CAS, then how are you going to demonstrate you know how to do it on a test.
I'm a very firm believer that everyone has strong abilities in math, just at an early age they're pushed aside. A book I read at work the other day (I'm a bookslave, mind you), was Myth of Ability: Nurturing Mathematical Talent in Every Child ISBN: 0802777074. Great discussion about the fact we all are able to do math to some serious capabilities. Also, look at Jump Tutoring (His website)
Making a point. I just think we're extremely undereducated in the realms of math. How many students going into university understand the diverse and reaching places of mathematics? Let e > 0.
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Other than that, I'm with you--110%, as it were. ;)
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Or should that be: Jinx, buy me a Coke. (Bleah, Coke.)
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As opposed to what other kind of finite field?
Never shall a student say "When will I use this?"
Heh, working in applied maths has finally given me a million answer to that annoying question, "what is all of this good for?"
functions exist in higher degrees than 2
By degree, you mean its degree when expressed as a (Taylor) polynomial, whenever possible?
Vive La Revolucion!
Heh, pick a spelling already! "Vive la Revolution!" in French and "¡Viva la Revolución!" in Spanish! Sorry, pet peeve, because I speak both of those languages, and despite similarities, they're not the same!
Reply
The rest, is just to exhibit mathematical points. I love saying finite fields of prime power order. It just rolls off the tongue.
And as a pure mathematician, I couldn't stand not having my abstractions. And I know what it's all good for, I just would prefer to develop those things that make it applicable.
And degrees, was in a very linearly, high school mentality, where all you deal with is trig functions, and power functions. So I guess you're partially right.
Reply
And oh, don't rally against CASes (but if you were rallying against that one in particular for being non-libre, then I'm with you). They're not the ones at fault, and they're an essential tool of modern mathematicians.
Rally against the kids who think that a CAS can solve their maths assignments for them, because it can't. You need to learn how to use a CAS, how to feed it information, how to extract output from it, and to know its limitations, and most importantly, its possible bugs. Mathematicians are the Pythia of the CAS Oracles, and the Oracle used to get high on fumes and spew out nonsense anwyays. :-)
Reply
But I completely agree with the last part. A CAS doesn't teach you anything. If you can't remember how to do it from the CAS, then how are you going to demonstrate you know how to do it on a test.
I'm a very firm believer that everyone has strong abilities in math, just at an early age they're pushed aside. A book I read at work the other day (I'm a bookslave, mind you), was Myth of Ability: Nurturing Mathematical Talent in Every Child ISBN: 0802777074. Great discussion about the fact we all are able to do math to some serious capabilities. Also, look at Jump Tutoring (His website)
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