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Comments:
<0> what do Riemann sums have to do with computing antiderivatives?
<1> for all the people in those college cl***es
<1> couldn't you learn from a book?
<1> it's possible (albeit slower)
<2> merus: I really don't even like Riemann's original definition. Darboux's definition of the Riemann integral is so much cleaner.
<3> yea.. but you can't get the diploma from the book
<4> Cale: Oh yeah, but I don't want to teach that to highschoolers.
<1> evdub...depends where you go to school...
<1> :)
<2> merus: why?
<1> some places the diploma rips right off the roll..single ply
<3> heh
<4> Cale: Hmmm. Good point.
<2> merus: I think that if we mention real numbers to highschoolers at all, we should tell them the *actual* rules that apply.
<0> at this point I'd lean toward going with the Daniell integral. or maybe the gauge integral. =)
<1> Cale and merus...I think there is some merit to your point
<4> Instead of lying to them? Yes, most certainly.
<2> i.e. the least upper bound principle should be discussed at length.
<2> and its consequences.
<1> schools do a terrible job about describing math...
<1> but there's a reason
<4> genoobie: What, politics?
<1> how do you ***ess someone's knowledge of the upper bound principle
<5> eh
<6> genoobie, hahaha, in my school. in one of the arts washrooms theres graffiti with an arrow to the toilet roll in stall with the caption "diploma dispencer, please take one"
<7> genoobie : Asking them to do proofs related to that.
<2> genoobie: by getting them to prove theorems on tests, like the intermediate value theorem.
<1> so, you're advocating a test of some sort
<5> it's not practical enough for HSs
<5> but that's besides the point
<5> American secondary education is too slow
<5> ditto elementary
<4> practicality is secondary
<7> Well, if you want to ***ess it, sure. If not, no.
<5> to mathematicians, yes
<1> right cyby my point...
<5> but educators always seem to want the "real world" connections
<2> Suppose that f is a continuous function on [0,1] and that f(0) < 0 and f(1) > 0. Show that f(x) = 0 for some x in [0,1].
<5> I don't care about practicality.
<5> but it's what they want
<5> so we had to learn that crap
<1> cyby the kids clamor for the real world connections too
<8> Not alway
<8> always*
<1> true
<8> I personally don't care about applications of math, for example
<2> genoobie: that's only because they don't understand the game
<1> but for instance...you all know what the jordan curve theorem is right
<5> I want math to be useless
<5> but anyway
<9> cyby: the real world connection is the only reason i care about mathematics
<2> They think that mathematics is *supposed* to be practical.
<1> or have a rough approximation
<5> this is getting into a discussion of education
<5> so, I withdraw.
<2> They think the only reason it would ever be interesting is in application.
<5> Manyfold: yeah, and I care about math because I can ignore said applications :P
<5> so, to each its own
<2> But they're wrong, it's just that the schools fail to show them that they are :)
<10> but if it has no use, why teach it to everyone? i think your way will lead to amthematics being optional
<11> cyby :p
<2> Manyfold: but surely you can see why someone would be interested in mathematics for its own sake?
<5> hi Copter.
<1> right with even fewer people taking it than before
<2> _llll_: sure, that would be fine with me
<11> cyby: hello
<5> they can still take "arithmetic"
<1> and then there will truly by a smaller need for math majors and perhaps it will disappear all together
<2> Actually, they could drop the math they're doing altogether, and just study logic, and that would make me a little happier.
<5> I can argue that art appreciation is useless for me, yet NYC still forced it down my throat
<0> Cale, he'd better, unless he knows something about the physical applications of the Riemann hypothesis that eludes me...
<9> Cale: i found the structures arising in physics far more interesting than structures arising through mere abstract reasoning
<5> *shrug* you can still make something mandatory
<1> jeez...is anything really useless...
<10> Cale: in that case no-one will take it, becasue maths is always "hard" (which may well have more to do with the way its taught), and it's easier to get good grades in something else. i dont believe this is going to be a helpful outcome
<1> people broaden your horizons
<1> :)
<8> Cale: Can you recommend a good book on logic? My university only offers a course in the philosophy department.
<1> _lll_ yes my point too
<2> _llll_: well, *some* mathematics should be non-optional
<7> Tell people why math is beautiful; let those who believe you take it up.
<2> Olathe: yes!
<6> math is not useless. i use it every darned day.. and not wussy math. like, fourier transforms and markov random fields etc
<1> well hmm...
<8> Are you a physicist or engineer?
<4> Dacicus: What's wrong with taking logic in the philosophy dept.?
<2> CoffeeBuzz: right, but the applications are not the major motivation for most mathematicians.
<1> let me tell you that my **** smells wonderful....come have a whiff...
<12> Mathematics is awesome :)
<6> Cale, but its the reason mathematics departments exist
<2> CoffeeBuzz: (though they need a few as excuses to get funding sometimes)
<6> Cale, perhaps ;)
<1> what...you don't believe me...just breathe deeper...:)
<2> CoffeeBuzz: Art departments exist
<8> merus: I don't have any more space in my schedule, for one thing.
<2> CoffeeBuzz: In fact, entire colleges devoted to art :)
<1> here's my thought and then I have to split
<4> Dacicus: Darn. Aristotle would be disappointed :(
<1> cram the head with stuff
<5> lol
<1> Dacicus who's aristotle
<10> art departments exist because anyone can do art
<6> Cale, art is useful. I love art. I direct plays and play music in a band. I cant draw a stickman worth crap but some pure art is interesting.
<1> I hated philosophy in school...
<12> a philsopher :)
<2> CoffeeBuzz: right, it's interesting even for its own sake
<1> never took it
<4> genoobie: *sigh*
<2> CoffeeBuzz: you can enjoy playing music
<1> oh wait...they crammed it down my throat...:)
<5> lol
<4> Tragedy.
<8> genoobie: Greek philosopher
<12> maths is awesome
<2> CoffeeBuzz: in the same way you can enjoy proving theorems.
<1> maf is cool
<12> art is can be maths
<12> and maths art
<2> Appleman1234: yes
<5> I sometimes think of mathematics as art
<12> fractals
<2> It's more of an art than a science.
<5> and mathematicians as artists, not scientists.
<12> especially fractals
<6> Cale, I agree, in some sense math is an art. just with some "rules"
<2> even non-fractal areas :)
<5> they don't have to create an image for me that looks pretty
<8> merus: On the other hand, I need to take four more math cl***es to get a math minor, and a mathematical logic cl*** would be interesting.
<5> I just have to find it beautiful
<5> it's my damn interpretation
<1> Appleman1234 sometimes mafs is like...a fragile...
<5> so I'm entitled to it
<12> most subjects are art and science :)
<1> hmm...nevr tewk spling in skool
<2> CoffeeBuzz: the rules are like the canvas or the instruments, they're just there to give you something to work with :)
<1> I'm self edjumugaitit
<12> Cale: so true
<2> and (and this isn't ever mentioned to highschool students), you can pick up different sets of rules just like you can pick up different instruments
<12> true :)
<2> If I want 1 + 1 = 0 to be true, then it can be true.
<0> Dacicus - you may find Peter Suber's online materials useful: http://www.earlham.edu/~peters/courses/log/loghome.htm and http://www.earlham.edu/~peters/courses/logsys/lshome.htm
<1> Cale yes...and boolean is taught in school
<6> its 10
<6> ;)
<8> Catfive: Thanks.
<2> genoobie: not just boolean logic, but other rings
<8> Catfive: Are they a good source if you know little to nothing, though?
<0> Dacicus - yes, start with the first one, and explore his (considerable number of) other pages.
<2> I think one thing which they largely failed to convey when I was there was that there were other perfectly good notions of "number" which weren't just subsets of C.
<1> I know there is more to math than people give credit for
<1> for instance, that m*** increases and time slows done and distance contracts as you approach the speed of light is a phenomenal revelation
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