Math in grade school, hs and college.

Well, I think most people at some point DO need to know more than the elementary school level you suggest. Take for example being able to calculate interest rates (compounding). Even if they don't have to make the calculations themselves, familiarity with certain concepts such as exponents and logarithms will enable them to understand "why" things work the way they do.

Also I think basic statistics could come in handy almost anywhere. With the amount of data we're fed, it's nice to be able to interpret its meaning. All businesses rely on data to evaluate their performance in certain areas.

Take for example running. My former coach collected tons of data from different cross country courses and different runners, and wanted to be able to assign difficulty ratings to courses based on the data. As I'm sure you can imagine, a lot of different factors have to be taken into consideration; it's somewhat similar to an economic regression with all sorts of assumptions violated. At the very least some familiarity with statistics is necessary to even contemplate such a project.

But I agree that a certain "elegance" is left out of classrooms at the introductory levels. My grades in math were very mediocre throughout high school (although I did well on "special" tests, always qualified for AIME, scored decent on the Putnam), mainly because the teachers bored me to death. They didn't emphasize either practicality or elegance. I think teachers at ALL secondary and up levels should demonstrate both in their classes.

I tried to teach geometry kids the basics of proofs this summer, but instead of starting with stupid theorems about triangles I did much more interesting examples. I also showed them "cool" things such as Fibonacci numbers, the golden ratio, expansion of pi...not that they will remember everything or ever use it, but hopefully to open their eyes up to the fact that math can be captivating.

On the flip side, most professors who teach upper-level undergraduate and graduate courses seem to leave out the applications side entirely. I understood Brouwer's fixed point theorem much more clearly from an internet site that used an example of a cup of coffee than I did from my professor's statement of the theorem and proof. And any number theory course without mention of cryptography has a glaring omission. As someone who plans to make a career out of using math not studying it, I kind of need some practical motivation unless it is something I really enjoy anyway (like combinatorics/number theory).

someone posted this a long time ago

"Some people really are just good at math, and others aren't."

i think this is very true, possibly even more true than it is for running... and I think running is a lot (not entirely) either you have the gift or you don't

math, even through the college years came pretty easily to me compared to some of the other math majors (which isn't to say i didn't work hard too)

running... i could run 120mpw forever and I doubt I would ever sniff a sub 15 5k

I agree.

yes, meth is a growing problem at all levels of academia....

What 5K time DID you run? It may not be all that bad compared to the vast unwashed masses.

anEconomist wrote:

someone posted this a long time ago

"Some people really are just good at math, and others aren't."

i think this is very true, possibly even more true than it is for running... and I think running is a lot (not entirely) either you have the gift or you don't

math, even through the college years came pretty easily to me compared to some of the other math majors (which isn't to say i didn't work hard too)

running... i could run 120mpw forever and I doubt I would ever sniff a sub 15 5k

So? Most people will never run a mile, hell, a quarter-mile, at that pace. And lots of people run lots of miles and don't run sub-15 either.

In both math and running, hard work will almost always beat all but the best talent that doesn't work hard. It's just that as runners on college teams, you LetsRunners see the best talent a lot. If you were, say, going for a Ph. D in math, you might see comparable talent to that.

math isn't difficult you just need practice, well I don't do 100mpweek but I have 14'40 at 5k. math is just like running it depends on quality of your training....

keep it going

i'm not trying to be a jerk, and maybe i am a jerk for thinking thisbut first, what i meant when i say i will never sniff sub 15k with 120mpw... i think that is true, i train at about 75mpw consistently (many years now) and I read voraciously about running trying to train as best as possible for the time i have...my 5k pr - 17:47... BUT I love it and I will keep at it (maybe that is why I love it) but my gut feeling is that even if I trained under the best and worked harder than anybody my guess is sub 15 wouldn't be in the cardssecond - you are right, i did do a phd program in math (however, after awhile I traded up for a phd program in economics - finance to be exact... looking back it was somewhere deep inside probably about the $$$$, oh well)and yes, same thing happens, in that phd program (it was a good one)... a person's view about constitutes a 'good' mathematician becomes very, very skewedwhen i ta'ed for undergrad calc classes i had kids who were smart no doubt, but who could bust their ass all day everyday and never have made it as a mathematician... they really struggled... much like I do with runningi would love to be an idealist and say hard work is everything but i really believe if we are talking in relative terms... to be one of the best at something it takes a unique combination of hard work AND talent

Dan Onymous wrote:

So? Most people will never run a mile, hell, a quarter-mile, at that pace. And lots of people run lots of miles and don't run sub-15 either.

In both math and running, hard work will almost always beat all but the best talent that doesn't work hard. It's just that as runners on college teams, you LetsRunners see the best talent a lot. If you were, say, going for a Ph. D in math, you might see comparable talent to that.

I completely understand/agree with your point... I am someone who is not gifted with a lot of running talent. I love it and do everything I can, but realistically, I know I will probably never run a sub-20 5k (i'm female). I am, however, pretty good at math; I'm not a math major (computer science) but math has always come easy to me. Last semester I tutored a teammate for a pretty basic-level precalc class and it kind of put things in perspective... she could go out and reel off 6:15 miles in a 5k no problem while I struggled running 7:10's, then in the classroom I could solve equations and figure out derivatives and such no problem, but she barely understood how to and really had a hard time with it.

To be good at either, you need to work hard. And I know I am a better runner than more talented people who dont work, and my teammate got a better grade in her math class than the people who were good at math but didnt do their homework. But hard work is not everything, as much as that sucks.

And what's frustrating is being good at math but loving running.

Mathematicans are able to conceptualize in a very abstract realm with a rapidity that most people will never attain. Real Analysis is an abstract study of real numbers and their properties, and Topology is a further abstraction of real numbers. Some prople feel more at home with this high degree of abstraction, and others are hopelessly buried and could never approach this ideal. It is a fact of life, and no one has discovered, or will discover a way to "make" a mathematician out of anyone that has not been born with this ability -- anymore than we could "make" a pro football player out of Gerry Lindgren.

I don't think Skuj would agree with you.

...but that doesn't mean that we shouldn't teach some theoretical math to the masses. Just that there are definitely limits as to how far this can go.

...

One thing that always grinds my gears is when people say "When are you ever going to need that?".

I don't mind when it's an earnest question, but when asked facetiously, implying that math is oftentimes useless, well that pisses me off.

Math has proven itself useful in all facets of life. Sure, someone in a non-math field who has little to do with it may only ever have to deal with performing Descartes' basic algebraic operations (+, -, x, /, and sqrt) on positive real numbers at the grocery store, but that is only one case and definitley doesn't describe everyone's situation. An someone in computer science or eletrical engineering, on the other hand, will make extensive use of the discoveries of Leonard Euler about the constants e, i, pi, and their relations. This is something that, for hundreds of years before the invention of computers, would have been considered completely useless in a practical sense by the layperson. Yet, entire fields, vocations, and ways of life now depend on those same discoveries.

Of course this is just one example, but it does illustrate that discoveries in mathematics may sit idle for many years before an application is found. This is understandable, since, after all, computer science must have been almost cetainly well beyond imagination for those in Euler's time.

I said above that math has proven itself useful in all facets of life... this doesn't mean that ALL* of math has proven itelf useful... but if you can name any particular branch of math, I'll bet you that it will someday have at least one, if not many, applications (if it doesn't already, that is).

*not to imply that the field of math has a fintite limit, since new discoveries and conjectures are made continually, and the field continues to expand and progress to ever higher and exciting hights.

And when I wrote "An someone", I really meant "Someone".

Don't know how that happened.

fadfsfdfd wrote:

Logs were hard to explain. Basically, the way i thought of them when i was little was that the log (10) of a nubmer is the number of zeros it has. So really really big numbers have kind of big logs.

I think a good way to do it is to talk about counting multiples of a number. A log base a, applied to a number, counts how many multiples of a number are contained in that number.

You can then extend the concept of a^x from positive integers x (a, a*a, a*a*a, ....) to all reals by calling it 'repeated multiplication.' Then that gives a good intuition for why, for example, log_a(sqrt(a)) = 1/2 : it's because you've multiplied a 1/2 of the times necessary to get a single a, so if you double the exponent you get a back.

It's less rigorous than the integral from 1 to x of 1/t dt, but I think it's very intuitive.

i think math is a total waste of time. i hear people talking about engineering and education that has made our lives better. really has it made peoples lives better are we happier now than before? yeah you get a computer and we spend too much time tracking useless information that doesn't improve our quality of life. instead of spending time with those that really matter. while at the same time claiming the reason we do what we do is for them. come on THINK about it. you can apply this logic to the other crap we've invented/created.

we study history so that we don't repeat the mistakes of the past. yet it seems we really don't learn anything because we keep repeating the mistakes of the past. so what good is history? i could go on applying it to every single subject.

so people don't get all upset, i'm not picking on any one group. i think that most education is a waste of time. i often think about stuff that most people would think is weird.

let say that before ours there was another civilization that learned everything that could possibly be learned. after finally achieving what they had always strived for, they realized that they were sad or dissapointed. it was then that they discovered the true meaning of life. so they got rid of all their technology and brought their children up to live simpler lives. to be one with nature and enjoy all the true gifts life has to offer.

so what if we lived shorter lives. shorter isn't a bad thing if the quality is 100's of times better. kind of the quality versus quantity in running. you can run thousand of miles a month but if they are all at 15 min pace you're gonna suck at the mile.

we as humans think we are superior and we think we own the planet we wonder why dolphins can't speak and they look at us and feel sorry for us because they know we have a long way to go before we can achieve the same level of understanding that they have. in the mean time they are truly worried that we may destroy the planet before we reach this level hence their delima.

sounds crazy but hey they have brains bigger than ours.

why not!

it could just as easily some extinct civilization. it could be something really different i just don't want to have to write a book on it, on lr.

If you assume that happiness is the ultimate goal then being stupid might be the best way to attain it. Intelligence and knowledge do bring certain amounts of discontent. But I'd rather be alive now than in, say 1308 or in 13,008 B.C. watching a lunar eclipse in terror because I thought some monster was eating the moon.

rock on, dude...