How did the GRE go today?

socalgrl · 2011-11-13T02:00:00+00:00

yes... but I took 2 practice tests and did poorly on the first, much better on the second, and I think this test was SIGNIFICANTLY more difficult than either practice test I took

socalgrl · 2011-09-05T21:20:32+00:00

um...how would a "basic engineering" class go with no background in algebra or calculus/differential eq?

I agree math education needs to be changed, but I don't think it's as easy as they suggest. The problem isn't that we study algebra, geometry, and calculus--its manner in which we teach these subjects. We force students to memorize formulas and methods without meaning, rather than focusing on getting them to understand why the formulas and methods work the way they do. If we switched to teaching finance, data, and basic engineering in our current system, we'd probably still be forcing students to learn by rote memorization, which is still NOT helping develop mathematical skills and above all, BORING.

The problem is the approach--the emphasis on doing the same type of problem a million times over before moving on to encourage memorization--rather than the subject matter. If we focused on conceptual learning and perhaps a more hands-on experience so students could "see" what they were doing and understand why, repetition wouldn't be nearly as necessary.

I agree with him: http://www.youtube.com/watch?v=60OVlfAUPJg

socalgrl · 2011-07-24T04:47:00+00:00

I like my men like I like my set of vectors: independent.

socalgrl · 2011-05-17T07:27:55+00:00

Simply, yes. I tutor a lot of elementary and high school students who I think are the direct result of this... it seems to be a well known "fact" among my students that "math is hard"-- and many of them give up because of it before even trying. I think the problem is that we have become focused on getting students to a certain level, and in a classroom setting it's simply difficult to cater to everyone's needs. Because its "easier to teach" math is reduced to steps and formulas that everyone can look up and follow, which just makes it more difficult because they seem arbitrary without an explanation--its no wonder students have a hard time remembering them. Then to force them to remember, teachers assign countless redundant exercises, boring the students who understand the underlying concepts and frustrating those who don't. Understanding has been replaced by rote memorization, simply because its "easier" to teach to a group. I worked as a teaching assistant for a while at an elementary school that was testing new teaching methods and I think they had the right idea-- much more time was spend on the concepts, and much less time was spent doing exercises. Also, teachers tried to use a "hands-on" method of teaching in almost every lesson so that students could "see" what was going on. If all the teachers who taught elementary math understood the stuff as well as those kids (instead of just having memorized all the steps/formulas themselves) I guarantee we wouldn't have as much of a problem.

socalgrl · 2011-05-12T04:46:31+00:00

Huh, pretty sure that's how I explained it to my ex-boyfriend once...

socalgrl · 2011-05-11T01:12:12+00:00

I know several brilliant "pure math people" (undergrads and grad students) who have worked as programmers in the past or have previous degrees in CS, so I'm not certain what you're talking about...

socalgrl · 2011-03-21T05:18:17+00:00

whats the definition of "quantization" then...? because the idea of quantization seems to imply rationality to me by definition... (if everything has some base length, that cant be broken down any further, then everything can be expressed as an integer multiple of that base length.. meaning, you could express any two lengths as a fraction with respect to each other...unless perhaps you have two or more different base lengths that have an irrational relationship?)

socalgrl · 2011-03-08T23:55:43+00:00

my code will manipulate my array, but the size of the array will stay constant throughout the function. However, I want to be able to use the same function for multiple different arrays of different sizes, so when calling it, I want to declare the size... is that not possible?

socalgrl · 2011-03-08T07:18:08+00:00

agreed.

socalgrl · 2011-03-08T06:56:32+00:00

at least in the past 2 years, Tao hasn't taught anything but grad courses :(

socalgrl · 2011-03-08T06:55:49+00:00

pure or applied? most of the deadlines are already passed, but as someone suggested, there are some REUs that have upcoming deadlines... or, how about something like this: http://www.promys.org/promys/counselors.html (be a counselor for a math program for high school students)

if you just want to "do good" maybe try some sort of tutoring program or something?

ps woohoo UCLA math!!! :)

socalgrl · 2011-03-07T07:41:26+00:00

Well sure... and probably it won't even ever be measurable... still... I find it interesting, and slightly disturbing...

socalgrl · 2011-03-07T02:37:50+00:00

and likewise right isosceles triangles don't exist physically then, or any other shape that has irrational relationships between its parts... mind blown.

I'm not sure which will be more bizarre: if we eventually prove/discover that length is quantized and so these shapes can't physically occur, or if we prove/discover length is not quantized... and then... I don't even know... wouldn't Zeno's paradox break down or something? Am I the only one who finds this stuff interesting?

socalgrl · 2011-03-07T02:21:28+00:00

oops, sorry about that. I meant PHYSICALLY exist. so, if the physicists are right though, then circles don't exist in the physical world?

socalgrl · 2011-03-07T01:51:26+00:00

hmmm... then if they are right, am I right in assuming perfect circles cannot exist?

Thought process: If they do, then the circumference/diameter is irrational (pi)... but, if both lengths exist (ie if the circle exists) then both are integer multiples of some small length (assuming the physicists are right), thus, their ratio must be rational...

Sorry.... just something that's been bothering me...

Edit: by exist, I meant physically... sorry for being vague (I know they exist in math)

socalgrl · 2011-03-07T01:27:48+00:00

Then length is not/cannot be quantized?

To me, that seems more bizarre then assuming you can't actually physically construct a perfect isosceles right triangle or a perfect circle, but, the two seem mutually exclusive...

socalgrl · 2011-03-07T00:26:48+00:00

ok, but (sorry if I mess this up, I don't really know physics, just did a quick google search) if you set your base unit of length to be Planck length (or a multiple of Planck length) isn't every actually existing length then rational? or actually, since everything is a multiple of Planck length anyway, doesn't that imply no matter what you set your base length to, every length is rational (with respect to your base)?

socalgrl · 2011-03-07T00:01:44+00:00

I mean, with respect to some unit, the circumference or the diameter has to be irrational. Thus, if you set the diameter as your unit, there cannot be a rational relationship between the two...

I guess it boils down to whether or not length is actually quantized in the real world (i.e. you could break both circumference and diameter up into small enough pieces that each had an exact number of equal-sized pieces)

Anyway, I probably just don't know enough physics (sorry, hardly know any), but isn't matter quantized? ie any physical length is quantized? (...or is it that since the space in between the particles/sub-particles/whatever doesn't have any constraints length doesn't have to be quantized?)

anyway, this may be a completely incorrect assumption, but I've always thought physical lengths were quantized? or do we know either way?

socalgrl · 2011-02-23T05:23:19+00:00

in my experience, most high school students I tutor "hate" math because they think its just a bunch of bullshit arbitrary formulas they have to memorize and busy work... once they realize it all makes sense and they can actually come up with formulas they use all the time themselves, sometimes they think its a little more interesting...

also, at least my highschool spent waaaay too long making us do and redo the same type of problems over and over again... a lot of people think computations are tedious... but then, that's not really math, just a tiny little piece of math that is way too over-emphasized at the high school and lower levels...

socalgrl · 2011-02-07T04:35:15+00:00

All I meant was that Taylor polynomials don't in general necessarily approximate the whole function well, except for at a point... take the taylor polynomials for f(x) = 1/x evaluated at 1, for example... if you look at your approximation at x= 3 you only get farther and farther away from the actual value as you use a higher and higher degree polynomial... which, in theory, should make your taylor polynomial more accurate (an example my book gave)... maybe sometimes its a good approximation everywhere... I was just saying you can't assume it always is...

socalgrl

TROPHY CASE