Great answer.
For instance, the Universe. We can always make a model, but we cannot get everything in it correct. Besides that we cannot always solve it on a computer, for instance.
But does that mean Math failed or humans? Humans obviously.
Humans failed to notice fractal math can explain patterns in nature.
Humans failed to notice how chemical reactions of the elements in the periodic table can be predicted using math.
Humans failed to realize that an aircraft can fly.
When it comes to humans, their illogical behavior can be difficult to model in math, but not impossible, just improbable. As a human myself, I find it hard to predict what Iāll do from day to day. 
I ābelieveā math is universal, itās just no one has a proof of this, just overwhelming experimental evidence.
Cool link:
Wolframās Math Disproves Intelligent Design
Youād be surprised how often the side effects of a brain well exercised in math occur. Youāll be able to quickly decipher whether a news articles is drawing bogus conclusions simply because the writer doesnāt understand the math behind it, for example.
To be honest if you put a GRE math test in front of me, Iām not going to do all that well, but the thing is itās mostly a lack of knowledge at my fingertips, rather than a lack of ability to solve the math problem. The thing is, even if you forget how, you can re-learn, and that is one of the most important things I got out of university. I cannot remember trig identities forever, the other day I made a mistake, I said tan(theta) = cos(theta) / sin(theta) when itās the other way around, sin(theta) / cos(theta), that caused me some headaches when I was trying to figure out why my software wasnāt working correctly. Thatās the sort of thing I have trouble remembering, but I was still able to solve an otherwise very complex problem, except for that one mistake.
I highly recommend this lecture for learning growth rates and the exponential function:
[media=youtube]F-QA2rkpBSY[/media]
Trig Functions are simply ratios of sides of a right triangle relative to some acute angle theta:
Sin(theta) = Opposite side/Hypotenuse
Cos(theta) = Adjacent side/Hypotenuse
Tan(theta) = Opposite side/Adjacent side
Remembering the acronym SOHCAHTOA is a useful mnemonic.
So Iāve been reading Rudin lately. Honestly, this is the best real analysis bookā¦ ever.
Iāve been meaning to mention some nice, free math books for a little while. If you want advanced undergrad/grad level material, Google āRobert Ashā. He has about 6 full books. Iāve only really looked at his basic algebra one and itās really good and has full solutions.
āLinear Algebra Done Wrongā is also good, as well as Heffersonās Linear Algebra book.
I also have something called the āCalculus Bibleā which might still be available. Itās an introduction to real analysis at a level a little below Rudin, but still rigorous.
Strang is always good for some Linear Algebra (his calculus book is also free online): http://www.dm.unibo.it/~regonati/ad0708/strang-FTLA.pdf
Another discussion of SVD: http://www1.math.american.edu/People/kalman/pdffiles/svd.pdf
Thereās so much good stuff in Wikipedia links too. A Conway article with a proof of the irrationality of sqrt 2 that I had never seen before: http://www.cs.toronto.edu/~mackay/conway.pdf
Yeah itās good but pretty demanding, not that thatās a bad thing. I donāt like analysis all that much so I only made it about halfway through. I love the chapter on topology. Every time drew a picture I had two circles for the domain and range, two points in the middle, then sometimes a smaller circle around each point for a neighborhood. Basically I just drew tits while learning math. And there were nipple piercings with chains connecting them to represent the function carrying a point to another point.
Guys, Iāve got a question.
< means less than, right?
So then, explain to me the equation: I<3U
Is there a proof, anywhere?
[SPOILER=]Had to, True Grave. :P[/SPOILER]
As I see it.
Simplify 9x-7i > 3(3x-7u)
[SPOILER=]-7i > -21u
i < 3u[/details]
- A similar topic to this was already done in another thread.
- If you discount the obvious reference to AIMspeak, I <3 U isnāt an equation. Itās an inequality.
- If you consider I and U to be real numbers, then I < 3 U is an inequality whose truth value is contingent on the choices of I and U, subject to the usual ordering relation on the set of real numbers.
Nice links. Looking at the SVD article reminded me about Principal Component Analysis, which I havenāt thought about in a while.
The visual proof of the irrationality of certain square numbers was interesting. Iāve never seen that way before. Itās probably obvious, but another way to do this is to use the rational root theorem to arrive at a contradiction (if you donāt feel like doing the number theoretic proof that is).
I loathe my schoolās math team. And math tournaments. That is all.
- This isnāt going to get old, anytime soon.
- Touche - 'twas tired; should have qualified it as such.
- The real question ought be whether <3 can be quantified, or if it is with the realm of reality, let alone real.
As I see it.
ive always wondered about something. back in grade school and in highschool i always used to be a mathwiz. i always had a 95 or 100 in tests and did this without sudying (i always directly understood everything in class while i wasnt even looking , just listening and rawing like i normally would do).
then all of a sudden something changed. i started smoking weed. some classes like dutch and english or german, classes i always was good in always had writing letyters in which is sucked. now after i started smoking, my math grades went all the way down. i had to study just to score a 55 to 75 (55 is the lowest posetive grade you can get). with my math skills dying my writing skills went up. my logic died, my fantasy riped?
now my question, does smoking weed really affect your math abilities that fucking much? cause it did with me. i was always great in math, my best class since forever. the ganja killed it, at least i think it was the weed. though i doubt theres been scientific studies about it. anybody else had this problem?
The more I study, the more I realize that:
- Elementary Group Theory is applied Number Theory
- Calculus is applied Linear Algebra, which in turn is just Functional Analysis
if we are talking pneumonics, then iād like to throw in PEMDAS. Itās the order of mathematical operations.
Y=MX+b is the one equation I think I will never forget. Dunno why, but that shit is imprinted on my brain.
considering that linearity is very important and useful in mathematics, itās a good thing you do.
btwā¦ pneumonic actually refers to the lung.
So this is probably obvious to some, but hereās something interesting about numbers: The digits of numbers you write down are really just the coefficients of the polynomial:
a_n10^n + a_(n-1)10^(n-1) + ā¦ + a_210^2 + a_110 + a_0 + a_(-1)10^(-1) + a_(-2)10^(-2) + ā¦
Seems kind of trivial, but if youāre studying infinite series and wondering why anyone would even think about summing up an infinite number of terms, one reason is that you can represent irrational numbers analytically (that is, you can define the irrational number in terms of a sequence that can be made as close to the number as you wish).
rejected by ucla, uw, ucd. rest of schools no response. Iām sad
safety schools? Whatās your GPA, GRE General & Subject Test score? Did you do any research/get paper(s) published?
Well, I applied for a Masterās Degree since my GPA is horrible and perhaps even worse very inconsistent. UC Santa Cruz and Irvine would be safeties I guess. My resume sucked so Iām not surprised Iām getting rejected by everything. Only thing I had really had going for me was a decent Putnam score for my school (which has traditionally been weak at the Putnam) which doesnāt mean anything anyway. My GRE Subject wasnāt very good, scored in 59th percentile. I should have retaken it. My GRE General was strong across the board but Iāve heard math programs donāt care about that much. Either way, I wouldnāt mind going to a CSU for a year and a half, get my M.A. with strong grades and then reapply for a Ph. D since UCs largely donāt provide financial assistance in the form of teaching assistantship to M.A. students. Itās a pretty big investment of time though and frankly a waste of money in the long run. I would need to think about it some more.
Have you spoken with your advisor about your situation? M.A. sounds like a plausible route, though yea it will cost you. How did you do in Analysis/Algebra/Combo? Those are the important courses to know inside and out. I donāt know if you know, but for most schools, you cannot obtain a Ph.D unless you pass Qualifying Exams in Analysis & Algebra. Also, have you done any research at all? I think itās safe to say that most programs want to see that you were involved somehow in research. You say your GPA was inconsistent. Which math courses did you do well/poorly in?