To work out angle 'a' of a right-angle triangle using the lengths of the sides:Buretsu said:
Sin(a) = Opposite / Hypotenuse
Cos(a) = Adjacent / Hypotenuse
Tan(a) = Opposite / Adjacent
TWEWY = The World Ends With You?
Poll: Lack of basic mathmatical skills
- Thread starter barbzilla
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Sin(a) = Opposite / Hypotenuse
Cos(a) = Adjacent / Hypotenuse
Tan(a) = Opposite / Adjacent
TWEWY = The World Ends With You?
FINALLY, someone who understands this: the order is arbitrary! Stop acting smug just because someone else is tripping up over it! It's like laughing at someone for not knowing the password to the tree-house. What are we, five!tensorproduct said:
Sorry, it just annoys me to no end how people point and laugh when some mathematically illiterate schlub doesn't apply the order correctly, or when people purposefully write things out ambiguously to force others to think about the order. I have never seen a single scientific paper which did anything that wasn't completely obvious with their equations. Even when there might be the slightest bit of ambiguity, most people just use parentheses to clear it right up.
That's interesting, is all LISP math written in prefix notation? I'm more familiar with postfix notation (oddly called reverse polish notation in some places). There's no need for parentheses: 2 4 ^ 3 * 1 + 5 -tensorproduct said:
Reading that over, I can see why we don't use it for most situations.
You're right that these statements are not ambiguous, but is it really so hard to vary the spacing and add some parentheses to guide the eye? If need to read the thing twice in order to see what it's asking, that's a failure on the part of the person who wrote the statement. Seeing as how I look at mono-spaced equations in code on a daily basis, I think it says something if it takes me a while to parse a few calculations.Insomniac55 said:
As for WebAssign, that service can go back to the firey pit from whence it came! My Physics homework is hosted there, and the numerical value of the answers it calculates are often off by 20% It's insane! Is the answer 800? Well, I say it's 780! I once had it mark my answer wrong for putting 3 instead of 2.9 when the answer to 3 decimals was 2.995.
OT: I enjoy math, but my arithmetic is terrible. I guess it's just the practical upshot of growing up with a calculator. I usually prefer to leave my answers in symbolic form until the very end. I find that mistakes are less frequent and more noticeable that way.
Captcha: easy as cake
sure, if it doesn't include arithmetic *shudder*
Well, my sad fact of last weekend was that when I was measuring up my desk for monitor space, I had completely forgotten how to figure out the hypotenuse of a triangle...
eventually, I just googled it finding it pointless to try and remember....
oh how stupid did I sound that day..... -.-
eventually, I just googled it finding it pointless to try and remember....
oh how stupid did I sound that day..... -.-
I had a good one the other night... Was doing my homework at 3 in the morning and got the answer right on my second attempt (out of three allowed attempts). Got the marks, showed up in the total at the top... But I noticed the 'submit' button was still present. Curious, I typed a random value in and hit 'submit'. It went through, was marked as wrong, used up my last attempt... and removed the marks I had earned in my second attempt! It knew I'd gotten the correct answer once, but it decided to only look at my last answer. Stupid design.cookyt said:
I don't think you've phrased your poll answers very well. For example, I really like Maths and it's really important to me but I'm not an engineer and nor will I ever be. That doesn't mean I don't need to use it all the time. Just saying the answers given are too focused and should be more general
I don't think you've phrased your poll answers very well. For example, I really like Maths and it's really important to me but I'm not an engineer and nor will I ever be. That doesn't mean I don't need to use it all the time. Just saying the answers given are too focused and should be more general
Lol, don't post much and don't really want to sound like an ass but order of operation is not arbitrary it exists to make math consistence. A small example problem to demonstrate this iscookyt said:
2+3*5
So if not using PEMDAS, say your left to right, then
2+3*5 = 5*5=25
But 3*5 = 5 + 5 + 5 so,
2+3*5 = 2 + 5 + 5 + 5 = 17
you can get two different answers to the same problem i.e. not consistent. Using PEMDAS you get the same answer no matter how you solve it. So I would have to disagree with you PEMDAS is not arbitrary.
Though I do agree that most of most of those Facebook problems are essentially trick questions and don't really test skill but attention to detail. Also I'm not hating on anyone who's not good at math, the beauty of math and science is the general person doesn't need to understand it to benefit from it. For example, the average person trusts their computer works even though they most like don't now how the math and science of how the computer works.
I agree with you about scientific (and mathematical) papers. If there is any ambiguity about what a formula means, then somebody done fucked up.cookyt said:
I will say that it's important for people to understand that there is some order. Sure, it's basically arbitrary, but as long as you're consistently arbitrary then it's meaningful. Though that discussion veers rapidly into philosophy of mathematics, and nobody wants that to happen.
All Lisp everything is written in prefix notation; which might not seem like a big deal, but it gives the language a huge amount of power. I'm aware of reverse polish, though I've never really worked in it. I can see how it would be very quick to punch into a calculator as soon as you get to thinking with a stack.
This is kind of a guess, but I think that the differences between our two notations represent the difference between functional and imperative programming. Fuck, I am such a nerd.
Except it is. We can formulate sets of rules other than PEMDAS and then, as long as we apply those rules consistently, we will get results consistent within that rule-set. The choice of PEMDAS as our evaluation scheme is entirely arbitrary. It is one of a multitude of conventions, each of which is as consistent as another.esperus said:
Both cookyt and myself have provided different evaluation rules based on the same sets of symbols, each of which is as arbitrary as PEMDAS.
I used to be pretty good at maths when I was young and particularly found algebra to be my strong-point. Unfortunately, I practically never use anything but 'life maths' right about now. I can make a wicked-accurate estimate at how much it's going to cost to make that Italian soup, but you'd have done better asking me eight years ago what X equals.
Mathematics is easily my worst subject, and I believe I have dyscalculia although I can't prove it. I can't visualise numbers or the operations I would have to do, and often I have massively painful migraines that can last for up to 4/5 hours at a time. It's really frustrating.
Seeing as I only graduated from high-school last year I didn't have a lot of time in which to forget how to do maths. This is good because I just started a college program in game development, this program includes computer programming which of course requires algebraic equations.
That said, order of operations always seemed pretty damn simple to me.
That said, order of operations always seemed pretty damn simple to me.
Over here in Blighty we were taught BIDMAS instead of PEMDAS which is Brackets Indices etc etc. Same shit just slightly different vocabulary.barbzilla said:
Anyway, it annoys me how many people think maths is a waste of time. Personally I quite enjoy maths (I guess I'd have to, seeing as I want to be a programmer) but I can sort of see why others would be frustrated by it. I don't get the mentality of people who flat out refuse the importance of things as simple as BIDMAS though.
Where is the poll option "Engineer? Hell, I'm a mathematician"? I'm finishing up my studies in Math (Applied Mathematics to Biology to be specific, I'm thinking of makng an epidemiologic model of malaria) and that "engine talk" seem low level. ABout PEDMAS or whatever,, consideting that multiplication/division and addition/substraction are the same operations, they are interchengeable.
My level of math? Well the most "advanced" class may be Mathematical Analysis (beatiful thing reall) and Theory of Meassure, although Group Theory may be advanced too. Calculus, at least in one variable, is first year stuff here. And I use it a lot.
It is very frustrating that people don't understand the basics of math (high school level) and evne worse because it shapes a good measure of things that they should understand.
My level of math? Well the most "advanced" class may be Mathematical Analysis (beatiful thing reall) and Theory of Meassure, although Group Theory may be advanced too. Calculus, at least in one variable, is first year stuff here. And I use it a lot.
It is very frustrating that people don't understand the basics of math (high school level) and evne worse because it shapes a good measure of things that they should understand.
We seem to be having two separate but quasi parallel discussions here: one on Basic Mathematical Skills and one on Basic Mathematical Notational Skills.
They?re related, but I?m not sure they?re the same thing.
Now I?m an old timer and have been out of college for well over a decade and a half. To me, if you use a pen and paper, one can write an equation the way it was meant to be written: multi-leveled and with many squiggly lines.
The challenge comes when one tries to notate an equation in a single line. And the only time you?d really do this is you?re writing code or creating a spreadsheet macro.
Just for giggles, I put the original equation "1+5*5-7/1*9" into an Excel spreadsheet AS IS.
The result was "-37".
Sure as hell looks like the Excel Algorithm followed PEMDAS order of operations and did:
- 7 multiplied times 9 while simultaneously multiplying 5 times 5 (63 and 25, respectively)
- Divided the product of 7 times 9 by 1 (63)
- Added 1 to the product of 5 times 5 (26)
- And finally subtracted the two remaining numbers (26-63 = -37)
Personally, as a old FORTRAN guy?I would have written it (1+(5*5))-((7*9)/1) for clarity...clunky as that may look.
But this definitely supports the validity of PEMDAS being the accepted (if not more widely used) system of notation.
So looks like I got schooled on basic mathematics notation.
But I can still do double integrals and Fourier Transforms. (he says meekly trying to keep self esteem in tact..)
They?re related, but I?m not sure they?re the same thing.
Now I?m an old timer and have been out of college for well over a decade and a half. To me, if you use a pen and paper, one can write an equation the way it was meant to be written: multi-leveled and with many squiggly lines.
The challenge comes when one tries to notate an equation in a single line. And the only time you?d really do this is you?re writing code or creating a spreadsheet macro.
Just for giggles, I put the original equation "1+5*5-7/1*9" into an Excel spreadsheet AS IS.
The result was "-37".
Sure as hell looks like the Excel Algorithm followed PEMDAS order of operations and did:
- 7 multiplied times 9 while simultaneously multiplying 5 times 5 (63 and 25, respectively)
- Divided the product of 7 times 9 by 1 (63)
- Added 1 to the product of 5 times 5 (26)
- And finally subtracted the two remaining numbers (26-63 = -37)
Personally, as a old FORTRAN guy?I would have written it (1+(5*5))-((7*9)/1) for clarity...clunky as that may look.
But this definitely supports the validity of PEMDAS being the accepted (if not more widely used) system of notation.
So looks like I got schooled on basic mathematics notation.
But I can still do double integrals and Fourier Transforms. (he says meekly trying to keep self esteem in tact..)
If your talking about the expression (1 + 3 * 2 ^ 4 - 5) you used before then yet you get different answers depending on how you evaluate. I understand the point, but my point was that PEMDAS ensure consistent answers when you do more complex things such as substitution. From the example I've showed in my post right to left method gives different results when using substitution.tensorproduct said:
Now I guess I should point out that, when I made the substitution 3*5=5+5+5, I inherently used PEDMAS, but this furthers my point that PEDMAS is important because it makes more complex techniques easier. If you didn't use PEDMAS then using substitution would be much harder to the point of uselessness as it would also become bound to order of operation rules i.e. say you had the two equations
5*x = 10
x = y + 1
then by L-to-R rule, considering you don't use parenthesis, then you would always need to solve 5*x = 10 then x = y+1, i.e. a simple L-to-R rules also makes the equations dependent on the order you solve them in. In PEDMAS, the order you solve the equations don't matter.
Also another point to make PEDMAS makes things easier when expressing equation. With PEDMAS, equation are not dependent on how they are written i.e.
4*5 + 3 = 3 + 4*5
are the same. However with other order or operation rules, you would have to be careful how you would express equations. Granted, the same can be said for PEDMAS but I would say it easier to work with PEDMAS then to ensure I got my terms in the correct sequential order. While this is a simple example, for more complex express I would say the L-to-R would become more complicated and less easier to understand.
Relating the to sciences, PEDMAS system lends it self much better for expressing mathematical models, take physics for example. If where trying to find the total energy of something, say E. Then considering just kinetic energy and potential energy,
E = P.E. + K.E.
E = mgh + 1/2 m v^2
but under a L-to-R you can think of the adding the two energy in the first, but in the second express you can't cause the equation is invalid under the L-to-R rules and must be expressed in another way which doesn't simple look like the K.E. added P.E.
Also, under other order of operations systems, algebra would become much harder. Imagine try to solve the following for x under a left to right rules
3 + 5*x + 2*5 = 90
now under left to right you would have to solve it this way
8*x + 2 * 5 = 90
40*x + 10 = 90
40x = 80
x = 2
the problem with the methods is as you can see you always have to unwrap the expression to solve it and IMO its harder to solve using PEDMAS. Furthermore in the 2nd to 3rd step, to solve for x, you have to a R-to-L operation to multiple the 5 out ( or you could of divided by 5 ), but the point it becomes more complicated the simply L-to-R operations and you have to things of the expression as a whole rather then parts. For the PEDMAS method
3 + 5*x + 2*5 = 90
5*x = 77
x = 77/5
you can simply subtract 3 and 2*5 cause their their the last operations to be applied (PEDMAS kinda work backwards when you rearranging equations) . You can think of the terms by themselves and not worry about the equation as a whole.
Sorry for the long post but to sum up my point, for basic mathematics it is quite arbitrary from a purely abstract point but for more complex mathematics applied to science it ensure consistency and simplicity.
I stated in an earlier post that the commonly used order of operations is useful for a whole bunch of reasons. That doesn't make it special. It is still an arbitrary evaluation scheme. It leads to no more mathematical consistency or truth than prefix or postfix notation would, as was stated before. And both prefix and postfix notation find application in a wide range of engineering, science and computing.esperus said:
You would be hard pressed to convince me that the ease with which we work with equations in PEMDAS/PEDMAS is anything but a cultural construct. If we had all grown up in a prefix world, we would have as much intuition for substituting and cancelling expressions in that scheme.
Abstract maths has almost nothing to do with order of evaluation. Axiomatic set theory or category theory are as abstract as you get, and syntax/notation in those fields looks nothing like every day arithmetic or algebra.
