[Sergio Tapia]

Ryano121, on 03 April 2012 - 10:18 AM, said:

Quote

share some practical examples where you found it useful to your application?

As you already said it really depends on what applications you will be making. If you were designing a database driven shopping website or something, then you would probably not need much Math to produce a good result.

But that is not to say that you won't use any Math. Say for example you were having a sale on your online shopping site or something. Say you needed to subtract 20% from each price. Okay that is pretty elementary, but it's still Maths. Most people won't use calculus in their day to day business, but a lot of people would use some very simple Maths like that.

As another example we focus heavily on modelling the stock market - which involves a lot of Math such as some pretty horrible calculus and a load of statistics. For someone making a shopping website, doing calculus has no real benefit, but for us its pretty essential.

Yes, I agree.

I guess it all comes down to what type of work you want to focus on.

This post has been edited by Sergio Tapia: 03 April 2012 - 07:27 AM

[lordofduct]

I did math long before I even first entertained the idea of learning to code. I wanted to do something with math, and I was in school with the plans to teach it on some level, but I was only taking math classes as the educator degrees for teaching math barely taught any math (wtf?).

To put it simply, I LOVE math.

When I came to programming, I noticed I could easily apply all the concepts of math that I already knew. And I don't just mean direct application of math. I could easily list thousands of direct application of math (any math oriented software like physics, accounting, encryption, blah blah blah), but software also can have math applied indirectly.

For instance the entire idea of functions/methods for me were super easy to pick up as they mirrored algebraic functions so easily.

C# delegates/function pointers made a ton of sense as well, because they as well mirrored algebraic function:
f(x) = 2x - 3
g(x) = 4x
f(g(x)) = 2(4x) - 3

variables - duhhhhhh

Arrays - basically just matrices, just none numeric types could go in it... but since a type actually is numbers in the end... it is!

object identity - graphs and fields... an object can be made unique by attaching attributes to it, those attributes just being other graphs and fields.




Every new thing I learned when I learned to code I could easily attach to a mathematical concept. And it helped reinforce what it is I was learning. It's easier to remember something if you can match it to something you already know. (it's how I remember names, I can remember the name of someone much more easily if it's the same as a historical figure I know. Names like Elizabeth (queen), George (washington), Eliot (t.s.), Oliver (wilde), etc... easy to remember).

Now I'm not saying it's for everyone. But it certainly doesn't hurt. And since I believe mathematics can be applied to every day stuff as well... I think it's important. General math (arithmetic, geometry, algebra) is an every day thing, one usually is using all 3 habitually through out the day just like language and science. From driving to shopping, lending money to borrowing money, budgeting time to balancing checkbook, working in the yard to cleaning up the house. I may use any number of theorems and laws from mathematics.

But again, you may not be like me. And just as my uncle has gotten by with out knowing how to read or write, and has a pile of money and a good life to show for it. You can EASILY get by with out mathematics.

BUT what blows my mind is when I meet a programmer, who calls themselves a programmer, and can't for the life of them divide 27 by 9.

"You can't divide 27 by 9?"
"Dude, why would I bother with that crap? That's what the computer is for!"
[actual response from a buddy of mine who is a 'programmer']

Yeah, I said you can get by with out knowing math. Just as you can get by with out knowing how to read or write. But my uncle NEVER went to school... where in the hell did you go to school!?

This post has been edited by lordofduct: 03 April 2012 - 07:42 AM

[Sergio Tapia]

In my mind things like operator precedence, algebra, etc aren't "math" math, just high school math. Maybe I take it for granted because I know about it already?

Things like advanced calculus and trees and whatnot, those are the things I don't know about, and consider "math" - in my head that is. I know that they are all math.

This post has been edited by Sergio Tapia: 03 April 2012 - 07:58 AM

[lordofduct]

Well in that case, that's a problem with your own definition of 'math'.

All of those things are math... just like James Joyce and Dr. Seuss are English. Just because some are easier than the other, doesn't make it less math.

Will you be unable to see the applications of very high level mathematics? Yes, it probably will be difficult for you to see the applications of such. But math is one of those studies where it's assumed you can't learn the higher levels well until you've really mastered the priors. You aren't going to do graph theory unless you really freakin' know your Algebra. Algebra has become so intuitive to you while you're finding the curvature of a hyper surface.

It's like how basic vocabulary is just second nature for you years later. That's STILL language, you just no longer think about it so much.

I bet you anything after you really master the even higher level maths, you'll start applying THOSE concepts to your every day problem solving techniques as well (if you've mastered those, you practice math a lot. And if you practice math a lot, you'll find you need to apply it to everything just to get the practice in).

So it's not math isn't important, it's that you can't see the math trees for the math forest is in the way.

[supersloth]

because it's hard for them?

[dorknexus]

who's hard for me?

[The_Programmer-]

Math is so dang easy. People that hate it just don't know enough about math so they don't want to expose themselves as being "dumb." Lol, I meant to say probably. I know some people that don't like math but they are great in science.

This post has been edited by The_Programmer-: 03 April 2012 - 10:06 AM

[Magixion]

Or they just don't enjoy it. Just because someone doesn't like math doesn't mean they suck at it.

[The_Programmer-]

Ummm. I didn't say they suck at it. I said that it is PROBABLY because they suck at it. Not that everyone who hates math sucks at it. Next time, please read posts thoroughly before you de-rep them.

[Duckington]

Because it confuses me and just looking at it usually gives me a feeling of dread. Quite how anyone can look at something like:



And just know what it means is beyond me, even something like that which is probably very simple as far as maths goes is just gibberish to me.

[dorknexus]

Mathematical notation is very concise, and, therefore, very dense.

[jon.kiparsky]

Sergio Tapia, on 03 April 2012 - 09:08 AM, said:

That good and all (and pretty much what I hear every time this is brought up), but can you share some practical examples where you found it useful to your application?

I don't think it's so much about practical applications. I think it's more that high-level math (not just arithmetic or calculation) shares a set of requirements with high-level programming, mostly centered around manipulating layered abstractions. Just being able to build and maintain a representation of a moderately complex program requires a lot of mental work of a similar sort to that required to build and maintain a representation of a mathematical problem. So it shouldn't be a surprise when we find that a lot of people who enjoy one also enjoy the other, and that the skills overlap to some extent. And I think it's also true that working on mathematical problems helps the mind to work on programming problems. So if "makes me a better programmer" counts as practical, I think math has to be considered practical.

But yeah, there's also the case where I was working on an app that had to evaluate a user's understanding of a hierarchical model based on their distribution of those objects in space. We ended up using three different approaches in parallel, all of them very mathematical. One involved parsing an implicit tree structure, if we weren't able to make a tree out of the structure then we used another one based on graph theory, and if the user hadn't drawn in the lines we used a trick based on intersection of convex hulls. It worked. Without math, it wouldn't have worked.

[e_i_pi]

It's not so hard once you study and practice it, as you are able to break notation down into it's components. I can guarantee you that you have coded way more complex stuff than that equation.

The Sigma notation (that big jagged E like thing) is just a for loop from 1 to N. N is the Natural numbers, so it's summing from 1 to infinity. g_i is equivalent to having an array g and taking the i^th term.

As dorknexus pointed out, notation tends to be very dense, which is highly apparent in this case. What's that equation for anyhow?

[ishkabible]

Quote

If it didn't exist, there would be no way to perform arithmetic operations

sorry, but this made me laugh. "you wouldn't be able to do what X does without having X"...really now? are you sure?

Mathematics is a unambiguous method of logically describing the world we live in; you don't even need numbers for 'math' to exist. you only a way of describing things in a logical manner; numbers just happen to do this well for humans. if we thought differently, we may never have come up with numbers.

@OP: I like math but the way it's taught is horrible. Quite frankly, we don't need to know how to make the calculations; only how to define the calculations, then we can create something else that uses our definitions to make the necessary calculations. the idea that we need to know how to add is pretty silly; I don't think I could tell you how to do long division anymore but I could definitely devise an algorithm to do it if you gave me some time. that's where the emphases needs to be, designing the algorithm to make the calculation not preforming the algorithm.

This post has been edited by ishkabible: 03 April 2012 - 04:43 PM

[jon.kiparsky]

Quote

Quite frankly, we don't need to know how to make the calculations; only how to define the calculations, then we can create something else that uses our definitions to make the necessary calculations. the idea that we need to know how to add is pretty silly; I don't think I could tell you how to do long division anymore but I could definitely devise an algorithm to do it if you gave me some time. that's where the emphases needs to be, designing the algorithm to make the calculation not preforming the algorithm.

That is probably the most horrifying notion I've heard all day.

Let me just call to your attention what you just said.

Quote

the idea that we need to know how to add is pretty silly

I don't even know where to begin. I suppose you must mean the idea of memorizing addition tables, followed by subtraction and division and so forth. I find this idea mind-boggling. I mean, for a start, how would you teach algebra to someone who doesn't have a grasp of arithmetic? How are you going to get the sense of

3x + 4 = 10

if you can't do the arithmetic to work out that ten less four gives six, and that six divided by three gives two?

I'd go the opposite way, myself. I think any human being of reasonable intelligence should be expected to have at least a basic competence in arithmetic - not being able to add or subtract, to me, is a little like not being able to tie your own shoes or get your trousers on the right way the first time around. It's a horrifying deficiency.

I agree that the standard math track in US schools - Algebra, geometry, trig, calculus - is probably due for revision, and I think that a lot of progress could be made by offering alternative tracks in math at an earlier age, but I don't see how you could seriously propose doing away with arithmetic.

I do think that it would be possible to include more abstract ideas earlier on. For example, a kid who understands basic arithmetic could be introduced to infinities through Cantors ideas pretty early on. (without the ability to multiply, though, it's a little hard to see them grasping the basic idea of mapping n->2n and really getting a grip on what that means). Introduction to boolean logic might come pretty early, and Smullyan's puzzle collections would make a great addition to any grade school math curriculum.

This might actually help a lot. Right now, I see kids who don't get to algebra until their freshman year of high school, which means they're doing arithmetic nonstop for eight years. That shit, I grant you, ain't right.

This post has been edited by jon.kiparsky: 03 April 2012 - 05:25 PM