[NeoTifa]

Because when people think about math, they usually think of numbers, and when your math starts getting more letters than numbers, it gets scary. Also, thanks to math, I now know almost the entire Greek alphabet, upper and lower case.

This post has been edited by NeoTifa: 03 April 2012 - 06:07 PM

[xxxjj18]

Because it makes me think......... O_o

Besides that, because the equations that need to be memorized simply intimidate those less-willing to actually put a little effort into their homework.

Don't get me wrong; if you're going to be an English major, then math certainly won't affect you, but to all of the kids ( at the high school level ) that claim they're going to a big ten school for engineering and don't even know the Quadratic formula.. They're in trouble :X

Personally I like math because I like to solve problems--hence me loving to program

Altogether, IMHO, I believe that people hate math because either:

a.) They don't care
b.) Its use of huge numbers and long functions intimidate them

or c.) If you make even one small error everything goes terribly, terribly wrong..

I hate thinking that I've solved an equation only to have my teacher/instructor show me the actual answer, to which I solemnly think "WTF!!!!" and give up

[macosxnerd101]

Sergio Tapia, on 03 April 2012 - 10:43 AM, said:

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.

The most common uses of trees in the real world are parsing XML/HTML and traversing a directory structure. You probably won't end up using a lot of calculus or number theory in your programs, honestly. Set theory definitely comes in when querying databases. Regular expressions are a part of natural and formal languages. Computational complexity theory comes into play when analyzing the tradeoffs of various algorithms. A basic understanding of hashing is good to have for security purposes in your application (ie., why hash and salt your passwords rather than just use basic cryptography). Otherwise, more advanced mathematics comes into play if you are working on a niche application.

Also, I'll leave a link to my blog entry Why math is important for programmers, including this excerpt from Martyr2's comment.

Quote

As I have always told people, math is not always 100% needed in programming and you can go pretty far without knowing large complex formulas. However, to be a productive programmer in industry you do have to know how to USE math and how to apply a given formula. Just knowing that a formula exists, where to find it, what the variables in it mean and being able to plug them in can get you even farther. To know that, you do need to know a bit of math.

Macosxnerd, as well as myself, know how many times we have had to help people with just the math let alone the code. Sometimes the answer is purely a math one than the programming. Don't let yourself be falsely convinced that math only appears purely in graphics programming or games. There are many more areas.

[peace_fixation]

Duckington, on 03 April 2012 - 10:06 AM, said:

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.

You are only confused because you don't understand the symbols, just like the first time you saw C source code you went WTF *&->something<<ouch(stop_it)

For the record, the capital sigma (weird E) is the summation symbol, and it means from i = 1 to i = N, perform an operation i.e. (g - min).

The subscripts are there because you have a bunch of values (like an array of N values), and each one is distinguishable by it's index, in your example, this goes for g, min and max. Subscripts in maths are always there so you know which number out of a few numbers you are talking about. Superscripts, on the other hand, are exponents (to the power of), but we don't have any of those in the example.

So your example just says, to calculate G, sum (g - min) from i = 1 to i = N and divide the result by the the sum of (max - min) from i = 1 to i = N.

If you saw it like this maybe it would be more intuitive:

void calculate_G()
{
  double g[] = { some values };
  double max[] = { some values };
  double min[] = { some values };
  int N = g.length(); // lets assume each array is the same length
  double G;
  
  // this is equivalent to the nasty looking equation
  G = sum_a_minus_b(g, min, N) / sum_a_minus_b(max, min, N);
}

// perform the summation of each (a - B)/> from i = 1 to i = N
double sum_a_minus_b(double a[], double b[], int N)
{
  double result = 0.0;

  for(int i = 1; i <= N; i++)
  {
    result += (a[i] - b[i]);
  }
  return result;
}

I'm studying comp sci/maths at school, and it kind of pisses me off that whenever someone asks me what I do at school, and I tell them, they're all like "oh shit, I hate maths it's so hard". It makes me feel like an arrogant twat and them feel stupid, when really, I struggle along with abstract concepts as much as the next guy, but you learn things step by step and you slowly develop an understanding of each concept, and eventually you can do some calculus, or linear algebra, or whatever. I remember the first time I learned some set theory in first year and I was really intimidated, but it was just a bunch of new symbols to learn, and now I know them and it's easy to read what's going on.

Think of it as a new language to learn: Java, German, Maths. Take it in bite size chunks, one thing at a time, and you'll get there

This post has been edited by peace_fixation: 04 April 2012 - 06:00 PM

[jon.kiparsky]

Damn, well said.

This post has been edited by jon.kiparsky: 04 April 2012 - 06:20 PM

[ishkabible]

jon.kiparsky: I want the concept of addition to be taught, not how to manually add 2 numbers using some mindless algorithm that you were taught without finding your self first. if just the concept's were taught, and not the calculation, peoples understanding would be much deeper. we have computers to add for us, and they do it a hell of a lot better too. unfortunately computers can't make the kinds of complex connections we humans can make based on the properties and concepts of things(well, it's probably a good thing actually); so that's what should be taught.

I think it was second grade that I was taught how to add arbitrarily large numbers using a simple lexicographical algorithm. My conceptual understanding of addition didn't change when I learned that, It didn't help me solve new problems. All it did was allow me to solve larger problems with when an unnecessary constraint was placed on me. like 50 years ago that was a pretty big mile stone becuase that constraint was in place; computers were not widely available. now that's not true anymore; so we need to shift what we teach from calculating to problem solving. it's the difference between mindlessly executing an algorithm and being able to create your own.

This post has been edited by ishkabible: 04 April 2012 - 06:54 PM

[hiddenghost]

Duckington, on 03 April 2012 - 12:06 PM, said:

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.

Any time you see that crap you have to realize it's mostly just compound symbols.

2, 3, or 4 symbols grouped together represent one instruction or variable.
In differential calculus you have derivatives, and integrals.
Derivatives are just a measurement from repeated division.
Integrals are just a measurement from repeated multiplication.
Together they discover formulas.

Derivatives are Eskimo Kisses, and Integrals are pretty quilts.
Formulas are hieroglyphics for people who are too succinct.

[hiddenghost]

ishkabible, on 04 April 2012 - 08:46 PM, said:

jon.kiparsky: I want the concept of addition to be taught, not how to manually add 2 numbers using some mindless algorithm that you were taught without finding your self first. if just the concept's were taught, and not the calculation, peoples understanding would be much deeper. we have computers to add for us, and they do it a hell of a lot better too. unfortunately computers can't make the kinds of complex connections we humans can make based on the properties and concepts of things(well, it's probably a good thing actually); so that's what should be taught.

I think it was second grade that I was taught how to add arbitrarily large numbers using a simple lexicographical algorithm. My conceptual understanding of addition didn't change when I learned that, It didn't help me solve new problems. All it did was allow me to solve larger problems with when an unnecessary constraint was placed on me. like 50 years ago that was a pretty big mile stone becuase that constraint was in place; computers were not widely available. now that's not true anymore; so we need to shift what we teach from calculating to problem solving. it's the difference between mindlessly executing an algorithm and being able to create your own.

Do you think 2nd graders should be learning group theory?

Actually there's a really cool method for teaching math using blocks.
http://www.crewtonra...re-numbers.html
And another that's really cool is Singapore math.
http://en.wikipedia....ore_Math_Method

ishkabible, on 04 April 2012 - 08:46 PM, said:

it's the difference between mindlessly executing an algorithm and being able to create your own.

That's exactly what calculus is. Creating your own.

[turboscrew]

Ask any top mathematician: mathematics is formal LANGUAGE.

The idea is to write the problem in mathematics, then state the problem in other ways by using rewrite rules (that are proven to preserve truth) until the answer is obvious.

Also, mathematical rewriting can never bring in any such information about the problem that the original problem didn't contain. Rewriting can only make some facts about the problem clearly visible.

I guess if this was told in the mathematics classes, there would be much less hate/fear against mathematics.

[WolfCoder]

I'm OK if I can reduce the problem into multiplying grids of numbers together to get more grids of numbers.

[jon.kiparsky]

Quote

we have computers to add for us, and they do it a hell of a lot better too. unfortunately computers can't make the kinds of complex connections we humans can make based on the properties and concepts of things(well, it's probably a good thing actually); so that's what should be taught.

This is an interesting position you're taking, and as I say I find it horrifying, but I think it's too interesting to reduce to senseless vituperation. So this is a serious question: Do you think that having a sense of the way particular numbers add up contributes to this ability to make the sorts of complex connections you're talking about?
I know that in my experience, being able to look at a number and see its factors or its multiples, for example, allows me to look at a set of numbers and see the relationships between them. I don't think I'd be able to see that if I hadn't spent a lot of time drilling arithmetic back in grade school, when I was, frankly, completely incapable of making the leap to more abstract concepts.

(Old joke: Little Timmy comes home from school and says to Mommy, "Mommy, Mommy, today I learned that five apples and seven apples make twelve apples!" And Mom says, "That's wonderful, Timmy. And how many bananas do five bananas and seven bananas make?" "I don't know, we didn't do bananas yet".)

I will happily grant you that there are kids - maybe you were one of them - who just get this earlier on. And I think we would agree that those kids should be given more advanced stuff to work on. But if they don't have the arithmetic, I still think that's important, and it should be a big part of getting them ready for the more advanced stuff.

(how are they going to enjoy primes if they can't see a number expand into its factors?)

[WolfCoder]

Quote

we have computers to add for us, and they do it a hell of a lot better too. unfortunately computers can't make the kinds of complex connections we humans can make based on the properties and concepts of things(well, it's probably a good thing actually); so that's what should be taught.

Actually, they can. One of my professors is really big on automated reasoning. Computers do quite well if they have to reason about logic. He's literally designed things like automated bug finding.

[turboscrew]

Couldn't find about it in the net, but I remember reading about "AM" inference system. It started with basic set theory axioms and ended up discovering the existence of (was it) real numbers.

[ishkabible]

jon: The idea is that you still learn arithmetic but rather than mindlessly following an algorithm to preform arithmetic you learn to make the algorithm. Arithmetic is kinda a bad example because it is so fundamental; it's what kids would build off of to create more complex algorithms but the idea is the same. The idea of applying this to addition is a bit radical, it was just an example.

Quote

Actually, they can. One of my professors is really big on automated reasoning. Computers do quite well if they have to reason about logic. He's literally designed things like automated bug finding.

Very interesting! if it's as good and diverse as humans, I really don't see what we humans have left reminds me of an XKCD comic about the games we can and can't beat computers at.

I think the issue here is *probably* the diversity of problems 1 entity can solve but I don't know enough about this stuff to do anything more than guess.

[jon.kiparsky]

Yeah, in general I agree that solving the problem is better than memorizing the answer. If someone tells you that the answer to the Koenigsberg Bridges is "no, they can't" you don't really get much from that. But if you draw dots and lines on paper until you realize that visiting a node in this problem requires two steps (arrive and depart) then you know the real answer.

That, by the way, would be a great problem for a kid. Especially if you sent them outside to run around a kid-sized model of the problem at recess...

It's really just arithmetic where I think you can't get past memorizing the basics.

This post has been edited by jon.kiparsky: 09 April 2012 - 09:45 AM