Need a simpe explanations please

[zinedine_88]

need a simpe explanations please...

Ok

I have the following questions...


1. Let say we have a general quadratic equation ax^2 + bx + c , and let's say that D>0
therefore we have two ZEROs, or ROOTs or SOLUTIONS for the equation.

my question is WHY DO WE HAVE TO FIND the ZEROs ... why is a solution considered the values for X when y=o?

Who made that assumption? Why is that the general idea of equations?
Can you give me an application where the ZEROs play an important role.

WE ALL STUDY MATH... but there are people like me who question the purpose of the little and simple things we do ( like solving quadratic equations..)


2. WHy do we need COMPLEX NUMBERS?

3. WHY is it so hard to prove the RIEMANN HYPOTheSiS?

WHY IS IT SO IMPORTANT TO FIND A PROOF for it, provided the fact that 1 000 000 bucks are offered for that so desired proof?

I need a simple explanations...I am just a freshman i college who has infinite number of questions ;))))


thanks a lot
:)

 

[HallsofIvy]

Ok

I have the following questions...


1. Let say we have a general quadratic equation ax^2 + bx + c , and let's say that D>0
therefore we have two ZEROs, or ROOTs or SOLUTIONS for the equation.

my question is WHY DO WE HAVE TO FIND the ZEROs ... why is a solution considered the values for X when y=o?

Who made that assumption? Why is that the general idea of equations?
Can you give me an application where the ZEROs play an important role.

Why are you focusing on 0? If you have any quadratic equation that says Q(x)= a (Q(x) is the quadratic a is some number) then Q(x)- a is also a quadratic and Q(x)= a has exactly the same solutions as Q(x)- a= 0.
But I really have to agree with your objection! If your goal in life is to say "Do you want fries with that?" you have absolutely no need to study how to solve equations. It's only people who care about facts and thinking that worry about such foolish things.

WE ALL STUDY MATH... but there are people like me who question the purpose of the little and simple things we do ( like solving quadratic equations).

Absolutely. Why a car would drive just as well if the pistons were a quarter of inch larger than the cylinder! Wouldn't it? Why it is just silly to worry about precise values! And that's all "solving equations" is about.

Why do we need COMPLEX NUMBERS?

I can't say why we need complex numbers because I know nothing at all about YOU. I know why I need complex numbers. I know why physicists and engineers need complex numbers (and why they need to solve equations). But I can't speak for you. You'll have to decide for yourself if you need complex numbers- or Shakespeare or Camus or any of the other things educated people think are good to know. Of course, it's hard to decide if you need something if you don't know anything about them in the first place.

3. WHY is it so hard to prove the RIEMANN HYPOTheSiS?

Damned if I know. How hard have YOU worked on it?

WHY IS IT SO IMPORTANT TO FIND A PROOF for it, provided the fact that 1 000 000 bucks are offered for that so desired proof?

That's a strange question! "Provided" the fact that $1000000 would make it at least as important at $1000000! Did you mean to ask why it is sol important that $10000000 is offered for a proof? If so, you might want to work on English grammer as well as mathematics.

I need a simple explanations...I am just a freshman i college who has infinite number of questions ;))))


thanks a lot
:)

Funny, when I was in college I considered having an infinite number of questions a good thing. You seem upset about it.

 

[Gib Z]

1) Are you asking, why is finding out for which values the quadratic equation is 0 is important? Because it is the best way to simplify a larger problem: When is the quadratic equation equal to some number k. If we want to solve the value of x when the quadratic is equal to k, then we must solve ax^2 + bx + (c-k) = 0. The general idea of equations is solving for the unknown value so that we can figure out what it is!

A simple example, a farmer knows he has 12 chickens, but then finds 3 dead in a shed. How would he find out how many chickens he has left without going back to count them all? By solving 12-x = 3 of course. That can be interpreted as finding the zero of x-9=0, quite straight forward.

2) Well, I'll repeat, "The general idea of equations is solving for the unknown value so that we can figure out what it is!" . We need complex numbers to extend the variety of equations that we can solve the unknown for! Eg $$x^2 + 1 = 0$$ can only be solved for x if we use complex numbers.

3) I'm not 100% sure why it's so hard to prove, I've never tried it myself. It is important to find a proof for it though because the truth or falseness of the hypothesis would lead to many other conclusions we can make from it, or refute many. Many current theorems acquire their result through the assumption of this theorem, so they will be proven if RH is proven. Many results on prime numbers is in this situation, so number theorists especially want this solved.

EDIT: Damn i type too slow.

 

[zinedine_88]

HallsofIvy - not impressive at all... not fun saying unpleasant things to people in the forum... not a nice guy...bad answers... that's all i can say...


Gib Z - thanks man...good guy ...good answers...knows more than HallsofIvy and treats people better!

these are my impressions... HallsofIvy - i am dumd i know... but I can't understand why did you post a reply to my questions since : 1 you didn't get what I was asking ( because of my bad english ... for which I appologize)
2 YOU DON't KNOW THE ANSWERS!?

it is amazing how easy it is to get an idea of somebody's personality even from a single post in a forum...

 

[CompuChip]

I agree that HallsofIvy's response may have been a little edgy, but your post indeed doesn't read very pleasantly with lots of obsolete whitespace and some OdD CAPiTaLizatION. Also, in general YELLING AT PEOPLE IS CONSIDERED IMPOLITE IN standard netiquette. I do not blame you for feeling misunderstood, but there are better ways to communicate this. We all make misjudgments from time to time, but to conclude from just one post that someone is a dumb annoying guy, is irrational and insulting (actually, thought your response was directed at HallsofIvy, I feel offended myself). I suggest you read some of his other 16,033 posts and then hopefully find out how amazing it is so get the wrong idea of somebody's personality even from a single post in a forum...
Finally, if you reread his post, you'll see that there is some valuable information in there, additional to Gib Z's post.

 

[Gib Z]

HallsofIvy - not impressive at all... not fun saying unpleasant things to people in the forum... not a nice guy...bad answers... that's all i can say...

Aww come on, even if that was a bit of a different post, check his other ones like CompuChip told you to =] Hes a nice guy!

...knows more than HallsofIvy

Maybe if you gave me another half-century! Not right now though =P

YOU DON't KNOW THE ANSWERS!?

it is amazing how easy it is to get an idea of somebody's personality even from a single post in a forum...

I assure you, Halls knows better than most people when it comes to mathematics! He has been doing it his entire life after all! And nope, in fact, a single post is never good to judge from! I remember there was a thread I posted in in my first month here, and then it got revived by the OP a year later who came back to have his word with me, I was a little rude there =] If you judged me by that, I would be ashamed!

 

[HallsofIvy]

Hey, I really am a dumb, annoying guy!

 

[ice109]

dude you should sign up for some freshman writing classes.

 

[epenguin]

Your questions

1. I had that feeling when I was at school time ago, mnyah mnyah, it seemed to me that the important thing was to find the numbers x for which e.g. x^2 - 4x would add up to -3, there seemed to be this mania for expressing it as finding the x for which (x^2 - 3x + 3) amounted to 0. I avoided expressing it that way whenever possible, I tolerated the other way since it was obviously equivalent so it didn't seem all that important and I never asked about this habit; and there weren't the places with nice people like here in those days either mnyah mnyah.

Now I realize that it was because it points you in the direction of a solution, and that this and maybe at least half the useful things in maths depend on the exceptional properties of the number 0! The key property that 0 X anything = 0. It is the only number with the property n X anything = n. So then all algebraic equation solving is about factorising expressions like (x^2 - 3x + 3), to (x – 1)(x – 3) because if any of the separate factors is 0 so is the whole expression by the above property.

Even if we can find solutions by other methods like guessing, trial and error or numerical approximation we would miss things. E.g. we would not have the simple theorem that the number of roots equals the highest degree in x. We would find instead only two solutions to x^3 -5x^2 + 7x = -3, (i). Then you would have a complicated discourse about exceptions I suppose. Instead if you see it as (x – 3)(x – 1)^2 = 0, you see it as three factors always, two of which happen to be the same.

Then e.g. in physics you have conservation laws, which say that despite this and that feature of the situation changing there are some things like total mass, or energy etc. which don’t, their changes add up to nothing. So it gives a feeling of finality somehow to have that nothing on one side of the equation. Then maybe it is used beyond where it needs to be, and not always used, you could say the change in this equals the balancing change in that, but it is not a bad habit.

2 You have the same sort of exceptions if you do not allow complex numbers and the same resolution maintaining the theorem if you do. When you first meet complex numbers when solving quadratic equations, they may seem an irrelevant nuisance and you wave them away; I think the ancient Islamic mathematicians did that while recognising their existence. But then in the fifteenth century Italian mathematicians found that if they had the crazy idea of believing this complex roots meant something and you could work with them like the familiar numbers, then that enabled them to solve any cubic equation like (i). Moreover you cannot do it algebraically without complex numbers even when the solutions are all ornery real numbers.

It was pure formalism without any concrete representation (such as now will be given you) of complex numbers, a leap into abstraction, therefore I think perhaps the most important step in the development of mathematics as we know it. The usefulness and indispensability of complex numbers (e.g. in quantum mechanics) has only ever increased since then.

3 About the Riemann hypothesis there are now popular books like “Dr. Riemann’s zeros” and “Music of the Primes” that ‘explain’ it to laypersons. Well at least they give you an idea of what it is all about and the academic gossip and sociology around those who work on it.

A thing that strikes me though reading these books is what a different thing almost maths of these people is from that of what we’re used to. I mean we are able to go through a chapter or a book and then master some methods with which we can handle a certain area of applications, maybe there are things we wouldn’t have thought of unaided, though some even of these are obvious with hindsight. But what these other guys do seems in a different world, like needing a team that takes a year to check through a proof and you wonder how anyone can possibly see the way to arrive at such a proof in the first place.

I would welcome some comments from professionals on this impression of mine, that maths, at least some of the cutting edge, has become qualitatively a different kind of enterprise from the sort of thing we common users know as maths? Maybe this is not the thread for it.

 

[zinedine_88]

WOWOWOWOWOW


i didn't say that HallsofIvy ... I SAID I AM A DUMB GUY... or maybe some of you need to attend a freshman grammar course.

WHAT I WROTE WAS:
"these are my impressions... HallsofIvy - i am dumd i know... but I can't understand why did you post a reply to my questions since : 1 you didn't get what I was asking ( because of my bad english ... for which I appologize)"

as u can see I am saying that I am dumb... I didn't say - YOU ARE DUMB... or someting..

that's a misunderstanding!

as far as my englishh skiiillllllllllllllllls I think i don't have to write well here ... sometimes that might cause some huge MISUNDERSTANDINGS but ... i don't really care...

I don't feel that writing in a forum by sticking to all the grammar rules is totally UNNECESSARY!

WHATEVER... I think somebody should delete this thread cuz:
1 - my questions are dumb
2- people are getting to hate me
3 - reading that thread is purely a waste of time(with some exceptions)
4- this thread is frustrating people

I DON't care what people think... just i had a bad day and that's why I answered to HallsofIvy kinda rude and not fun and very helpful reply.
I appologize to everybody!
I will probably not ask any other questions in the forum since you are at such a high level! ( i am not sarcastic)!


take care guys ...thanks to whoever replied and devoted some time to answer my questions...