solving Quadratics help

[kingkickolas]

yeah i went and seen him he explained it i was like duuuuuh *facepalm* i believe maths should teach you the basics like taxes, mortgage repayments, and money managing!

in life how does defining a function help anyone in life. has Pythagoras therom  ever made anyone's life easier! NO!

 

I think this attitude completely misses the point of mathematics.

 

I would encourage you to read A Mathematician's Lament by Paul Lockhart, a small, fun to read, 140-page analysis of how poorly math is understood by the public, and how it is taught in schools.

It can be found here for free online, or for about $10 on Amazon, which is well worth it in my opinion.

[kingkickolas]

thats maths that shit is just phylosophy now that we have learned the stuff we need for physics... 

 

i mean seriously, defining a function because it helps define another function. but to define that function, we define another functon that is the identity of the first function... what the hell

 

idk, its not really complicated to me, just seems like stuff they should teach math students, and give me stuff that i can use, not philosocrap

 

I think I'd have to disagree with you again.

Often some of the biggest advancements in physics have been because of the work of mathematicians. An excellent example would be Emmy Noether, whose work in abstract algebra helped her develop her Conservation-Symmetry law, which is, to date, one of the most helpful and beautiful theorems of physics and mathematics.

 

The "philosocrap" and definition of functions that you mention might seem useless to you, but they are invaluable tools for the researchers on the leading edge of physics.

 

 

Not only that, but on a personal note, I think it's very much worth it for the sake of knowledge and discovery and development of mathematics.

[LukaP]

I think I'd have to disagree with you again.

Often some of the biggest advancements in physics have been because of the work of mathematicians. An excellent example would be Emmy Noether, whose work in abstract algebra helped her develop her Conservation-Symmetry law, which is, to date, one of the most helpful and beautiful theorems of physics and mathematics.

 

The "philosocrap" and definition of functions that you mention might seem useless to you, but they are invaluable tools for the researchers on the leading edge of physics.

 

 

Not only that, but on a personal note, I think it's very much worth it for the sake of knowledge and discovery and development of mathematics.

i agree completly, but they are shoving this in year one we are learning to do mechanics through calculus at physics, and maths shoves us defining functions through functions. all i meant to say is that they should teach us the stuff we need at the moment first, and then go to more abstract things.

[Nineshadow]

i agree completly, but they are shoving this in year one we are learning to do mechanics through calculus at physics, and maths shoves us defining functions through functions. all i meant to say is that they should teach us the stuff we need at the moment first, and then go to more abstract things.

Oh man,and here I am when our teacher tries to explain to us inequalities...

"That is smaller or equal than that.Why?You'll learn in the 11th grade." (currently 9th)

 

Like really...some exercises are so annoying.

[LukaP]

Oh man,and here I am when our teacher tries to explain to us inequalities...

"That is smaller or equal than that.Why?You'll learn in the 11th grade." (currently 9th)

 

Like really...some exercises are so annoying.

i remember in primary/elementary we learned letters one by one at slovene, but at math, we had to read the tasks to complete them... like wtf

[Nineshadow]

i remember in primary/elementary we learned letters one by one at slovene, but at math, we had to read the tasks to complete them... like wtf

In the first year of Physics we had to use trigonometry,which we learned at Math a year later.

[kingkickolas]

i agree completly, but they are shoving this in year one we are learning to do mechanics through calculus at physics, and maths shoves us defining functions through functions. all i meant to say is that they should teach us the stuff we need at the moment first, and then go to more abstract things.

Oh I see, I didn't know you were in year one. All the stuff that you're learning in math will probably be useful later, or may not be useful in physics at all.

I mean, strictly speaking, you can get through undergrad physics knowing just calculus and maybe a little linear algebra. But you can't just expect a math class to teach only things that are applicable to physics. Math is a field of study in itself, and I think it's nice that they're showing you some of that in year one. That being said, not everyone is a mathematician, so you might not necessarily enjoy it

 

 

Oh man,and here I am when our teacher tries to explain to us inequalities...

"That is smaller or equal than that.Why?You'll learn in the 11th grade." (currently 9th)

 

Like really...some exercises are so annoying.

 

Yeah, there are really very few people who teach mathematics properly. It really takes a great teacher to make an impact on you.

I think this book would also help you out a lot to understand what math is -- and not what's being sort of crammed down your throat at school:

 

I think this attitude completely misses the point of mathematics.

 

I would encourage you to read A Mathematician's Lament by Paul Lockhart, a small, fun to read, 140-page analysis of how poorly math is understood by the public, and how it is taught in schools.

It can be found here for free online, or for about $10 on Amazon, which is well worth it in my opinion.

 

[LukaP]

Oh I see, I didn't know you were in year one. All the stuff that you're learning in math will probably be useful later, or may not be useful in physics at all.

I mean, strictly speaking, you can get through undergrad physics knowing just calculus and maybe a little linear algebra. But you can't just expect a math class to teach only things that are applicable to physics. Math is a field of study in itself, and I think it's nice that they're showing you some of that in year one. That being said, not everyone is a mathematician, so you might not necessarily enjoy it

oh dont take me wrong im enjoying it (even tho im a complete physicist) but i just find it silly that we learn this now...

[jameshumphries47]

Oh I see, I didn't know you were in year one. All the stuff that you're learning in math will probably be useful later, or may not be useful in physics at all.

I mean, strictly speaking, you can get through undergrad physics knowing just calculus and maybe a little linear algebra. But you can't just expect a math class to teach only things that are applicable to physics. Math is a field of study in itself, and I think it's nice that they're showing you some of that in year one. That being said, not everyone is a mathematician, so you might not necessarily enjoy it

 

 

 

Yeah, there are really very few people who teach mathematics properly. It really takes a great teacher to make an impact on you.

I think this book would also help you out a lot to understand what math is -- and not what's being sort of crammed down your throat at school:

i lover maths but i just dont see any usefulness in half the stuff we know! for instance why in life would you want to find the area of a triangle is, or the angle, if you get a job in a bank do they go "right then do question 1.4.5.4 and  want you to work out the mass of this cylinder!" they dont! but hey ho i enjoy it anyway. i love getting a rant out! and ill have a skim through that book, thanks!

[Nineshadow]

-/-

Oh,I know what math is.We talked about it with our Literature/Philosophy/Grammar/Latin/etc. teacher.Heck,we discussed a lot of things with her.From politics,to why some things happened/happen, to existential questions(eg. are we condemned to freedom or sense?).

 

Math's been quite easy.Heck,I wish we would have to solve quadratics now.

[Nineshadow]

i lover maths but i just dont see any usefulness in half the stuff we know! for instance why in life would you want to find the area of a triangle is, or the angle, if you get a job in a bank do they go "right then do question 1.4.5.4 and  want you to work out the mass of this cylinder!" they dont! but hey ho i enjoy it anyway. i love getting a rant out! and ill have a skim through that book, thanks!

Oh...that's actually useful.

 

Please tell me how knowing this might help you in reality :

[jameshumphries47]

Oh...that's actually useful.

 

Please tell me how knowing this might help you in reality :

well, the way i look at things like this, if these questions were not invented, there will be no real need to learn this  

[LukaP]

Oh...that's actually useful.

 

Please tell me how knowing this might help you in reality :

what is this? seems something that could be useful in physics quite alot

[TideRower]

what is this? seems something that could be useful in physics quite alot

Triangle inequality for the p-norm.

[Nineshadow]

what is this? seems something that could be useful in physics quite alot

Minkowski's

Triangle inequality for the p-norm.

 

^^

[LukaP]

Triangle inequality for the p-norm.

god am i retarded haha. i see it now. 

 

that is actually useful

[kingkickolas]

i lover maths but i just dont see any usefulness in half the stuff we know! for instance why in life would you want to find the area of a triangle is, or the angle, if you get a job in a bank do they go "right then do question 1.4.5.4 and  want you to work out the mass of this cylinder!" they dont! but hey ho i enjoy it anyway. i love getting a rant out! and ill have a skim through that book, thanks!

Math isn't supposed to be practical. A lot of it happens to be, and that's great, but it's really not about the real world.

It's an imaginative exercise and a way of thinking. In its most general sense, I think math can be called "the study of objective axiom-based proof." It teaches you how to objectively know something to be true or not, given a certain set of conditions. These conditions may be (and often are) not associated with the real, physical world.

When it is applicable, it's fantastically useful. But when it's not, it's worth doing for its own sake.

 

It really has nothing to do with banking or your taxes. A lot of people make this mistake (because math is commonly associated with "numbers"), but I think the class they're trying to describe is an economics class, not a math class.

 

 

Oh,I know what math is.We talked about it with our Literature/Philosophy/Grammar/Latin/etc. teacher.Heck,we discussed a lot of things with her.From politics,to why some things happened/happen, to existential questions(eg. are we condemned to freedom or sense?).

 

Math's been quite easy.Heck,I wish we would have to solve quadratics now.

Glad to hear it!

[Nineshadow]

@LukaP

 

Here's a math problem our teacher gave us as homework...

X_n = 

 

Demonstrate that x_n < 1.

 

I would be happy and bored to hell if I'd go back to quadratics...

[LukaP]

@LukaP

 

Here's a math problem our teacher gave us as homework...

X_n = 

 

Demonstrate that x_n < 1.

 

I would be happy and bored to hell if I'd go back to quadratics...

we had that in high... thats just the arithmetic series no? (assuming k is an integer)

 

actually this is even easier. you take the result for k=1 and you see its <1. then as you notice, the lower part is a quadratic function, so for k=2, the lower part is more than 2x @k=1... from that you can then use induction to figure that this sum converges to 1

[Nineshadow]

we had that in high... thats just the arithmetic series no? (assuming k is an integer)

 

actually this is even easier. you take the result for k=1 and you see its <1. then as you notice, the lower part is a quadratic function, so for k=2, the lower part is more than 2x @k=1... from that you can then use induction to figure that this sum converges to 1

To be honest, I don't fucking know.

 

And we haven't been thought induction yet.

[kingkickolas]

@LukaP

 

Here's a math problem our teacher gave us as homework...

X_n = 

 

Demonstrate that x_n < 1.

 

I would be happy and bored to hell if I'd go back to quadratics...

 

we had that in high... thats just the arithmetic series no? (assuming k is an integer)

 

actually this is even easier. you take the result for k=1 and you see its <1. then as you notice, the lower part is a quadratic function, so for k=2, the lower part is more than 2x @k=1... from that you can then use induction to figure that this sum converges to 1

 

 

Nice problem!

Well, the sum doesn't converge to 1 actually. I'd make a comparison to the sum of 1/k^2, which is known to converge to (pi^2)/6.

[LukaP]

 

 

 

 

Nice problem!

Well, the sum doesn't converge to 1 actually. I'd make a comparison to the sum of 1/k^2, which is known to converge to (pi^2)/6.

 

i just guessed, since most of these would converge to 1 on our exams i cba to go calculate it this late

[Sammael]

Is it bad that I recognize most of these?.. 

 

 

No, that was kind of basic stuff just jumbled together, I was trying to find some crazy advanced looking alien schematics, but that was the best I could do.

 

That strange alien writing on agents of shield would have done well enough though.

 

[LukaP]

No, that was kind of basic stuff just jumbled together, I was trying to find some crazy advanced looking alien schematics, but that was the best I could do.

 

That strange alien writing on agents of shield would have done well enough though.

 

 

that looks like circuits (well it resembles that)

[Nineshadow]

 

 

 

 

Nice problem!

Well, the sum doesn't converge to 1 actually. I'd make a comparison to the sum of 1/k^2, which is known to converge to (pi^2)/6.

 

I think I solved it though.

 

x_n= 

 

Now, is obviously smaller than 

So,applying this for all of them,we get :

x_n < 

x_n < 

x_n < 

 

Here comes the tricky one :

x_n < 

So  we get :

x_n  < 

x_n < 

Because 1/(2n+1) is subunitary , that means that 1 - 1/(2n+1) is smaller than 1.

Thus,  < 1/2 * 1 = 1/2 < 1 => x_n < 1