Ryou's Math Help Thread

[Ryoutarou97]

So I've seen a few math topics here and a lot more on other forums, so I figured I would make a thread. Also I'm sitting in math right now and should probably be on topic. This is as close as I can get.

 

I am currently taking calculus, so I can do any problems up to there in difficulty so feel free to ask away. Any solved problems will get stuck into a spoiler in case someone needs it.

[as96]

I would search on Google for a list of hard near to impossible problems, but I'm too lazy to do that.

[AnonymousGuy]

I used to be able to do math...then I graduated and subsequently haven't had to do anything beyond basic arithmetic and rarely algebra.  College is like one of those movies where it's based on a book and they split the last book into 2 movies to make it last longer.

[Nineshadow]

I've done a rather nice and not that hard maths problem yesterday. We're currently at injections , surjections  and inverse functions. Nothing too hard.

f:[1,∞] -> [ , ∞)

f(x) =

Demonstrate that f is a bijection and find f^-1.

[Ryoutarou97]

 

I've done a rather nice and not that hard maths problem yesterday. We're currently at injections , surjections , surjections and inverse functions. Nothing too hard.

f:[1,∞] -> [ , ∞)

f(x) = 

Demonstrate that f is a bijection and find f^-1.

...I don't believe I've ever done this (apart from inverses). A quick wikipedia search says that one would first find the inverse then prove that's in ℝ. Gimme a bit to learn how to do this then I'll get back to you. Just out of curiosity, in which class did you do this? Precalc/whatever you call the one before calc?

 

Edit: Also, I hate you forever for even suggesting this. Like, come on. How am I supposed to type out my work to this?

 

x^3 = [y^4 - 4y^3 + 10y^2 - 12y + 9]

 

I thought it factored into 

x^3 = (y-3)^2*(y+1)^2

...cried when I got to the y^2 term. Why would you do this. Just why. (unless I made a mistake somewhere)

[Nineshadow]

 

 

...I don't believe I've ever done this (apart from inverses). A quick wikipedia search says that one would first find the inverse then prove that's in ℝ. Gimme a bit to learn how to do this then I'll get back to you. Just out of curiosity, in which class did you do this? Precalc/whatever you call the one before calc?

 

Uh...we don't exactly have that in Romania.

10th grade. 2nd year of high school.

Last year we studied identities , inequalities , other stuff like that , then we moved onto linear functions, then quadratic , then vectors , trigonometrical functions and then applications of trig in geometry.

This year we'll study complex numbers (which we kinda know already) , exponential functions , injectivity , surjectivity , bijectivity , inversable functions , logarithms and some other stuff with functions , then we'll move onto permutations , arangements, combinations , Newton's binomial , then financial mathematics and finally some more trig, geometry and vectors.

[techswede]

I've done a rather nice and not that hard maths problem yesterday. We're currently at injections , surjections  and inverse functions. Nothing too hard.

f:[1,∞] -> [ , ∞)

f(x) =

Demonstrate that f is a bijection and find f^-1.

"not that hard"... I'd literally die if i even considered trying that.. 

[Nineshadow]

"not that hard"... I'd literally die if i even considered trying that..

That's pretty easy compared to some other problems

[techswede]

That's pretty easy compared to some other problems

I'm 23 and i'm struggling with fractions. Easy is subjective

[Ryoutarou97]

Uh...we don't exactly have that in Romania.

10th grade. 2nd year of high school.

Last year we studied identities , inequalities , other stuff like that , then we moved onto linear functions, then quadratic , then vectors , trigonometrical functions and then applications of trig in geometry.

This year we'll study complex numbers (which we kinda know already) , exponential functions , injectivity , surjectivity , bijectivity , inversable functions , logarithms and some other stuff with functions , then we'll move onto permutations , arangements, combinations , Newton's binomial , then financial mathematics and finally some more trig, geometry and vectors.

Our 10th grade curriculum is similar except we skipped injectivity and all those and replaced them with induction, some set theory, some related material, and a bit of other misc. stuff. We have different levels of students in the same classes, so a 10th grader might take class with a 9th grader and an 11th grader, so rather than calling it 10th grade we call it precalculus and then calc is usually an 11th grade class, though the material seems to be mostly the same. 

[Ryoutarou97]

I would search on Google for a list of hard near to impossible problems, but I'm too lazy to do that.

I figured someone would. I had my ignore hat ready.

[Nineshadow]

Our 10th grade curriculum is similar except we skipped injectivity and all those and replaced them with induction, some set theory, some related material, and a bit of other misc. stuff. We have different levels of students in the same classes, so a 10th grader might take class with a 9th grader and an 11th grader, so rather than calling it 10th grade we call it precalculus and then calc is usually an 11th grade class, though the material seems to be mostly the same. 

Ah, induction. We did that last year.

[Ryoutarou97]

Ah, induction. We did that last year.

Alright, I give up on the problem. I worked through two math classes and a good bit at home. I've got no idea. That's a good one, how's it done?

[Guest Philosophy]

Let f(x, y, z) = xy + 3y 2 z 3 + ln(xz). Compute ∂ 2f ∂x2 and ∂ 2f ∂y∂z 

 

Formatting is horrible in plain text. 

[Ryoutarou97]

Let f(x, y, z) = xy + 3y 2 z 3 + ln(xz). Compute ∂ 2f ∂x2 and ∂ 2f ∂y∂z 

 

Formatting is horrible in plain text. 

...I agree. I have no idea what that's asking. Could you format it in non-text in an image? Does x2 mean x^2 or 2x? huh? (also I'm taking calc 1/2/3 not really sure which, so this might take me a bit to learn partial derivatives, but I should have it back within a day or so if I'm able to do it).

[Guest Philosophy]

...I agree. I have no idea what that's asking. Could you format it in non-text in an image? Does x2 mean x^2 or 2x? huh? (also I'm taking calc 1/2/3 not really sure which, so this might take me a bit to learn partial derivatives, but I should have it back within a day or so if I'm able to do it).

Don't worry about doing it. But yeah, an image would be better than trying to write equations in plain text. 

[Nineshadow]

Alright, I give up on the problem. I worked through two math classes and a good bit at home. I've got no idea. That's a good one, how's it done?

It's a really nice problem, I gotta tell ya.

The solution is quite long though , here you go (I hope you can understand it, my "calligraphy" isn't my strong suit)   :

(there's a small error to the end of the one above, where it says f surjective it should have been w surjective)

[NeatSquidYT]

Ryou's Perfect Math Class

 

[Ryoutarou97]

It's a really nice problem, I gotta tell ya.

The solution is quite long though , here you go (I hope you can understand it, my "calligraphy" isn't my strong suit)   :

 

(there's a small error to the end of the one above, where it says f surjective it should have been w surjective)

 

...two pages of work? It took two pages of work? Are you a sadist? Wow, I totally did not do that. I didn't even get close. That was a really good, problem, I'll see if a few of my friends can get it, though i have my doubts.

[Shoob]

How can one enjoy Math is beyond me. I'm currently at double integrals and the thought that there are triple integrals scares me. :c

[Ryoutarou97]

Ryou's Perfect Math Class

 

AHAHAHAHA! That was amazing. That was utterly amazing. 

[NeatSquidYT]

AHAHAHAHA! That was amazing. That was utterly amazing. 

the video or the reference I made to the video?

[Nineshadow]

...two pages of work? It took two pages of work? Are you a sadist? Wow, I totally did not do that. I didn't even get close. That was a really good, problem, I'll see if a few of my friends can get it, though i have my doubts.

You can do it quicker, it's just not as nice . Not even close.

 

I've dug up an older thread of mine recently. Here's what I had last year at a test in the first semester if you're interested in doing more Maths :

1.Demonstrate that is divisible by 19 whatever value of n (natural)

2.Demonstrate that  (n natural and bigger or equal to 2)

3. [] = ?

where [x] is the smallest integer smaller or equal to x.

4. Calculate 

5.  a + b + c + d = 1

     Demonstrate that < 8

6.Calculate 

7.Demonstrate that 

8.Demonstrate that >= 3/2  ( Nesbit's inequality)

 

Things got way different in the 2nd semester though.

And another one :

X_n = 

 

Demonstrate that x_n < 1.

[Ryoutarou97]

the video or the reference I made to the video?

Both. I haven't seen it in a while, and the reference was great too.

[Ryoutarou97]

You can do it quicker, it's just not as nice . Not even close.

 

I've dug up an older thread of mine recently. Here's what I had last year at a test in the first semester if you're interested in doing more Maths :

1.Demonstrate that is divisible by 19 whatever value of n (natural)

2.Demonstrate that  (n natural and bigger or equal to 2)

3. [] = ?

where [x] is the smallest integer smaller or equal to x.

4. Calculate 

5.  a + b + c + d = 1

     Demonstrate that < 8

6.Calculate 

7.Demonstrate that 

8.Demonstrate that >= 3/2  ( Nesbit's inequality)

 

Things got way different in the 2nd semester though.

And another one :

X_n = 

 

Demonstrate that x_n < 1.

Why so many proofs? Alright, Getting started.