Mathematics Thread

[RussianWhiteBoi]

How can a branch of math be the "hardest" if everything connects to each other? It's like you have a million puzzles pieces, and just as you learn a new branch of math you manage to put together a hundred pieces.... only to find out a thousand more are missing. What's difficult for someone depends on which puzzle pieces are already assembled.

Spoiler

sais the man who hasn't even taken calculus yet

 

[Sa967St]

Twenty people are to travel in a bus from the airport to the hotel at the resort. The bus is designed for use in a tropical climate; it can carry twelve passengers outside and eight inside. If four of the passengers refuse to travel outside and five will not travel inside, in how many ways can the passengers be seated if the combinations of passengers inside or outside is not considered except to take into account these wishes?

Answer:

Spoiler

330

The answer seems low, and it's not even close to what I thought it was.
How did you arrive at that?

 

[RussianWhiteBoi]

We only care about whether someone is seated outside or inside, not the actual seat that they sat at. That being said, since four people refuse to travel outside and five refuse to travel inside, the remaining 11 people need to be seated. 4 need to be placed inside, and the remaining 7 will be outside. In other words, the problem boils down to choosing 4 people out of 11, irregardless of order.

EDIT: a problem I've been working on, ideas?
"Let us agree to say that a non-negative integer is “scattered” if its binary expansion has no occurence of two ones in a row. For example, 37 is scattered but 43 is not, since the binary expansion of 37 is 100101 in which the ones are all separated by at least one zero, while the binary expansion of 43 is 101101 which has two ones in successive places. For an integer n ≥ 0, how many scattered non-negative integers are there less than 2^n?"

I believe that the the answer is the sum of the first n fibonacci numbers, but that seems like a wierd answer...

 

[Sa967St]

Spoiler

We only care about whether someone is seated outside or inside, not the actual seat that they said that.

Ah, alright, but that doesn't seem to obvious from the question:

If four of the passengers refuse to travel outside and five will not travel inside, in how many ways can the passengers be seated if the combinations of passengers inside or outside is not considered except to take into account these wishes?

Spoiler

I arrived at 3186701844480000 ((12P4)*(8P5)*11!), assuming he was asking for every possible way all the passengers can be arranged, given the conditions.

 

[hic0057]

Off topic, does anyone know of a way to privately learn some of these things through the internet or something. My school does not have any special maths programs for people with abilitys in that area (which is only really me though) so I'll like to be sort of self taught in these things

 

[ressMox]

Off topic, does anyone know of a way to privately learn some of these things through the internet or something. My school does not have any special maths programs for people with abilitys in that area (which is only really me though) so I'll like to be sort of self taught in these things

Khan Academy has some great videos and tutorials where they explain things in fairly basic terms. Should help for all the lower level and introductory type things (probably from around limits and factorization to common methods of integration and intro to differential equations) but I don't think they've added anything high-level atm. However, what they currently offer should suffice for a while.

For exercises, you could probably find old calc pdfs lying around somewhere on the interwebs, some universities also make their problems sets publicly available. Other than that, there may be some site lying around with a bunch of useful calc exercises and tests/quizzes.

 

[MostEd]

my first year of igcse requierd a ti 84 plus
but i happened to go to russia after the first year, so its sitting here dusting

 

[ben1996123]

Off topic, does anyone know of a way to privately learn some of these things through the internet or something. My school does not have any special maths programs for people with abilitys in that area (which is only really me though) so I'll like to be sort of self taught in these things

I learned all the calculus I know from here.

 

[vcuber13]

i learned from http://www.youtube.com/user/patrickJMT

 

[samehsameh]

EDIT: a problem I've been working on, ideas?
"Let us agree to say that a non-negative integer is “scattered” if its binary expansion has no occurence of two ones in a row. For example, 37 is scattered but 43 is not, since the binary expansion of 37 is 100101 in which the ones are all separated by at least one zero, while the binary expansion of 43 is 101101 which has two ones in successive places. For an integer n ≥ 0, how many scattered non-negative integers are there less than 2^n?"

I believe that the the answer is the sum of the first n fibonacci numbers, but that seems like a wierd answer...

43 = 101011

 

[samehsameh]

I found that program a few days ago, its very good for me because i can set it to copy to latex code so i can type my equations in MathType then paste them over, which is a lot easier as the latex code for the question you posted previoisly would be \[{x^{\sinh (x + y)}} = \frac{{{2^{\ln (xy)}}}}{{{y^{\csc (x)}}}}\] which is an arse to get all of the {} in the right places

 

[ben1996123]

"Bump". I just felt like saying that its pretty awesome that \( i^{i}=\frac{1}{\sqrt{e^{\pi}}} \)

 

[qqwref]

I got top 25 in the Putnam mathematical competition this year

And Ravi Fernando, another cuber, got top 15.

 

[ben1996123]

I got top 25 in the Putnam mathematical competition this year

And Ravi Fernando, another cuber, got top 15.

What sort of stuff did you have to do in it? I'd like to enter some sort of competition like this some time.

 

[qqwref]

It's not really easy to describe. You can find some past problems here.

 

[ben1996123]

It's not really easy to describe. You can find some past problems here.

Looks pretty difficult

 

[qqwref]

Yeah, and this year's was especially hard - the best person only got 91 out of 120 possible points o_0

 

[asportking]

Hey, I'm hoping someone can help me with this: Next year (my junior year), I'm planning on taking A.P Physics, A.P Bio, and Calculus II/III. However, there's some scheduling conflicts, and I might not be able to fit all of it in, but I could if I took Calc online instead of going to the college. How important would you say it is to have some experience in college classes? The thing I'm worried about is my senior year, having my first college class be some crazy advanced math class (I'm not really sure what comes after Calculus III, I think there's a variety of classes I could take, but I'm betting it won't be any easier).

 

[tozies24]

Hey, I'm hoping someone can help me with this: Next year (my junior year), I'm planning on taking A.P Physics, A.P Bio, and Calculus II/III. However, there's some scheduling conflicts, and I might not be able to fit all of it in, but I could if I took Calc online instead of going to the college. How important would you say it is to have some experience in college classes? The thing I'm worried about is my senior year, having my first college class be some crazy advanced math class (I'm not really sure what comes after Calculus III, I think there's a variety of classes I could take, but I'm betting it won't be any easier).

First, you should decide what you want to do with college, for example, what kind of a major are you looking at, or what kind of school. I would definitely consider taking the Calculus II and III and have that a high priority. AP Physics is probably a good class to take especially if you are looking at an engineering discipline or mathematics in college. Likewise, if you are looking at biology or biological sciences, then do AP biology. I don't think you should stress too much about college classes being hard since you are a junior and are already in Calc II. The first college class you would most likely take is a linear algebra and differential equations (Assuming that Calculus III is multivariable). In my opinion, differential equations are really not that bad when you learn them so you shouldn't be worried. Multivariable and linear algebra are both at about the same level of difficulty but they are just different. Hopefully this helps.

 

[asportking]

First, you should decide what you want to do with college, for example, what kind of a major are you looking at, or what kind of school. I would definitely consider taking the Calculus II and III and have that a high priority. AP Physics is probably a good class to take especially if you are looking at an engineering discipline or mathematics in college. Likewise, if you are looking at biology or biological sciences, then do AP biology. I don't think you should stress too much about college classes being hard since you are a junior and are already in Calc II. The first college class you would most likely take is a linear algebra and differential equations (Assuming that Calculus III is multivariable). In my opinion, differential equations are really not that bad when you learn them so you shouldn't be worried. Multivariable and linear algebra are both at about the same level of difficulty but they are just different. Hopefully this helps.

Thanks for the information! I'll admit, I don't really need to take A.P Biology, although it's mainly the A.P Physics that's the scheduling conflict (A.P Physics and Calc II/III are probably going to be the same hour, and A.P Bio might be the same hour as well). I'm definitely planning on taking both physics and calc no matter what, but the main question I'm getting at is if taking classes at the college in person are any more difficult than the same courses taken online (like maybe it's a more strict environment, or maybe the class moves a little faster), because if they are, I'd rather start off taking college classes in a relatively easy class like Calculus II rather than linear algebra.