Mathematics Thread

[cosmicway 1,333]

How many rearrangements of the first N natural numbers exist so all the numbers are in the wrong place ?

Examples:
For N = 1, set = {1}, arrangements = (1). It does n't count so the answer is 0.

For N = 2, set = {1,2}, arrangements = (1-2), (2-1). Only the (2-1) counts and the answer is 1.
For N = 3, set = {1,2,3}, arrangements = (1-2-3), (1-3-2), (2-1-3), (2-3-1), (3-1-2), (3-2-1). The (2-3-1) and the (3-1-2) count so the answer is 2.

What is the formula ?

[cosmicway 1,333]

The previous one is a little difficult.

Can be googled but I 'm not letting you know the words to look for !

Here is another one:

You are given the number sequence 4, 11, 18, 25, 32 ... .

It's an arithmetic progression with starting term = 4, common difference = 7.

You form decimal numbers thus:

0.4

0.411
0.41118
0.4111825
0.411182532

i.e. you put the digits of the next term of the sequence to the right every time.

These numbers tend to a limit which we call L.
Prove that L is an irrational number.

[cosmicway 1,333]

What is the chance of us breathing one of the molecules in Julius Caesar's last breath ?
Google to find the values of the physical parameters involved, to work out your answer.

[cosmicway 1,333]

Riddle for Liverpool supporters.

If you find the solution Liverpool are going to win the league:

You are given the set of the first 50 natural numbers N = {1,2,3 ... 50}.

You pick two numbers at random and take them away from the set but add the value of their absolute difference.

So if you pick 40 and 50 their difference is 10 and the new set is N1 = {1,2,3 ... 39,41 ... 48, 49,10}, that is 40 and 50 are gone and a 10 is added since |50-40| = 10.

Continue in this vein until you are left with only one number.
Prove -using analysis- that when you are down to one number, that number is always odd.

[cosmicway 1,333]

Once upon a time there was a postman who was very good in maths.

A lady says to him I will give you a riddle to see how clever you are. I have three daughters, the product of their ages is equal to 36 and the sum is equal to the number of the house across the road. What are the ages ? The postman was unable to answer and so the lady says I 'm going to help you by saying the eldest one is a blonde. Hearing this, the postman instantly gives the answer. What was it ?

[Unionjack 7,531]

Two cats called '1,2,3' & 'un,deux,trois' had swim race across channel.
1,2,3 cat won because un, deux, trois cat sank!

Ive not got the mind for maths apart from gramms,ounces,pounds and kilos. I got behind in maths lessons so used to dread having them so ended up just dossing round the West End getting into mischief.

[Unionjack 7,531]

My maths teacher (well quite a few of my teachers) methods of teaching was to spend the lesson writing copious blackboards of facts and we student were expected to write them down and learn them parrot fashion.

This of course is all very well unless like I was a very slow writer which meant that as I was only half way thru the blackboard the wanker of a teacher was erasing it to write another soddin one! And of course this carried on thru the lesson. And by the end of it I had only got half the notes. And multiply that thru the school term it soon mounts up

And with that happening not only in Maths but English Language,History,Geography,French I had enough of it so by the 4th year I was skiving off up the West End alot.

But At 17 summet happened and I was convinced to goto Tech college to get my exams. I found the teachers there to be 100% different and they taught students by conversations, asking questions,giving answers. I became like a sponge taking anything that I could in.

So in 2 years I had passed 8 O'levels and 2 A'levels. Not alot as far as academia is concerned but for me that was a miracle.

I learned everything apart from bloody Maths hahaha

Anyway I just came across a very interesting Youtube channel. It explains maths in a way that I understand and I thought I'd share it

https://www.youtube.com/user/numberphile

[Hostedenis 556]

Once upon a time there was a postman who was very good in maths.

A lady says to him I will give you a riddle to see how clever you are. I have three daughters, the product of their ages is equal to 36 and the sum is equal to the number of the house across the road. What are the ages ? The postman was unable to answer and so the lady says I 'm going to help you by saying the eldest one is a blonde. Hearing this, the postman instantly gives the answer. What was it ?

Possible ways to make 36 with a product of three:

1 1 36

1 2 18

1 3 12

1 4 9

1 6 6

2 2 9

2 3 6

3 3 4

The sum of their ages is then

38

21

16

14

13

13

11

10

Meaning, by looking at the house number, the postman should know their ages unless the house number would be thirtheen, in which case two set of ages are possible. Since he replies he can't know the answer with the given data, the house number must be 13. Since the lady then says the eldest is blonde, she has an eldest daughter, hence 2 6 6 isn't possible and their ages are 2 2 9.

Postman doesn't have to be that good in math to solve this (just logical reasoning) and in fact they still could be twins or born in the same year with one of them being older (although having the same age at that time) so I get what the riddle wants you to do but it's not entirely worded right.

Haven't actually solved maths on here before but I'm bored and waiting for Stones news

[iseah100 5,612]

Gonna be asking questions in this since I'm taking a math class this semester. Ok.

[termninja 5,290]

I study at Faculty of Mathematics (programming though), and definitely teachers can fuck you completely up with math. Math is an incredible thing yet I've heard and witnessed numerous occasions in which teachers failed to make students understand basics concepts and motivate them to work.

In my faculty things are very different because you get so much theory about everything with lots of explanations and examples and I've really learned a lot despite thinking I wasn't really good at Math before starting my studies.

Never give up guys, find strength and shove that middle finger up hater's arse!

[EBH 283]

I'll just leave this here

[Rmpr 8,977]

I'll just leave this here

Thats high school math, meh

[zolayes 14,489]

Thats high school math, meh

Junior High School

[EBH 283]

Thats high school math, meh

Great, I was hoping somebody could explain it to me. Now you have to do it, Mr High School

[CHOULO19 24,332]

Great, I was hoping somebody could explain it to me. Now you have to do it, Mr High School

What is there to explain? It's very basic:

When dealing with complex numbers (that is numbers that have both a real and an imaginary component) you can represent them as vectors or points on the trigonometric circle because obviously any point will have a component on the real (cosine) and imaginary (sine) axis. This point will have an angle (call it Theta or Fy or whatever) whose sine will be equal to the imaginary component (divided by the magnitude) and the cosine to the real part. It can also be shown that this is equal to exponential of that angle (in radians) times 'i' (square root of minus 1).

[EBH 283]

What is there to explain? It's very basic:

When dealing with complex numbers (that is numbers that have both a real and an imaginary component) you can represent them as vectors or points on the trigonometric circle because obviously any point will have a component on the real (cosine) and imaginary (sine) axis. This point will have an angle (call it Theta or Fy or whatever) whose sine will be equal to the imaginary component (divided by the magnitude) and the cosine to the real part. It can also be shown that this is equal to exponential of that angle (in radians) times 'i' (square root of minus 1).

Thank you. Please don't assume there's nothing to explain! I'm a total novice at maths

I guess my questions are not purely mathematical, they're sort of philosophical, more concerned with understanding how it is that maths forms the universe, rather than understanding how maths itself works. How can this one formula be transformed algebraically into every possible structure in the universe?

[EBH 283]

Do you guys have any experience with websites like PatrickJMT and Khan Academy? They do a good line in maths education, I've been told, and I want to start learning from scratch.

http://patrickjmt.com/#arithmetic

[CHOULO19 24,332]

Thank you. Please don't assume there's nothing to explain! I'm a total novice at maths

I guess my questions are not purely mathematical, they're sort of philosophical, more concerned with understanding how it is that maths forms the universe, rather than understanding how maths itself works. How can this one formula be transformed algebraically into every possible structure in the universe?

Maths doesn't shape the universe. It's a just one lens of reasoning we see the universe through. Sure, the mathematical formulas and models we come up with are influenced by the universe around us but arguably the main factor remains the human brain and how it constructed to analyze the world and define 'logic'. There is no reason to believe that the universe is shaped by how we perceive it. In fact, there has never been any evidence that any being, human or not, can acquire any 'truth' about the universe.