Learning Greek..

Greek language is sooooo easy, you just can’t imagine! I am almost able to speak more or less fluently already 😀 And it’s so intuitive! For example, can you guess what does a word [ne] mean in Greek? What does you intuition say about that? Well, of course – it’s `yes`! 🙂 What else could it be!

 

Just a Simple and Innocent Question

Is it true that every even number greater than 2 can be written as a sum of two primes?.. 😉

Jack Edmonds – One of the Last Century’s Greatest Mathematicians

I am turning to all of you, my dear readers, with this announcement/application.

 

I have to tell about the great American mathematician Jack Edmonds, and his works in my PhD course after a couple of weeks, and I am now collection all possible information regarding to this man. I have read his most famous article `Paths, Trees, and Flowers`, I have found some citations other people said about him, I have studied some problems connected with his work, etc.

 

What am I asking – can you tell me something more about Jack Edmonds, like some facts from his biography, some interesting stories about him or that he has told, about his personality, etc. It surprised me how little information I could find about his life, including the title of his dissertation – I just couldn’t find it.. So, can you point me, where can I find something more about him? The most valuable would be to get to know, what impact his most famous work left on the subsequent mathematicians – either your own opinions or citations of some famous mathematicians or other people..

 

P.S. Some photos of Jack Edmonds would also be appreciated.

 

Today Is the Anniversary of My Death..

According to this source I have 55 years to live, starting from today.. Quite scary.. 😉

The Curiosity About Prime Numbers

Everybody knows prime numbers. Most of us like prime numbers. Many of us love prime numbers. Some of us have noticed some curious things about prime number. Let me mention some of them:

2 – the curious thing about the prime number 2 is obvious – it is the smallest prime
3 – the smallest odd prime
11 – the smallest 2-digital prime
16 – the smallest number that is the fourth degree of some prime

Etc..

So, if we keep our mind busy thinking about curiosity of small integers, we will certainly be able to think of something interesting (related to primes) about every positive integer. But how far can we go? OK, we can think curious things about integers smaller than 10 – I’ll assume everyone can do that. Well, maybe we can assign a curio to every integer smaller than 100 as well. I guess, not everyone could do it so well this time, but, in fact, it could be possible for some of us. But what’s next? Can we go further till 1000? Can somebody tell me, for example, what is the curiosity about the integer 857 (it must be related to prime numbers)? Not instantly, I guess.. Therefore I was amazed by the theorem I found in this site:

Theorem. Every positive integer n has an associated prime curio.

And do you know what? There exists a proof for this theorem as well:

Proof: Let S be the set of positive integers for which there is no associated prime curiosity.  If S is empty, then we are done.  So suppose, for proof by contradiction, that S is not empty.  By the well-ordering principle S has a least element, call it n.  Then n is the least positive integer for which there is no associated prime curio.  But our last statement is a prime curio for n, a contradiction showing S does not have a least element and completing the proof.

Well, I don’t know about you, my dear reader, but I found this proof very exiting. It actually means we could think of a prime curiosity for every positive integer, if only we thought hard enough and long enough. Very beautiful result, indeed!

What Does This Function Do?

1. Please, give your answers in comments – what does the function written below do:

a)      recognizes prime numbers

b)      recognizes prime numbers in interval [100;999]

c)      neither a) nor b) is correct

d)      other variant (please, specify)

2. And the second question is – is this function a correct solution if the task is as follows: `Please, write a function that recognizes all the prime numbers consisting of exactly 3 digits`:

a) yes

b) no

The function (in C++):

bool f(int x) {

 for (int y=2;y<x;y++)

  if (x%y==0) return false;

 return true;

}

P.S. I wish all of you wrote your thoughts in order to make a student of mine understand the essence of the thing!

Question of the Day

Have you ever drunk some coffee during the coffee drinking time?

And, what do you know, I couldn’t remember any such occasion..

Music – a Special Form of Mathematics

Music is the pleasure the human mind experiences from counting without being aware that it is counting

/Gottfried Leibniz/

I read it here and I found it to be true!

Random Number Generator – As Easy As 01, 10, 11..

Someone told me it is not a trivial task to make a good function generating a random number. What a fool I was to believe him! It turns out you can write down the function very easily. For example, in C++:

int getRandomNumber() {

   return 3; // proven to be random – obtained by throwing a dice

}

Not too complicated function, eh?

Blog Stats Is an Interpolation of What?

When looking at the diagram of `Dashboard à Blog Stats` in my WordPress, I can’t stop wondering about this curve – it must be an interpolation of some function. How could this function look like? What would be other arguments of this function except for the date (what are factors that affect the value of this function)? Can anybody define it precisely? Or not so precisely?