Maths Project!

As a final year student I'm required to do one project in mathematics, which is what I have always wanted to do! To make it more interesting, I have decided to write about this project here as a blog post.

The topic for my project is "computational number theory ", more specifically on primality tests and integer factorization algorithms.

Why I chose this topic?

I have interests in both mathematics and computer science and I had this in mind for some time to do some concrete work in both the fields. Also nowadays I'm studying algorithms, so I thought it a good idea to choose my project related to algorithms.

In my first year in college I read a book on number theory:
Elementary Number Theory by David Burton

It's an amazing book, especially the part of the theory of congruence, Chinese remainder theorem and continued fractions. I had developed some interest in number theory after reading that book.

So when it comes to project, honestly I couldn't think of anything else but Number Theory in which i already have good knowledge and experience.

Exactly what my project is about?

Prime numbers and Primality tests and Integer Factorization, which is one of the most important topics in number theory, will be the main focus of my  project. The subject of primality of a number has been the focus of many scientific studies and several different theories has been developed for many years. Based on these theorems, primality of large numbers has been investigated. There are also computer algorithms to test primality of large numbers. I will be discussing different methods, algorithms to check primality and to factor large integers. I will also discuss about the best and worst cases for such algorithms, try to compare them and explain which algorithm is best in what condition.  The Best method/algorithm will determined by comparing the test results with different methods/algorithms.


Apart from primality and Integer Factorization I will be giving an Introduction to some of the named primes such as Mersenne primes, Gaussian primes, irregular primes etc.

[untitled]

"Don't let anything stir you off the path you have drawn for yourself! Forge ahead in the end! Stick to it! Make yourself proud! Be everything you can be!"

while you're alive, you need a reason for your existence. Being unable to find one is the same as being dead.
when you give up your dreams and everythinng else, they're gone!
still complaining huh?
..!!!!!!!listen to yourself whining and complaining like some sorry little victim. you can whimper all day for all I care, youre nothing but a coward !!!!!!!....
....remember one thing , once you questioned your own belief, its over!

Untitled

What I thought as my worst fear was perhaps my most loyal companion. For the better part of the two decades, I remember myself wondering, whining, and crying myself to sleep over not being able to communicate what I felt within me. I wondered why I wasn’t the perfection that my sibling seemed to effortlessly master and contain; pondered over not being fun or frolic like my peers. I was told that this was the way achievers behaved, but I look down at my empty hands sometimes and feel nothing but the sting of remorse and regret. I wanted to laugh. I have tried. But someone always chides me. Maybe that is only because that is how they usually talk. How can I tell them that though I would want to brush it aside and laugh along, I am unintroduced to that luxury I love staring at them when they do that? How do people find it so easy to look so light? Can I too learn that secret? I don’t know who I should ask. I want to tell all of them that I am grateful that they are around. I want to give them a hug sometimes…I want to wink at them…I want to call out their name just to feel that they are around me. And I want to tell them. But what if they don’t like me? I have tried telling people how I feel. I have tried telling them of the things that amuse me, things that make me happy…and things I thought they too would love to see. But there has hardly been a time when I told them and they stayed. They all choose to leave and it is my fault. I am boring…intolerable sometimes. I can only bleed on paper but I cannot tell you how much I want to learn to talk like them, be like them…to smile, to have friends, to hangout, to have secrets to share and inside jokes to laugh at. I know it is stupid. I try to imitate them. I try to learn from them. But when they recoil away from me, I am afraid to call them back. I want to ask them how I can be like them. I want to know if I can be one of them. I want to tell them that it is not that I do not care. Just that I am afraid to accept the fact that I feel lonely mostly. I want to contradict the people around me calling me friendless and arrogant, and for which I must myself firstly believe that I am not scared of this claustrophobic confine and void that looms larger within me…so I pretend to be the one choosing…I pretend that I love who I am; I pretend that I can genuinely spell and paint my loneliness in the brightest shade of wondrous solitude. I must admit I am wrong and the wet pillow on my bed and the pile of patient paper are all that I can bring to you as witnesses to this crumbled me. And yes, I have loved. Whatever else I did half-heartedly, I have loved with all my heart and soul. I have loved like to love was the last of the human freedoms left to me, and I have picked up every piece of me like shards of broken porcelain and tried to lay them in careless fashion for their kind perusal. There was nothing that could interest them there either. But as memoirs penned on sleepless nights, I bequeathed from all the unrequited love a reminiscence that I poured into the open arms of my paper. I have murmured names to empty nights, chanted lines of confidence to memories…but I somehow surely lacked the courage to love myself that way. Had I perchance, I would never had written this to you. But I will continue to love and dream…till whatever last remains of me. If you have read till here, I would like to thank you for bearing with me and I would like to tell you that I indebted for your patient company. I don’t know what else to say but I hope that the above passages – unedited, written in the middle of a sleepless, drowsy night – will tell you all that I wanted to. I have always wanted to tell you how much your presence, every single moment of slightest conversation, a wave across the room, meant for me. I wanted to hold your hand and tell you my fears, thank you for just crossing my path. I wanted to show you a million minute scars. But I was just afraid. All I can tell you is a sorry…for being awkward and stupid sometimes. Good night.

little motivation

few days back i had been working on my PR for some organization , it was about a mathematical entity called the quaternion’s and i did not have any single idea about what quaternion’s are?. so i started learning about that from ground on by myself. Initially i was excited and wanted to learn as quickly as possible.
Later, after some days, then I had some difficulties which I got depressed about. My task was to understand the rotation of the quaternion function at the rate of a vector provided(whaaaaaaaattt??), I believed if I don’t understand the derivation, there is no point to just code that formula without actually understanding it. I did not sleep at all that night, trying to see the clear picture. But no use , I realized it’s the morning already. I made fresh myself, had a bath, went for breakfast and then head to college. I was really sad and was thinking about leaving the idea and doing something else.

Next I entered my class , grabbed my seat , said good morning to my friends, and then looked up to the blackboard. To my surprise there was this great quote written there -“everything you don’t know is something you can learn.”
I was like woooooooooo!!, that was cool, really cool, that line charged me up.

That’s all , I was like I don’t need anything else, no more bad thoughts, no more give up , I did not think about anything but to finished what i had started.

today I have successfully done my PR to the organization and It Is under discussion right now. But I’m not done yet I’m already working on other things(modules) with more energy and now I am not scared of doing something i don’t fully understand, the thing is, If I want, I can learn it!

Joke time

1. A cafe patron ordered a pastry, then changed his mind and replaced it with a cup of coffee. When he finished his coffee, he started leaving without paying. The waiter approached him:
—You didn't pay for coffee!
—But I had it instead of the pastry.
—You didn't pay for the pastry either!
—But I didn't have the pastry.


2. I bought a book online "How to implement an Internet scam." Somehow, though, it's been a while, and I still haven’t received it.