Every student, who has learned programming, must have written a program to determine whether a given positive integer is a prime number. Basically in order to determine whether a positive integer n is prime, we search for any number in the range [2, n − 1] which can divide n. Some of you would have designed a slighly better implementation where you search √ for any divisor of n from the range [2, n ]. Does either of these two implementations correspond to an eﬃcient algorithm ? Ponder over this question deeply. Let us try to design an eﬃcient algorithm for a problem which looks as simple and innocent as the problem discussed above. First, we give a deﬁnition. Deﬁnition 1. A positive integer is said to be bit-sum prime if the sum of the bits in its binary representation is a prime number. For example 6(110), 14(1110) are bit-sum prime numbers, whereas 29(11101) is not a bit-sum prime number. Design and implement an algorithm which receives a 64-bit integer n and outputs the count of all the bit-sum prime numbers less than n. Test it for a really large number, for example, execute your algorithm for 123456789123456789. Hint: Your algorithm/program is NOT supposed to enumerate all the bit-sum prime numbers. Instead, it has to just report the count of all the bit-sum prime number. Hence the output will be just a single number. Notice that you will have to use clever programming skills also in this problem.

every art is beautiful and so is the art of algorithm design ...

...Partial Sums of the Riemann Zeta Function
Carlos Villeda December 4th, 2010
Chapter 1 Introduction
1.1 Riemann Zeta Function
In 1859, Bernard Riemann published his paper “On The Number of Primes Less Than a Given Magnitude”, in which he deﬁned a complex variable function which is now called the Riemann Zeta Function(RZF). The function is deﬁned as: ζ(s) = Σ 1 ns (1.1)
Where n ranges over the positive integers from 1 to inﬁnity and where s is a complex number. To get an understanding of the importance of this function, one needs to know some history about it. Dating back to the times of Euclid, the prime numbers have been studied in great deal. What makes them the most interesting over the other numbers is that they hold a special property of not being able to be decomposed into to separate integers. The only numbers that the primes are divisible by is one and themselves. Another, more interesting topic about the primes is their distribution. The question that is asked is “Are the primes distributed in a regular pattern or just randomly placed throughout the integers?” This question is answered by the Riemann Hypothesis to an extent.
1
In 1737, Leonard Euler was one of the ﬁrst to work with the RZF given above; but it did not have the name it has today. It wasn’t until a century later when Riemann’s name was attached to it for his work. Euler had showed that the RZF was...

...my family (guys) try and tell me to do something they say things like “no guy is gonna want a girl who can’t cook or want a girl who bites her nails or want a girl with such an attitude” as if my only purpose for living was to please some guy
I also need feminism because when my little cries, gets upset, or happy or expresses any emotion he’s told by family members (also guys) to stop acting like a girl. As if being a means keeping things bottled up and being tough all the time or that being a girl or even a little feminine is bad
Girls and boys are expected to act a certain way always to please someone else or to be someone else. To act like anything but them. And that is why I need gender equality. And why boys and girls need feminismmy family (guys) try and tell me to do something they say things like “no guy is gonna want a girl who can’t cook or want a girl who bites her nails or want a girl with such an attitude” as if my only purpose for living was to please some guy
I also need feminism because when my little cries, gets upset, or happy or expresses any emotion he’s told by family members (also guys) to stop acting like a girl. As if being a means keeping things bottled up and being tough all the time or that being a girl or even a little feminine is bad
Girls and boys are expected to act a certain way always to please someone else or to be someone else. To act like anything but them. And that is why I need gender equality. And why boys and girls need...

...the town. So, I got out at 8am in the
morning with the determination that if I learn driving this time, I will stick to it. My
driver drove from Moghbazar lane to the junction and stopped the car suddenly
saying, “Now it’s your turn.” With a nervous smile, we exchanged seats and I
adjusted the driver’s seat making sure my legs reach the clutch and break easily. I also
made sure that the side mirrors and the rear view mirror were
adjusted so that I can see comfortably. Finally, I buckled up my seat
belt, ignited the car and we set off to Dhaka University area, one of
the areas with widest lanes. Since it was early morning, the roads
were free of congestion and I drove very comfortably and
confidently. Simultaneously, I was also a bit nervous.
I drove around many wide and almost empty lanes of Dhaka University for half an
hour and then through Nilkhet we started heading towards Dhanmondi. Reaching
Dhanmondi, we found an empty ground many beginners go for learning. Infact, I
practised my driving in that particular place. Over there I learnt to do reverse and
parking. I spent approximately twenty minutes to learn to drive a car in the reverse
direction. But sadly my performance was not upto the mark. The worst was the
parking practice. My driver placing four bricks on four sides, made a rectangular
parking space and taught me to park it. I found it a very difficult task. After two hours
of driving we set off to home through Bijoy Shoroni...

...
FP061 – BUSINESS INFORMATION TECHNOLOGY 061
STUDENT ID : 700013988
NAME : SHEREEN ALEXANDER
GROUP : 1C3
ESSAY TOPIC : DEPENDENCY OF HUMAN ON COMPUTERS
TABLE OF CONTENT
#1. Introduction………………………………………………………………………………….…………..3
#2. What are computers?.................................................................................................................3
#3. The evolution of computers?..................................................................................................4
#4. How humans depend on computers?..................................................................................5
#5. Communications……………………………………………………………………………….............6
#6. Work purposes……………………………………………………………………………………...…..7
#7. Entertainment………………………………………………………………………………………...…8
#8. Conclusion and personal views…………………………………………………………...……...9
#9. References…………………………………………………………………………………………....…10
#1. INTRODUCTION
“It’s not that we use technology, we live technology (Reggie n.d.)”. Technology is the collection of device that makes it easier for us to manage and create information. Computer is a technology that can process, store data and receive. Computer is also a tool where people can connect through website. Moreover, there are a lot of different elements inside a computer and the elements serve different purposes. All the element need to work together in order for the computer to function.
#2. WHAT IS COMPUTER?...

...What is the closed-form expression for the below sum of Geometric
Progression (GP) sequence, S n ?
S n a aR aR 2 ... aR n
(1)
where R is called the common ratio (between consecutive terms) of the GP
sequence.
The reason why we want to derive a closed-form expression for S n is for the sake
of calculating the summation, or otherwise we need to add all terms one-by-one
together, which does not make a sense if the number of terms is huge, say a
million terms!
Most importantly, we based on the closed-form expression to derive the PV
and FV expressions for both ordinary annuity and annuity due.
Steps:
1. Multiply the both sides of equation (1) by the common ratio, R , to have
S n R aR aR 2 aR 3 ... aR n1 (2)
2. Then subtract equation (1) by equation (2), (or vice versa; it doesn’t matter
which subtracts which as the result will be the same.), i.e.,
S n S n R (a aR aR 2 ... aR n ) aR aR 2 aR 3 ... aR n1 (3)
3. Notice that all terms on the right hand side except for the first and last term,
a, aR n1 , are cancelled. So, equation (3) becomes,
(4)
S n (1 R) a aR n1
4. Remember our objective is to calculate S n . From equation (4), S n is obvious to
equal to,
a aR n 1 a(1 R n1 )
Sn
(1 R)
(1 R)
(*)
5. We are done. Equation (*) is the closed-form expression of that we want to
obtain.
Applications:
1. The PV for ordinary annuity, e.g. constant end-of-period cash...

...by Peter is 3 times as heavy as the papaya bought by Paul. If the watermelon bought by Peter has a mass of 4.2 kg, what is the mass of the papaya?
kg
There is 0.625 kg of powdered milk in each tin. If a carton contains 12 tins, find the total mass of powdered milk in the carton.
kg
Marcus bought 8.6 kg of sugar. He poured the sugar equally into 5 bottles. There was 0.35 kg of sugar left over. What was the mass of sugar in 1 bottle?
kg
Bottom of Form
C. NUMBER THEORY
i. DIVISIBILITY RULES
Rule #1: divisibility by 2
A number is divisible by 2 if it's last digit is 0,2,4,6,or 8.
For instance, 8596742 is divisible by 2 because the las t digit is 2.
Rule # 2: divisibility by 3:
A number is divisible by 3 if the sum of its digits is divisible by 3
For instance, 3141 is divisible by 3 because 3+1+4+1 = 9 and 9 is divisible by 3.
Rule # 3: divisibility by 4
A number is divisible by 4 if the number represented by its last two digits is divisible by 4.
For instance, 8920 is divisible by 4 because 20 is divisible by 4.
Rule #4: divisibility by 5
A number is divisible by 5 if its last digit is 0 ot 5.
For instance, 9564655 is divisible by 5 because the last digit is 5.
Rule # 5: divisibility by 6
A number is divisible by 6 if it is divisible by 2 and 3. Be careful! it is not one or the other. The number must be divisible by both 2 and 3 before you can conclude that it is divisible by 6.
Rule # 6: divisibility by 7
To...

...-------------------------------------------------
Prime number
A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2 and 3 in addition to 1 and 6. The fundamental theorem of arithmetic establishes the central role of primes in number theory: any integer greater than 1 can be expressed as a product of primes that is unique up to ordering. This theoremrequires excluding 1 as a prime.
-------------------------------------------------
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of theintegers. Number theorists study prime numbers (which, when multiplied, give all the integers) as well as the properties of objects made out of integers (such as rational numbers) or defined as generalizations of the integers (such as, for example, algebraic integers).
Integers can be considered either in themselves or as solutions to equations (diophantine geometry). Questions in number theory are often best understood through the study ofanalytical objects (e.g., the Riemann zeta function) that encode properties of the integers, primes or other...

...Many people have eaten dim sum without actually knowing what it is. For one thing I know is that I never knew what it was when I was younger. I just thought it was just Chinese food, never thinking that it had a background of its own. Who knew it would have such an interesting background, or meaning? Dim sum is more than just Chinese food; it has its own story and customs.
Before I started researching dim sum I already knew a few things about it. I knew that it was derived from tea drinking. I knew that it was mainly Cantonese in origin. I also knew that dim sum is supposed to be enjoyed with family and friends.
I wished to have more knowledge about dim sum. I wanted to know more about its origins. I wondered how old dim sum was, if it had changed over the years. I also wondered about its traditions and how the style has lasted so many years. I decided to look on the internet for information. I also decided to look at some Chinese cook books at the local library. With that thought, I thought that I might even be able to find a whole book about dim sum at the library, if luck decided to be on my side. I knew that if I looked I would hopefully the right kind of information I wanted.
I searched many pages on the internet about dim sum. I found the information I was looking for. But a lot of the sources were not valid in a way that I could use the pages that I...