Your test will be on April the 8th, 2008. That is a week from today.

For COMP 2103 the test will cover chapter 4.5, 4.6 and all of  5 (follow the SLIDE numbering, not the book).

Tuesday April 1st: I will go over 4.5 and 4.6 (review). You will be turning in three assignments . We go to cheap office 2010 software computer lab to demonstrate your program. I will grade and cheap office 2010 software return Thursday so you can review for your test.

Thursday April 3rd: Last class before your cheap office 2010 software test. We will go over Chapter 5. Make sure you have your questions ready.

For COMP 3053

Your test will cover chapter 5 and 6 on the 8th of April.
Tuesday April 1st: You’re turning in Assignment 7
There will be cheap office 2010 software an in-class assignment on this day so make sure you cheap office 2010 software don’t miss class. This assignment is cheap office 2010 software on your slide, about breadth-first and depth-first search.

On Thursday we will cover chapter 6 (Gaussian elimination, horner’s rule…)

Dr. R’s cellphone number:

1-281… you didn’t actually think I was going to cheap office 2010 software put his cell phone on the internet, did you?

(skip to the line break for the impatience)

For Mathematic major, after you cheap office 2010 software take all your Calculus and basic linear algebra you’d advance to cheap office 2010 software Advanced Calculus. Advanced Calculus is quite a big leap from the cheap office 2010 software “normal” mathematics you’ve been studying so far. Now you’re not learning mathematics to cheap office 2010 software solve an equation, to find a value or evaluate an expression anymore. In Advanced Calculus (senior level courses at most College and Universities in America) you cheap office 2010 software will learn about series and sequences and their properties and more. You’d be exposed to thinking very very fine (small) and cheap office 2010 software also accept values and concepts that is larger than the cheap office 2010 software largest thing you know so far.

It’s a cheap office 2010 software big leap in understanding and requires a mature mind capable of abstract thinking. After you cheap office 2010 software master the basics of sequences, convergence… of Advanced Calculus you’d be cheap office 2010 software ready for the next step that is beginning Analysis. Intro to cheap office 2010 software Analysis is a course designed to bridge the gap from cheap office 2010 software Undergraduate Mathematics to a Graduate level training in the field. It’s abstract, it’s hard, it’s fun, it’s not compact(!)… you either get it or you don’t sort of thing.

This writing is about a classical problem in analysis. It’s would be cheap office 2010 software quite straightforward to some people while does not seem “logical.” Your common sense may work for cheap office 2010 software you or against you in this case. Let’s see…

——————————————————————————————

There is this hotel called Hotel Infinity. It has infinitely many rooms. Each of these rooms already has cheap office 2010 software a guest in it. Now a new guest arrive.

None of the cheap office 2010 software guests at the hotel will share a room with anyone. And no cheap office 2010 software one is leaving either.

So how do you accommodate the new comer? Or can you accomodate him at all?

Logically (common sense perhaps?) if every single room in the cheap office 2010 software hotel is filled then we can say the hotel is cheap office 2010 software full!  Meaning no more guests can be accommodated? Well but that’s the cheap office 2010 software logic for a normal hotel, this is Hotel Infinity where we have cheap office 2010 software infinitely many rooms remember? Having all the rooms filled and “NO VACANCY” is two very different thing here.
To accept this cheap office 2010 software solution you must first accept that Hotel Infinity has infinitely many rooms. This IS the cheap office 2010 software key. Infinitely many rooms means it WILL NEVER RUN OUT OF ROOMS (whether the newest room found has a guest in it or not).

To accommodate the cheap office 2010 software new guest, you would tell the guest in room1 to move to cheap office 2010 software room 2. Guest in room 2 move to room 3, room 3 move to cheap office 2010 software room 4 and so on. You tell guest in room n to move to room number n+1 and cheap office 2010 software son on. Because you have infinitely many rooms there will always be cheap office 2010 software a room for everyone to move in to. By doing this cheap office 2010 software you have just freed up room 1! Now just send the new guest to this room

Yes you cheap office 2010 software just check a guest into a hotel where all the rooms are cheap office 2010 software filled! Let your imagination roams

The problem is extended when Continue’Em Tours send there entire fleet of buses to cheap office 2010 software your hotel. Their fleet has infinitely many buses each carrying infinitely many guests… You own Hotel Infinity, you can accommodate a lot (understatement) of people. But how do you accommodate Continu’Em Tours guests?

Consider:
.              3128
.          x
.              2123
.       ————
(1)           9384
(2)         6256
(3)       3128
(4)     6256
.      ————-
.        6640744

This is cheap office 2010 software 5th grade arithmetic. We all know how this multiplication works. Let’s look at the first row (1).
3 times 8 = 24 we write 4 and “save” 2.
3 times 2 = 6 we dump the 2 saved from the previous round so we write 8.

and so on.

But, why did we save 2 from 24?? When we first learn this multiplication at 5th grade I don’t think any of us ask this cheap office 2010 software question. The reason is being you are working with decimals (base of 10). Meaning the cheap office 2010 software digit 1 space to the left of the least significant bit (LSB) means how many 10s the cheap office 2010 software value has. The digit 2 spaces to the left of the cheap office 2010 software LSB means how many hundreds you have, and so on.

so for 1291 :

you have 1000 + 200 + 90 + 1

or simply, as agreed upon in base of 10, to be written as 1291.

Now, this is definitely not the only way to represent number! For some odd reason you would like to write 1291 in say.. base 5!

The answer is 20131
To verify you can see:

2*5^4 + 0*5^3 + 1*5^2 + 3*5 + 1*5^0
= 2*625 + 0*125 + 1*25 + 3*5 + 1
= 1291

Please take my word for cheap office 2010 software it that this representation of 1291 decimal in base 5 is cheap office 2010 software unique (it is). Now our question would be cheap office 2010 software if the multiplication method we learned from 5th grade still work on number of a cheap office 2010 software base other than 10? Let’s consider a small example of multiplying 29 x 67 (decimals).

29 (base 10) = 104 (base 5)
67 (base 10) = 232 (base 5)
.                         104
.                      x
.                         232
.           ————

Remember back in decimal everytime we have cheap office 2010 software something larger than 10 (or the base) we do a carry out (or “save” or “remember”)? It is cheap office 2010 software the same thing here. But instead of 10, everytime you have cheap office 2010 software something larger than 5 you have to carry out 1 for cheap office 2010 software each “5″ you have over.

so for 2 x 102:

2×4 = 8 write 3 carry 1
2×0 = 0 write 0 + 1 = 1
2×1 = 2 write 2

so for the first round we have

.           104
.          x
.           232
————-
.           213

Similarly for the other 2 operations we end up with this multiplication:

.           104
.          x
.           232
————-
.           213
.         322
.        213
————-
.        30233

For the cheap office 2010 software final step of adding the 3 values together. When you cheap office 2010 software add 2+2+3 this is 7 you write 2 (instead of 7) and carry 1 over to the next addition of 3+1. This becomes 3+1+1 = 5 so you write 0 and carry 1 over to the final addition of 2+0. For this last one 2+1 (carry out) = 3 you write 3.

This final value 30233 of base 5 corresponds to cheap office 2010 software 1943 decimal. Which is indeed the product of 29 x 67 in base 10. :))

So there multiplication works with numbers of other bases also!

// bint.cpp : Defines the entry point for the console application.
//

#include “stdafx.h”
#include <vector>
#include <string>
#include <iostream>

typedef std::vector<int>::size_type v_sz;
typedef std::vector<int>::iterator v_it;

std::vector<int>& init(std::string, std::vector<int>&);
void disp(std::vector<int>);
std::vector<int>& add(std::vector<int>& result, std::vector<int> first, std::vector<int> second);
struct bint
{
std::vector<int> v;
};

int _tmain(int argc, _TCHAR* argv[])
{

std::string my_string = “123721846239864913265023423414379271021143241878456849752984751203980982342354362945298754350986797698729874979274932796570698709809820983393811128749879179827548719879468709398347039284153495123102987394875989347581093803948335698273416710723469187623127630875629528641908475863465981761012037164873262576128767816543″;
std::string p1 = “34288″;
std::string p2 = “14129″;
std::vector<int> m;
std::vector<int> a,b;

init(p1, a);
init(p2, b);
init(my_string, m);

disp(a);
disp(b);
disp(m);

std::cin.get();
return 0;
}

std::vector<int>& init(std::string the_input, std::vector<int>& v_out)
{
for (int i = the_input.size()-1; i > -1; i–)
{
int tmp = the_input[i] - 48;
v_out.push_back(tmp);
}
return v_out;

}

void disp (std::vector<int> v)
{
for (v_sz i = v.size()-1; i < -1; i–)
std::cout<<v[i];
std::cout<<std::endl;
}

std::vector<int>& add(std::vector<int>& result, std::vector<int> x, std::vector<int> y)
{
int const BASE = 10; //working with decimals

return result;
}

A common trouble from massive multiplayer online role playing game (MMORPG) is the “lag” that cheap office 2010 software seems to always happen whenever there is a large concentration of player in the cheap office 2010 software same area. Users complain endlessly about this issues, citing “there’s no reason the service could be this bad, ” or ranting that their game provider, who is “racking in several tens of millions of dollars per month, yet could not improve their service even after 2 years.”

The most common rant is probably “upgrade the server!!” But in many cases the server (cluster) is not the issue, it is the network that is being exhausted. Let’s examine the case a bit closely.

Consider an MMORPG environment where there is only 1 “zone” and cheap office 2010 software all the players are always in the same area and requires attention from cheap office 2010 software the server and network resources. In a real MMORPG this is cheap office 2010 software not likely the case but the scope of this writing is cheap office 2010 software focused in situations where large amount of users present in the cheap office 2010 software same area. We will see how the resource have to scale to cheap office 2010 software accommodate larger number of players than normal.

We’re discounting the cheap office 2010 software overhead of data processing to look at the network performance and cheap office 2010 software scaling issues only.

Suppose each player needs to update 1KB (one kilo byte) of information with the server every 2s. This is only about 512 bytes / second for each user, a cheap office 2010 software very conservative assumption. With home residential cable connection at 3.2MBit, you cheap office 2010 software are downloading at 400KB/s or about 400,000 bytes a second, for comparison.

Consider an cheap office 2010 software area where there are 100 players all with the need to cheap office 2010 software update his status with the server and require the server to cheap office 2010 software update him with the status of the 99 other players around him.

Each player are sending in 0.5 KB/s to the server. In total there are 50KB/s input to server.
For each of these 2KB data packages (not packet) received the cheap office 2010 software server has to process and update the other 99 player with what cheap office 2010 software it receives. This implies the server is sending out almost 100*99*0.5 = 4,950KB/s or 39.6MBit . This is very manageable for even an OC-3 line.

Now look at 500 players. This number is cheap office 2010 software easily achieve when there is an in-game “event” of some sort. With just 5 times the cheap office 2010 software users than the previous case we’re looking at the server serving 500*499*0.5 = 124,750 KB per second (998Mbit/s). Compare to cheap office 2010 software the case of 100 users this 5 times increase in users has cheap office 2010 software resulted in a 25 times increase in bandwidth required. Thus the cheap office 2010 software amount of bandwidth required scales with the square of number of users.

As you cheap office 2010 software can see with 500 players, who only need to update around 500 bytes of data to cheap office 2010 software the server every second, the server already exceed the capability of an cheap office 2010 software OC-12 line. This is also for just ONE realm with the cheap office 2010 software spike concentration of users. I highly doubt any game company reserves a cheap office 2010 software full duplex OC-12 line for each of its realm server (or server cluster for one realm).

So make sure they can cheap office 2010 software always handle 500 users in one place at a time they’d need a faster connection! But upgrading an cheap office 2010 software OC-12 line to OC-24 or OC-48 is really nothing like upgrading your cheap office 2010 software home cable service from bare minimum to a Deluxe fully loaded package. It is cheap office 2010 software really huge money we’re talking here.

Say they’re upgrading the cheap office 2010 software connection to supports 500 player at a time. And what cheap office 2010 software good will this do? Due to cheap office 2010 software the increased connectivity of the server the number of players on the cheap office 2010 software realm is also increased (to bear the cost of the new connection). This has resulted in another “big event” with 1000 users! which means it’d need almost 4Gbit of bandwidth… and so on.

The game company has cheap office 2010 software to balance the expenses and maximize profit. They sample the data in their virtual world to cheap office 2010 software see normally how many players would be in the same area at the cheap office 2010 software same time and try to accommodate that. They are usually “nice” and cheap office 2010 software anticipate some overhead. But it would not make good business sense to cheap office 2010 software have a network ready to serve 500 player at tremendous cost while “on average” there are cheap office 2010 software rarely more than 100 concentrated at any location in the cheap office 2010 software “world.”

So next time you’re going to complain “server sucks” trust me it’s not going to change, not for your 15US a month.