"School Thread" or "Math + Seil = *headdesk*"

[Seil]

Math is stupid. It would be so much simpler if we were analyzing poetry or something.

http://i165.photobucket.com/albums/u59/Poetisch/calvin_hobbes_mathreligion.gif

[Hanuman]

Hail Eris.

[Terex4]

Geo me try, geo me fail.

I don't even know what trig is and calculus sounds like a total mindfuck to me.

[Tev]

Hail Eris.The goddess of strife or the cell phone? One's built on math...

[Ecks]

Geo me try, geo me fail.

I don't even know what trig is and calculus sounds like a total mindfuck to me.

Trig is where you apply algebra TO geometry, and calc is just more fuckery with trig, alongside some more fuckery with graphs.

IT FUCKING SUCKS. I had two whole years of calc, alongside a year of geo, and a year of trig. My entire high school math career was four long years of fuckery with imaginary numbers and concepts.

GLAD THAT'S OVER.

[Bard The 5th LW]

I personally prefer history.

[Locke cole]

And you don't even want to know about Ordinary Differential Equations. I'll just let you decide what it means when the teacher says that a problem is at the easy part once it's reduced to "just" trig or "just" calc.

And that I know he's right.

[Pip Boy]

Math is stupid. It would be so much simpler if we were analyzing poetry or something.

I find that statement so backwards and ironic that I cannot comprehend it. Not that math is for everyone, or that poetry is cthulhu fthagn to everyone, but to me personally math is ultra awesome easy in that it must make sense 100% of the time, and learning math is entirely based on rational processes and not on the irrational language conventions used in that nasty poetry gibberish.

What math course are you not understanding?

[CelesJessa]

I'm glad I don't have to work with math anymore, outside of the math used in 3D animation.

I just get to figure out massively powerful programs with insane amounts of options.

http://img227.imageshack.us/img227/6083/maya0.jpg

[Grimpond]

CJ, first I read your post/image, then my eyes wandered down to your sig image. and it is a perfectly logical followup.

[Seil]

I think it's less "I hate math," and more "my teacher is insane and tries to teach us everything about something in a few sentences."

Or it could just be that I'm fail:

1/2(4x - 8)-2/3(-3x+6) = 4x-8

[Pip Boy]

I think it's less "I hate math," and more "my teacher is insane and tries to teach us everything about something in a few sentences."

Or it could just be that I'm fail:

1/2(4x - 8)-2/3(-3x+6) = 4x-8

1/2(4x - 8) - 2/3(-3x + 6) = 4x - 8
distribute the half and negetive two thirds

2x - 4 + 2x - 4 = 4x - 8

combine like terms

4x -8 = 4x -8

add 8 to both sides, divide by four

x=x

No definite solution

[BattyAsHell]

Math is stupid. It would be so much simpler if we were analyzing poetry or something.

http://i165.photobucket.com/albums/u59/Poetisch/calvin_hobbes_mathreligion.gif

Heh, I was arguing something like this years ago, but with regards to colors...

[bluestarultor]

I deal with math as a programmer and web designer, but it's definitely not calc. Or at least I HAVEN'T used calc. I had to take Calc I twice to pass it, but part of that is because the first time around was at 8AM when my insomniac roomie kept me up until at least 2AM nightly, if not later. There are days I ended up in class without remembering how I got there.

I do remember some of the stuff, like integration and deintegration, vaguely, but only the shortcuts. And, well, stuff like what "5!" means, if not the name, and sigma notation. But I highly doubt that's all I was taught.

[Seil]

1/2(4x - 8) - 2/3(-3x + 6) = 4x - 8
distribute the half and negetive two thirds

2x - 4 + 2x - 4 = 4x - 8

combine like terms

4x -8 = 4x -8

add 8 to both sides, divide by four

x=x

No definite solution

That's the part I'm screwing up on. I keep trying to "Solve" it, instead of what they want me to do. The answer is right, by the teacher's terms:

1/2(4x - 8) - 2/3(-3x + 6)
= 1/2(4x)+1/2(-8)-2/3(-3x)+2/3(6)
= 2x-4+2x-4
= 4x-8

The "/" in this case means a fraction, not division.

[Grimpond]

The "/" in this case means a fraction, not division.

I'm pretty sure thats how he did it. Unless my math is terribul too.

[Squall Leonhart]

I remember a while back I was actually studying algebra, calculus, equations and currently, probability & statistics. It was interesting, even though I failed Calculus I and I'm glad that's over with, but I kinda thought it was fun while it lasted, mainly, because I had a very good professor.

Still, I don't really know how you can actually use Equations in a Logistics career...

[Wigmund]

My horrific performance in Calculus and Physics due to among other things my inability to comprehend large equations in which it is nothing but letters and symbols with no real tangible link to the real world has prompted me to decide that I no longer want to be a Physics major (also stress, anxiety and depression had a hand in this).

Next semester I'm exploring Geology, Biology and Chemistry to see if I like what I find there. They have math, but at least it's linked to something and it doesn't feel like someone was making up shit as they went along. I've already passed the highest required math classes required for any of those majors, so that's gonna help.

[Eltargrim]

That's the part I'm screwing up on. I keep trying to "Solve" it, instead of what they want me to do. The answer is right, by the teacher's terms:

1/2(4x - 8) - 2/3(-3x + 6)
= 1/2(4x)+1/2(-8)-2/3(-3x)+2/3(6)
= 2x-4+2x-4
= 4x-8

The "/" in this case means a fraction, not division.

You've done the LHS (Left-hand-side) correctly, now compare it to the RHS.

They're the same.

You can then distill it down to x = x. That's the solution. X is an arbitrary number; it could be -10, 5000, 42, i; it doesn't matter. The equation given will hold no matter the value of x.

And that's it. Solved. Don't overthink things.

Locke: I feel your pain. This year saw a condensed course on ODEs, PDEs, and series solutions. I am just about done with Frobenius. Seriously, that fucker can go spin. I don't care how helpful his solutions are, reindexing things makes my head spin.

EDIT: My Lackadaisy compatriot, math in chemistry is very dependent on what route you take. A lot of algebra is a given, and you will see matrices if you head towards quantum disciplines. But it still feels like they make shit up unless you understand the fundamentals. Physics is actually really good for explaining stuff if you understand the first principles.

Edit edit: fractions and division are indistinguishable. 5x/3 is the same as 5 times x divided by 3.

Edit edit edit: I too used to hate math. Then I realized that if I actually practice it's not that bad.

[Seil]

That was an example - it's not the one I did. I think my problem is that when I see "-4x+5(3-5x)" I think it means "-4x plus 5" instead of just negative-four-x positive-five.

[Eltargrim]

That is a problem. Order of operations is important. Brackets are not implied, and coefficients are very important. Coefficients!

[Squall Leonhart]

That was an example - it's not the one I did. I think my problem is that when I see "-4x+5(3-5x)" I think it means "-4x plus 5" instead of just negative-four-x positive-five.
5 multiplies (3-5x) and you get

-4x + 15 -25x.

Similar terms are reduced:

15 - 29x

Since there's no "=", that's as far as I can go, but it shouldn't be that hard.

[Sithdarth]

Maybe later tonight I'll blow all your minds with Fractals, Modular Arithmetic, and the fundamental theory behind RSA encryption. I can teach you how to do RSA encryption by hand and prove to you why it works. I can also do things with number theory that'll really make you think I'm magic.

[Squall Leonhart]

By the way, this (http://www.wolframalpha.com/) might help you in studying and checking homeworks and stuff like that. I know it did with me.

[Wigmund]

All mathematicians are charlatans who make up stuff so they'll have jobs making the rest of humanity wonder what the fuck they're working on.

We need to return to the good old way of experimentation where you tried various things until shit stopped exploding. Fuck calculations, hit that shit with lightning until it starts working.

EDIT: My Lackadaisy compatriot, math in chemistry is very dependent on what route you take. A lot of algebra is a given, and you will see matrices if you head towards quantum disciplines. But it still feels like they make shit up unless you understand the fundamentals. Physics is actually really good for explaining stuff if you understand the first principles.

Algebra I can handle, same with matrices to a certain extent; complex differentiable calculus in regards to variable fields with no real understanding in how the fuck it relates to anything at all on the other hand...

As for the physics and mathematics requirements of the fields I'm looking into, I've already completed the required courses - so I'm not too worried there.

[rpgdemon]

I deal with math as a programmer and web designer, but it's definitely not calc. Or at least I HAVEN'T used calc. I had to take Calc I twice to pass it, but part of that is because the first time around was at 8AM when my insomniac roomie kept me up until at least 2AM nightly, if not later. There are days I ended up in class without remembering how I got there.

I do remember some of the stuff, like integration and deintegration, vaguely, but only the shortcuts. And, well, stuff like what "5!" means, if not the name, and sigma notation. But I highly doubt that's all I was taught.

Trig, on the other hand, is insanely useful in a myriad of situations.

[Grimpond]

Fuckin' Nerds!.

[Professor Smarmiarty]

Algebra I can handle, same with matrices to a certain extent; complex differentiable calculus in regards to variable fields with no real understanding in how the fuck it relates to anything at all on the other hand...


Quantum chemistry does get pretty dicey, it's all noncommutative and stuff. On the other hand I do quantum chemistry and my mathskills are atrocious- computers save my ass everyday!

[Seil]

B rackets!
E xponents!
D ivision!
M ultiplication!
A ddition!
S ubtraction!

[synkr0nized]

Math is stupid. It would be so much simpler if we were analyzing poetry or something.

I can see the appeal of being able to make up an answer and still be correct, but the right/wrong division of logic is much more straightforward.

[The Artist Formerly Known as Hawk]

Fuckin' Nerds!.

Agreed. I have no fucking clue what anyone in this thread is talking about!

We need to return to the good old way of experimentation where you tried various things until shit stopped exploding. Fuck calculations, hit that shit with lightning until it starts working

YES!

[BloodyMage]

Your problem is that you're doing maths. Solution: stop.

[A Zarkin' Frood]

School: In two weeks I'll be done with it, like, forever... until I decide to study some more. Which may happen, because I hate my job.

Maths: If I didn't miss two or three whole years I'd probably be a math wizard or something. Maybe not, I can't know.
Also: I'm pretty sure fractions are divisions for retards who don't know what a comma is.

[Eltargrim]

Quantum chemistry does get pretty dicey, it's all noncommutative and stuff. On the other hand I do quantum chemistry and my mathskills are atrocious- computers save my ass everyday!

<3 Maple and Matlab. Great if you are actually doing the math; less great if you have to show work.

[Corel]

So does this mean the heading of desks minus Seil is equal to Maths?

I've been doing it wrong all these years.

[A Zarkin' Frood]

I believe "math" may be a variable here.

[Melfice]

We need to return to the good old way of experimentation where you tried various things until shit stopped exploding. Fuck calculations, hit that shit with lightning until it starts working.

Hell naw.
We need to go back to the good old way where you try various things until shit start exploding.

Alternatively, we just turn on the telly and watch Mythbusters. I mean, you get the same result, minus sweating on our side.

[Revising Ocelot]

School was good preparation for life. I thought only 50% of the school population that were bullies and/or jerks hated me for my ginger hair, but then I found that 50% of the world hates ginger hair. It's an acceptable variant of racism.

Meh!

[Sithdarth]

Ok so here's a quick primer on modular (congruence) arithmetic. Basically it goes like this:
a ≡ b mod m ↔ a - b = k*m where a, b, m, and k are all integers.

So for example:
5 ≡ 2 mod 3
5 ≡ 1 ≡ -3 mod 4
5 ≡ -1 mod 6

Basically if a = q*m + r, 0 ≤ r ≤ (m-1) then a - r = q*m and a ≡ r mod m where r is called either the remainder or the least non-negative residue of a mod m.

Now there are some nice rules for modular arithmetic. For example, if a ≡ b mod m and c ≡ d mod m then:
a + c ≡ b + d mod m
a - c ≡ b - d mod m
a*c ≡ b*d mod m

Here are a few examples:
What is the remainder when 123*257*425 is divided by 7?
123 ≡ 4 mod 7
257 ≡ 5 mod 7
425 ≡ 5 mod 7

123*257*425 ≡ 4*5*5 = 100 ≡ 2 mod 7
So the remainder is 2.

What is the remainder of 37*77 when divided by 39?
37 ≡ 37 mod 39 and 37 ≡ -2 mod 39
77 ≡ 38 mod 39 and 38 ≡ -1 mod 39

37*77 = (-2)(-1) ≡ 2 mod 39
So the remainder is 2.

Just one more rule now:
If n > 0 and a ≡ b mod m then a^(n) ≡ b^(n) mod m
So for example:
What is the remainder when 2^(13) is divided by 33?

2^(5) ≡ 32 ≡ -1 mod 33
2^(13) = (2^(5))^2 * 2^(3) = (-1)^(2) * 8 ≡ 8 mod 33
So the remainder is 8.

Just for fun here is Little Fermat's Theorem:
Given a prime integer P two things must be true:

i) For any integer a, a^(P) ≡ a mod P
ii) If a is not a multiple of P then a^(P-1) ≡ 1 mod P

With this you have the mathematical foundation to understand RSA encryption which I'll write up later.

PS: That's only a small fraction of what I've learned about modular arithmetic this semester. There are ways to do pretty much all of the equation solving you do normally with modular arithmetic which can solve some pretty unusual problems. Then of course we moved into fractals. I'm contemplating back tracking a bit and showing you some of the spherical and hyperbolic geometry I did this semester too.

[Seil]

You lost me about the time you wrote "≡." What the crap is a "≡?"

[Sithdarth]

It means congruent. It's like equals but stronger. Things that are congruent need not be strictly equal but things that are equal are always congruent. I plain English it's a bit like "the same as" or "similar to".

Edit: and I have no idea why it replaced some of the subtraction signs and the ' with question marks.

[Seil]

It's like equals but stronger.

Wut? (http://www.fresnobeehive.com/archives/upload/2007/03/keanu-reeves-big.jpg)

[Sithdarth]

Wait I said that backwards congruence is actually weaker than equals. It's an easy mistake to make. For example, take similarity and congruence from geometry. All congruent triangles are similar but not all similar triangles are congruent. Congruence is a stronger statement than similarity in geometry. Similarity means something like the same shape while congruent means same shape and size (i.e. it is more restrictive and therefore stronger). Likewise in modular arithmetic congruence is weaker because everything that is equal is also congruent but everything that is congruent is not equal. For all practical purposes you can treat congruence as equals in modular arithmetic.

It is showing up as three horizontal lines stacked on top of each other like an equals sign with an extra line right? Because that's how its supposed to look and I have no idea if it's in any sort of standard font package.

[Eltargrim]

That is how it shows up, and you're the first person I've seen use congruent outside of the uni. I also like your taste in avatars, dimension-warping hobo.

[phil_]

Yeah, all that math stuff Sith just posted, the modular equations and all that? Just looking at it makes me want to go on a world-spanning quest to find the god-slaying sword and kill the spirit of math.

[Professor Smarmiarty]

My ex was a math fine arts major and would like it was all numbers where NUMBERS SHOULDN'T BE. Occasionaly there would be a plus sign and I'd be like- I know what that does.

[Pip Boy]

Ok so here's a quick primer on modular (congruence) arithmetic. Basically it goes like this:
a ≡ b mod m ↔ a - b = k*m where a, b, m, and k are all integers.

So for example:
5 ≡ 2 mod 3
5 ≡ 1 ≡ -3 mod 4
5 ≡ -1 mod 6

Basically if a = q*m + r, 0 ≤ r ≤ (m-1) then a - r = q*m and a ≡ r mod m where r is called either the remainder or the least non-negative residue of a mod m.

Now there are some nice rules for modular arithmetic. For example, if a ≡ b mod m and c ≡ d mod m then:
a + c ≡ b + d mod m
a - c ≡ b - d mod m
a*c ≡ b*d mod m

Here are a few examples:
What is the remainder when 123*257*425 is divided by 7?
123 ≡ 4 mod 7
257 ≡ 5 mod 7
425 ≡ 5 mod 7

123*257*425 ≡ 4*5*5 = 100 ≡ 2 mod 7
So the remainder is 2.

What is the remainder of 37*77 when divided by 39?
37 ≡ 37 mod 39 and 37 ≡ -2 mod 39
77 ≡ 38 mod 39 and 38 ≡ -1 mod 39

37*77 = (-2)(-1) ≡ 2 mod 39
So the remainder is 2.

Just one more rule now:
If n > 0 and a ≡ b mod m then a^(n) ≡ b^(n) mod m
So for example:
What is the remainder when 2^(13) is divided by 33?

2^(5) ≡ 32 ≡ -1 mod 33
2^(13) = (2^(5))^2 * 2^(3) = (-1)^(2) * 8 ≡ 8 mod 33
So the remainder is 8.

Just for fun here is Little Fermat's Theorem:
Given a prime integer P two things must be true:

i) For any integer a, a^(P) ≡ a mod P
ii) If a is not a multiple of P then a^(P-1) ≡ 1 mod P

With this you have the mathematical foundation to understand RSA encryption which I'll write up later.

PS: That's only a small fraction of what I've learned about modular arithmetic this semester. There are ways to do pretty much all of the equation solving you do normally with modular arithmetic which can solve some pretty unusual problems. Then of course we moved into fractals. I'm contemplating back tracking a bit and showing you some of the spherical and hyperbolic geometry I did this semester too.

Look out guy, I think witchcraft may be bannable offense on this forum.

[krogothwolf]

He's a witch! HE'S A WITCH!!!!

I use simple math for my daily life! Even work, all the crap math I learned through high school and college have become worthless to me and I have forgotten all it. All you need is addition, subtraction, multiplication and division. Oh and, NO ONE CARES WHEN THE TWO TRAINS WILL PASS EACH OTHER GOD DAMNIT! NO ONE!!!!

[Fungrus]

schnip

That's pretty interesting actually, but don't you do physics? What part of physics is modular arithmetic needed for?

[Seil]

To Mr. Sithdarth, my rebuttal:

http://www.gdargaud.net/Humor/Pics/MathSucks.jpg

I can see the appeal of being able to make up an answer and still be correct, but the right/wrong division of logic is much more straightforward.

Woah, just saw this. It's not that I enjoy the fact that many answers can be right in Lit while in Math only one answer is right for one problem.

It's that most of my English profs. are really wacky guys, while me Math teacher is insane. Also, I can't wrap my head around numbers, but writing, reading, analyzing, critiquing... English just comes easier to me, alright?

[The Artist Formerly Known as Hawk]

Ok so here's a quick primer on modular (congruence) arithmetic. Basically it goes like this:
a ≡ b mod m ↔ a - b = k*m where a, b, m, and k are all integers.

So for example:
5 ≡ 2 mod 3
5 ≡ 1 ≡ -3 mod 4
5 ≡ -1 mod 6

Basically if a = q*m + r, 0 ≤ r ≤ (m-1) then a - r = q*m and a ≡ r mod m where r is called either the remainder or the least non-negative residue of a mod m.

Now there are some nice rules for modular arithmetic. For example, if a ≡ b mod m and c ≡ d mod m then:
a + c ≡ b + d mod m
a - c ≡ b - d mod m
a*c ≡ b*d mod m

Here are a few examples:
What is the remainder when 123*257*425 is divided by 7?
123 ≡ 4 mod 7
257 ≡ 5 mod 7
425 ≡ 5 mod 7

123*257*425 ≡ 4*5*5 = 100 ≡ 2 mod 7
So the remainder is 2.

What is the remainder of 37*77 when divided by 39?
37 ≡ 37 mod 39 and 37 ≡ -2 mod 39
77 ≡ 38 mod 39 and 38 ≡ -1 mod 39

37*77 = (-2)(-1) ≡ 2 mod 39
So the remainder is 2.

Just one more rule now:
If n > 0 and a ≡ b mod m then a^(n) ≡ b^(n) mod m
So for example:
What is the remainder when 2^(13) is divided by 33?

2^(5) ≡ 32 ≡ -1 mod 33
2^(13) = (2^(5))^2 * 2^(3) = (-1)^(2) * 8 ≡ 8 mod 33
So the remainder is 8.

Just for fun here is Little Fermat's Theorem:
Given a prime integer P two things must be true:

i) For any integer a, a^(P) ≡ a mod P
ii) If a is not a multiple of P then a^(P-1) ≡ 1 mod P

With this you have the mathematical foundation to understand RSA encryption which I'll write up later.

PS: That's only a small fraction of what I've learned about modular arithmetic this semester. There are ways to do pretty much all of the equation solving you do normally with modular arithmetic which can solve some pretty unusual problems. Then of course we moved into fractals. I'm contemplating back tracking a bit and showing you some of the spherical and hyperbolic geometry I did this semester too.



God damn that's a lot of maths. I have only 2 questions;

a) Is any of it revelvant to making time travel possible?

and b) Is any of it relevant to making the flying car possible?

[Wigmund]

God damn that's a lot of maths. I have only 2 questions;

a) Is any of it revelvant to making time travel possible?

and b) Is any of it relevant to making the flying car possible?

No, as a) involves hitting one's head on a toilet seat and stealing plutonium from Libyans, and b) involves using a) to travel into the future and steal flying car technology to return to now so that b) will be possible so that you can use a) to travel into the future to steal b).

[Sithdarth]

That's pretty interesting actually, but don't you do physics? What part of physics is modular arithmetic needed for?

Well it's actually closely tied to group theory which is important to the Standard Model as well as String and M-theory. As the resident string theorist at my College would say "Theoretical Physics is a science locally isomorphic to Mathematics." On top of that I picked up a secondary major in Mathematics so now I do as much Math for Math's sake as I do Math for Physic's sake.

God damn that's a lot of maths. I have only 2 questions;

a) Is any of it revelvant to making time travel possible?

and b) Is any of it relevant to making the flying car possible?

I don't know, maybe. It depends on what string and M-theory come up with and how important group theory becomes to them. It is however the very foundation of RSA (also known as Public Key) encryption which is what every bank ever uses to do transactions and keep your information safe. Without modular arithmetic we wouldn't have online banking. Hell we wouldn't have online stores or anything else online having to do with finances. Speaking off I'll see about getting a little primer on RSA encryption written up.

To Mr. Sithdarth, my rebuttal:

*picture removed*


Well that's just because you haven't learned to love Math yet.

Edit: Ok so here is a little bit on RSA encryption:
The first thing you need is a couple of secret numbers that you tell no one.
You will need two prime numbers with as many digits as possible, let's call them p and q, and an integer N greater than zero such that gcd(N,(p-1)(q-1)) = 1. (That is to say N and the product (p-1)(q-1) have no common factors.)

Then you use these numbers to find an integer M such that M*N ≡ 1 mod (p-1)(q-1). There is a very easy way to do this using the Euclidian Algorithm.

The Euclidian Algorithm works like this:
If a=q*b + r then gcd (a,b) = gcd (b,r) (gcd stands for greatest common divisor)
Which means you can work out a gcd like this:
a = q1*b + r1
b = q2*r1 + r2
r1 = q3*r2 + r3
r2 = q4*r3 + r4
and so on until you hit zero

Some examples:
Find gcd (252,198)
252 = 198*1 + 54
198 = 54*3 + 36
54 = 36*1 + 18
36 = 18*2 + 0
So gcd(252,198) = 18

Now we can use this to write gcd(252,198) as a linear combination of 252 and 198 by running the algorithm backwards like so:
18 = 54 - 36*1 (from the third equation)
36 = 198 - 54*3 (from the second equation)
Putting them together:
18 = 54 - (198 - 54*3)
18 = 54*4 - 198
54 = 252 - 198*1 (from first equation)
Putting the last two above together gives:
18 = (252 - 198*1)*4 - 198
18 = 252*4 - 198*5
And thus is 18 written as a linear combination of 252 and 198.

Now you can use this procedure to find an M such that M*N ≡ 1 mod (p-1)(q-1). For example:
Let p = 11, q = 13, and N = 7 then:
M*7 = 1 mod (10*12)
7*M +z*120 = 1
120 = 7*17 + 1
7 = 1*7 + 0
Then writing 1 as a linear combination of 120 and 7 we have:
120 - 7*17 = 1 so M = -17 ≡ 103 mod 120 (120 - 17 = 103)

Now that you have M you publish it and the product p*q (but never p or q by themselves). So when someone wants to send you a message say a number X they do it like so:
Y = X^(M) mod (p*q) where Y is the number they send you (which must be reduced by modular arithmetic so that is less than p*q) and X is the number they wanted to encrypt.
Then to decode the message you do this:
Y^(N) mod (p*q) where N is your secret exponent. This will give you back the original X.

To continue from the example above say someone wants to send you the letter C and you agreed previously that A = 0, B = 1, C = 2, and so on. Thus:
Y = 2^(103) mod 143 (since 11*13 = p*q = 143)
At which point we are going to need a method called repeated squaring to get to Y which goes something like this:
2 ≡ 2 mod 143
2^2 ≡ 4 mod 143
2^4 ≡ 16 mod 143
2^8 ≡ 256 ≡ 113 mod 143
2^16 ≡ 113^2 ≡ 12769 ≡ 42 mod 143
2^32 ≡ 42^2 ≡ 1764 ≡ 48 mod 143
2^64 ≡ 48^2 ≡ 16 mod 143

2^103 = (2^32)^(3) * 2^(4) * 2^(2) * 2^(1) = 48^2 *48 *16 * 4 *2 = 16 * 16 * 48 * 4 * 2 = 113 * 48 * 4 * 2 = 43392 ≡ 63 mod 143
Thus they send you Y = 63.

Then to get back the message you do this:
63^7 mod 143
63^2 ≡ 108 mod 143
63^3 ≡ 83 ≡ -60 mod 143
63^4 ≡ 81 ≡ -62 mod 143

63^7 = 63^4 * 63^3 = (-60)(-62) = 3720 ≡ 2 mod 143
Thus you have decoded 63 into 2 and know that they send you the letter C.

That in a nutshell is RSA encryption.

[The Artist Formerly Known as Hawk]

I don't know, maybe. It depends on what string and M-theory come up with and how important group theory becomes to them. It is however the very foundation of RSA (also known as Public Key) encryption which is what every bank ever uses to do transactions and keep your information safe. Without modular arithmetic we wouldn't have online banking. Hell we wouldn't have online stores or anything else online having to do with finances. Speaking off I'll see about getting a little primer on RSA encryption written up.


... I'll take that as a "No" then.