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First year Math - A TA's Perspective

 
Old 08-26-2009 at 02:44 PM   #76
Mowicz
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Quote:
Originally Posted by mellye View Post
Looking at it more closely, I think the whole borrow 10 part of the hindu arabic system just sorta happens in my head without me knowing... Since it's the easier of the steps... I think.
The problem is, you're faced with learning something new right? The new thing is always more difficult than what you know...like reverse polish notation for instance (I won't get into that, but wiki it if you're curious).

Let me break the Roman calculation down further:

I means 1
V means 5
X means 10
C means 100
M means 1000

Problem: CMLXXXII - CLVI

1) Start by looking at which letters appear in their proper order (that is, from biggest to smallest). C is 100, but it appears before M (1000) so you have to make a mental note that the C is out of order. (This of course, means the CM = 900, and is not MC = 1100). This is typically done by underlining the letters, or marking them in some other way:

CMLXXXII - CLVI

2) Cancel all the letters you see that are in order:

CMLXXXII - CLVI - Cancel the L's:
CMXXXII - CVI - Cancel the I's
CMXXXI - CV

3) For letters which appear out of order (ie. have underlines on one side and not the other)... ADD letters to the underlined side, and cancel them on the other:

CMXXXI - CV - Add a C to the LHS (left hand side), remove it from RHS (right hand side)
CCMXXXI - V

4) For each letter which does not appear in your expression, look for the next highest letter and 'break' it into smaller units (this is analogous to the concept of "borrowing")

CCMXXXI - V - Split one of the X's into VV (since 10 = 5+5)
CCMXXVVI - V

5) Repeat steps 1 - 4 until no letters remain on the RHS.

CCMXXVVI - V
CCMXXVI

And we're done. (:

Last edited by Mowicz : 08-26-2009 at 02:53 PM.
Old 08-26-2009 at 02:47 PM   #77
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Quote:
Originally Posted by EasternHeat View Post
But Mike, as we all know addition and subtraction is grade 2 stuff. Overall you need much more than that. I mean if you want to have fun using the Roman numerals to add and subtract for fun, go ahead by all means
Well if you want to talk details, my point is that math is a dynamic thing...it's always changing, and it adapts to fit what is necessary at the time.

Romans didn't need much beyond the grade 2 stuff, so why make your system of arithmetic more ugly than needs be?

And I mean even now, with the advent of binary code, hexademical, and all these different 'bases' for counting (particularly in regards to computing), it's already changed substantially from even the Hindu-Arabic system.
Old 08-26-2009 at 02:48 PM   #78
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Ahhhhhh! My brain is on the verge of exploding! XD

PS- Hosni Mubarak sucks >.<, but Egypt doesn't haha =), and definitely agree about UAE. It's probably the only M.E. country that's doing something beneficial for themselves at the moment =/
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Old 08-26-2009 at 02:54 PM   #79
mellye
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Quote:
Originally Posted by Mowicz View Post
The problem is, you're faced with learning something new right? The new thing is always more difficult than what you know...like reverse polish notation for instance (I won't get into that, but wiki it if you're curious).

Let me break the Roman calculation down further:

I means 1
V means 5
X means 10
C means 100
M means 1000

Problem: CMLXXXII - CLVI

1) Start by looking at which letters appear in their proper order (that is, from biggest to smallest). C is 100, but it appears before M (1000) so you have to make a mental note that the C is out of order. (This of course, means the CM = 900, and is not MC = 1100)

2) Cancel all the letters you see that are in order:

CMLXXXII - CLVI - Cancel the L's:
CMXXXII - CVI - Cancel the I's
CMXXXI - CV

3) For letters which appear out of order... ADD letters to the left side, and cancel them on the right:

CMXXXI - CV - Add a C to the LHS (left hand side), remove it from RHS (right hand side)
CCMXXXI - V

4) For each letter which does not appear in your expression, look for the next highest letter and 'break' it into smaller units (this is analogous to the concept of "borrowing")

CCMXXXI - V - Split one of the X's into VV (since 10 = 5+5)
CCMXXVVI - V

5) Repeat steps 1 - 4 until no letters remain on the RHS.

CCMXXVVI - V
CCMXXVI

And we're done. (:
Oh wow. I think I see it now... I get what you mean by you'll never forget a one...

This system is really... amazing... actually... It's so intriguing. I'm having fun with this. haha.
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Old 08-26-2009 at 02:55 PM   #80
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Okay so I went back and read the thread, I think I get it too. It's so complex for something that we take so easily! XD

Thank you for the enlightenment Mowicz
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Old 08-26-2009 at 02:56 PM   #81
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Quote:
Originally Posted by Mowicz View Post
Well if you want to talk details, my point is that math is a dynamic thing...it's always changing, and it adapts to fit what is necessary at the time.

Romans didn't need much beyond the grade 2 stuff, so why make your system of arithmetic more ugly than needs be?

And I mean even now, with the advent of binary code, hexademical, and all these different 'bases' for counting (particularly in regards to computing), it's already changed substantially from even the Hindu-Arabic system.
I know that haha I wasn't saying it wasn't good at the time but of course it changed to the other system because it was much more needed and I highly doubt binary code will replace this system in the general sense because students are simply not gonna be doing 00110100101001101 (plus the general population is getting dumber in the West its pretty sad...there's a rift between the smart and dumb the middle is disappearing...same with the middle class poor/rich). However with computers and systems of course it will be used.
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Old 08-26-2009 at 03:00 PM   #82
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Quote:
Originally Posted by EasternHeat View Post
Yes I did watch a documentary about it. Though its also a bad thing since bankers are pretty much owning the world (not to mention starting world wars and crashing markets all to make money).
Was it Zeitgeist?
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Old 08-26-2009 at 03:08 PM   #83
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Quote:
Originally Posted by EasternHeat View Post
I highly doubt binary code will replace this system in the general sense
Define 'general sense.' The problem is, you're saying what applies particularly to you, right?

I mean to me, I haven't seen H-A arithmetic in at least 3 years...everything changes to integrals and summations and weird functions because you can do things with those that you can't do with H-A symbols...so I barely even use + - * and / (or rather I can, but I have to specify what they are...they're just symbols otherwise).

I know I'm not what you meant by 'general sense' but everything is relative to who you are...many people can't even understand the H-A arithmetic...often times through no fault of their own.

So the Take home point: It hasn't changed for some people and that's fine, if all your need is + - * and /...but to say 'general sense' doesn't really make sense because what is a general sense? Honestly in computing if you calculate in base 10...you're going to pull your hair out. The H-A system paved the way for modern mathematics...but then, Roman numerals paved the way for the H-A system (Not to mention Euclidean Geometry and all that jazz lead to the Cartesian plane, and just about every non-numeral aspect of math).

And as for me, it's already changed for me, and I rarely ever use it anymore in my studies...I use it in my day to day life when it's what's convenient. If I was doing straight addition / subtraction, ideally I'd convert it to Roman numerals and add those because I do them a lot faster and more accurately that way (but a lot of times I'm too lazy to do so haha).

Last edited by Mowicz : 08-26-2009 at 03:13 PM.
Old 08-26-2009 at 03:13 PM   #84
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Quote:
Originally Posted by jhan523 View Post
Was it Zeitgeist?
LOL no that movie was messed up...the first part about religion was really messed up.
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Old 08-26-2009 at 03:15 PM   #85
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Quote:
Originally Posted by EasternHeat View Post
LOL no that movie was messed up...the first part about religion was really messed up.
Lol, they were just showing the relationship between all the different gods/heroes/messiahs. But yeah, I watched the movie more for the economic conspiracy stuff.
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Old 08-26-2009 at 03:17 PM   #86
Bobby66
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Quote:
Originally Posted by Mowicz View Post
The problem is, you're faced with learning something new right? The new thing is always more difficult than what you know...like reverse polish notation for instance (I won't get into that, but wiki it if you're curious).

Let me break the Roman calculation down further:

I means 1
V means 5
X means 10
C means 100
M means 1000

Problem: CMLXXXII - CLVI

1) Start by looking at which letters appear in their proper order (that is, from biggest to smallest). C is 100, but it appears before M (1000) so you have to make a mental note that the C is out of order. (This of course, means the CM = 900, and is not MC = 1100). This is typically done by underlining the letters, or marking them in some other way:

CMLXXXII - CLVI

2) Cancel all the letters you see that are in order:

CMLXXXII - CLVI - Cancel the L's:
CMXXXII - CVI - Cancel the I's
CMXXXI - CV

3) For letters which appear out of order (ie. have underlines on one side and not the other)... ADD letters to the underlined side, and cancel them on the other:

CMXXXI - CV - Add a C to the LHS (left hand side), remove it from RHS (right hand side)
CCMXXXI - V

4) For each letter which does not appear in your expression, look for the next highest letter and 'break' it into smaller units (this is analogous to the concept of "borrowing")

CCMXXXI - V - Split one of the X's into VV (since 10 = 5+5)
CCMXXVVI - V

5) Repeat steps 1 - 4 until no letters remain on the RHS.

CCMXXVVI - V
CCMXXVI

And we're done. (:

Hotness. I love it.
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Old 08-26-2009 at 03:25 PM   #87
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Quote:
Originally Posted by jhan523 View Post
Lol, they were just showing the relationship between all the different gods/heroes/messiahs. But yeah, I watched the movie more for the economic conspiracy stuff.
I wonder why they didn't talk about Islam. They put everything else together. But then again Islam also validates the existence of Judaism and Christianity as well as Abraham, Moses, Jesus, etc.
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Old 08-26-2009 at 03:30 PM   #88
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Quote:
Originally Posted by EasternHeat View Post
I wonder why they didn't talk about Islam. They put everything else together. But then again Islam also validates the existence of Judaism and Christianity as well as Abraham, Moses, Jesus, etc.
I don't know and I really don't want to get into that issue. Zeitgeist should be taken with a grain of salt. I like the movie for how they made these crazy connections, but it's not like I completely believe in everything they say.

Anyways, this thread is supposed to be about Math...
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Old 08-26-2009 at 03:34 PM   #89
EasternHeat
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Quote:
Originally Posted by jhan523 View Post
I don't know and I really don't want to get into that issue. Zeitgeist should be taken with a grain of salt. I like the movie for how they made these crazy connections, but it's not like I completely believe in everything they say.

Anyways, this thread is supposed to be about Math...
I agree to both those statements

but...economics is all about math

haha
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Old 08-26-2009 at 03:37 PM   #90
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Haha, it's really interesting how this topic got side-tracked like that >.<.

Back to math ?
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