Author Topic: The Math Lovers Club v. 3.1416  (Read 35448 times)

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Offline Jamesman42

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Re: The Math Lovers Club v. 3.1416
« Reply #175 on: February 10, 2012, 06:29:06 AM »
Anyway, I might as well formally introduce myself to the Club. I'm a first-year at the University of Chicago. I'm a computer science major, but I'm going to have to take plenty of math in the next few years. It's not my favorite thing, but I do like it and I have at least a little bit of a knack for it.

Yeah, I can tell you are good at understanding your math, keep it up! You're my go to guy for complex numbers now (essentially making you my forum bitch). There is no arguing that, ask darklol.


Offline Jamesman42

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Re: The Math Lovers Club v. 3.1416
« Reply #176 on: February 11, 2012, 01:17:46 PM »
Question regarding that complex number problem...why we can assume that x doesn't equal 0, when we haven't defined that...we end up dividing by x at one point.

Offline theseoafs

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Re: The Math Lovers Club v. 3.1416
« Reply #177 on: February 11, 2012, 01:41:18 PM »
Yeah, I noticed that too. Probably best to amend the conclusion by saying the |z| = 1 if x=/=0.

Offline Jamesman42

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Re: The Math Lovers Club v. 3.1416
« Reply #178 on: February 11, 2012, 02:11:27 PM »
Haha, that's what I told my friend IRL, that was my amendment to it. She isn't satisfied with that answer. She says "We can't assume that x =/= 0 since they don't tell us that.

Offline theseoafs

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Re: The Math Lovers Club v. 3.1416
« Reply #179 on: February 11, 2012, 02:58:10 PM »
Well, unless there's some other, more clever solution we missed, that's the only way the proof works.

Offline 73109

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Re: The Math Lovers Club v. 3.1416
« Reply #180 on: February 11, 2012, 02:58:59 PM »
University of Chicago, eh? That's my #2 choice.

Offline theseoafs

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Re: The Math Lovers Club v. 3.1416
« Reply #181 on: February 11, 2012, 03:00:12 PM »
This means that you have good taste.  ;) Obviously I'll be happy to answer any questions you have about it.

Offline RuRoRul

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Re: The Math Lovers Club v. 3.1416
« Reply #182 on: February 11, 2012, 03:40:43 PM »
Hey, I'm a third year Maths student and I also work as a tutor for first and second years at my university. Just about that complex number problem, particularly in regards to the whole x=/=0 thing:

Let w = u +iv (i.e. real and imaginary part), but Im(w) = 0 so w = u (where u is real)

From the line  w(z^2 + 1) = z:
u(x^2 - y^2 +1 +2ixy) = x +iy

Equate real and imaginary:
x = u(x^2 - y^2 +1)   and     y = 2xyu

Look at the second of these simultaneous equations first: y = 2xyu  => y - 2xyu = 0 => y(1 - 2xu) = 0.

Since we are given y =/= 0 we have (1 - 2xu) = 0. Looking at this equation, if x = 0 then we would have 1 = 0, which means that there is no solution with x = 0  for these two simultaneous equations. So we're not just assuming x=/=0, we've arrived at the conclusion that x=/=0 through our working.

We can then put u=1/(2x) and substitute that into the first equation, which with a little bit of working leads to x^2 +y^2 = 1

From there it should be clear to anyone doing a class involving complex numbers that |z| = 1. There is essentially no step in working between those two lines, you just need to know the definition of the modulus of a complex number as thesoaf said.

Note: Just looking at the given information of the problem, look what happens when we put x=0, so z = iy (purely imaginary)

(We have that y=/=1 here, because we are given (z^2+1)=/=0 which if x=0 => y=/=1)

w=z/(z^2 + 1) would give w = yi / (1 - y^2) = i (y/(1-y^2))       

This is a purely imaginary number. But we are given that Im(w) = 0, which would mean that y=0. But we are also given y=/=0, so assuming x=0 and arriving at y=0 is proof by contraciction that x=/=0.

So it's never just assumed that x=/=0. Even though we aren't explicitly given that in the problem, x=/=0 is implied by the two bits of information we are given, namely that y=/=0 and Im(w)=0.
« Last Edit: February 11, 2012, 03:52:50 PM by RuRoRul »

Offline Jamesman42

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Re: The Math Lovers Club v. 3.1416
« Reply #183 on: February 11, 2012, 03:52:41 PM »
:clap:

Offline MrBoom_shack-a-lack

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Re: The Math Lovers Club v. 3.1416
« Reply #184 on: November 11, 2012, 09:33:54 AM »
I always love when someone show in a simple way of how amazing and overwhelming math and numbers can be:

https://www.youtube.com/watch?feature=player_embedded&v=kPBlOdYZCic
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Offline jsem

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Re: The Math Lovers Club v. 3.1416
« Reply #185 on: November 11, 2012, 12:29:42 PM »
Except he can't be 100% certain, only nearly certain.

Offline Ħ

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Re: The Math Lovers Club v. 3.1416
« Reply #186 on: November 11, 2012, 01:28:30 PM »
"All great works are prepared in the desert, including the redemption of the world. The precursors, the followers, the Master Himself, all obeyed or have to obey one and the same law. Prophets, apostles, preachers, martyrs, pioneers of knowledge, inspired artists in every art, ordinary men and the Man-God, all pay tribute to loneliness, to the life of silence, to the night." - A. G. Sertillanges

Offline rumborak

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Re: The Math Lovers Club v. 3.1416
« Reply #187 on: November 11, 2012, 06:35:58 PM »
So, a bit of a longer story: My company has been hiring like crazy lately, but we have a really had time finding capable people. One thing we make them all do now is to write a code example. The task is to write a small simulation of two cars racing each other, with the trick that each car has a certain probability of actually moving per turn. The result of the simulation is how many car A won over car B after 100 races.
So, while the coding exercise itself isn't all too hard (even though it successfully weeds out the bad ones), we also casually ask the question "does the simulation outcome agree with your mathematical analysis?"
Thing is, the mathematical derivation is nowhere straightforward. None of the candidates ever got anywhere, and I'm pretty sure none of our guys knows what even the correct derivation is. So, this weekend I rectified the issue by deriving the probability of car A winning. What was really exhilerating was that my derivation agreed exactly with the outcome of one candidate's program.  It was all infinite sums of conditional probabilities and shit, and within a few seconds my program spit out the same number as the simple simulation took half an hour to do.
"I liked when Myung looked like a women's figure skating champion."

Offline SeRoX

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Re: The Math Lovers Club v. 3.1416
« Reply #188 on: November 11, 2012, 06:46:33 PM »
Even I finished genetic engineering my only favourite subject is not biology, at least overall, it's math. I think I'm really good at it. The only reason I didn't choose it before starting the university is biology (genetic and evolution)'s been my first love since collage. Plus, biology upgrades itself constantly and takes you into very big world you can't even imagine. But still math remains as my secret love inside.
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Offline Ħ

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Re: The Math Lovers Club v. 3.1416
« Reply #189 on: November 11, 2012, 06:50:07 PM »
I love math for the fact that you just can't argue with it. It is the most objective, truth-preserving language out there.
"All great works are prepared in the desert, including the redemption of the world. The precursors, the followers, the Master Himself, all obeyed or have to obey one and the same law. Prophets, apostles, preachers, martyrs, pioneers of knowledge, inspired artists in every art, ordinary men and the Man-God, all pay tribute to loneliness, to the life of silence, to the night." - A. G. Sertillanges

Offline rumborak

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Re: The Math Lovers Club v. 3.1416
« Reply #190 on: November 11, 2012, 06:54:05 PM »
The weird part is, the math I deal with at work is never completely accurate. It's all probabilities and approximations. It's essentially the engineers approach to math.
That's why I loved Nate Silver's approach to election prediction. He never predicted anything really; all he gave was probabilities of events.
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Offline kári

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Re: The Math Lovers Club v. 3.1416
« Reply #191 on: November 12, 2012, 12:57:18 AM »
So, a bit of a longer story: My company has been hiring like crazy lately, but we have a really had time finding capable people. One thing we make them all do now is to write a code example. The task is to write a small simulation of two cars racing each other, with the trick that each car has a certain probability of actually moving per turn. The result of the simulation is how many car A won over car B after 100 races.
So, while the coding exercise itself isn't all too hard (even though it successfully weeds out the bad ones), we also casually ask the question "does the simulation outcome agree with your mathematical analysis?"
Thing is, the mathematical derivation is nowhere straightforward. None of the candidates ever got anywhere, and I'm pretty sure none of our guys knows what even the correct derivation is. So, this weekend I rectified the issue by deriving the probability of car A winning. What was really exhilerating was that my derivation agreed exactly with the outcome of one candidate's program.  It was all infinite sums of conditional probabilities and shit, and within a few seconds my program spit out the same number as the simple simulation took half an hour to do.
Now I have to try this. Could you give a little more details?

You and me go parallel, together and apart

Offline rumborak

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Re: The Math Lovers Club v. 3.1416
« Reply #192 on: November 12, 2012, 07:48:34 AM »
Edit: Changed my mind about the post.
« Last Edit: November 12, 2012, 08:01:26 AM by rumborak »
"I liked when Myung looked like a women's figure skating champion."

Offline Tanatra

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Re: The Math Lovers Club v. 3.1416
« Reply #193 on: January 20, 2013, 06:08:50 PM »
Thought I'd bump this thread to show everyone a prank that I decided to play on my Advance Natural Resource Economics instructor.

The class deals very heavily in optimal control theory, which entails optimization across a time path. As an example, it could be used to find a differential equation representing the optimal ore extraction schedule for a gold mine - based on current and projected gold prices, the rate of extraction, and constrained by the amount of gold reserves available. It's still highly theoretical and at present only appears in economic research papers, but I find it an interesting topic.

I just got back from the classroom, where an unorthodox application of optimal control manifested during the night, or at least that's the story that I'm prepared to tell. Maybe ghosts wrote it up on the white-board, it would certainly be fitting:


Offline MrBoom_shack-a-lack

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Re: The Math Lovers Club v. 3.1416
« Reply #194 on: September 29, 2013, 02:01:37 PM »
Interesting little nugget in The Simpsons:

https://www.youtube.com/watch?v=ReOQ300AcSU
"I said to Nigel Tufnel, 'The door is open if you want to do anything on this record,' but it turns out Nigel has a phobia about doors." /Derek Smalls

Online SomeoneLikeHim

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Re: The Math Lovers Club v. 3.1416
« Reply #195 on: September 29, 2013, 02:30:10 PM »
"We can walk our road together, if our goals are all the same
We can run alone and free, if we pursue a different aim"

Offline Implode

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Re: The Math Lovers Club v. 3.1416
« Reply #196 on: September 29, 2013, 02:53:37 PM »
Awesome channel. Subbed.

Offline Dublagent66

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Offline Kotowboy

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Re: The Math Lovers Club v. 3.1416
« Reply #198 on: October 02, 2013, 12:13:31 PM »
Quote
Re: The Math Lovers Club v. 3.1416

Maths.  :hat


:neverusethis:

Offline Implode

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Re: The Math Lovers Club v. 3.1416
« Reply #199 on: October 02, 2013, 02:44:23 PM »

Offline Kotowboy

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Re: The Math Lovers Club v. 3.1416
« Reply #200 on: October 02, 2013, 02:53:00 PM »
Can't watch. ginger troll will eat me.

Offline MrBoom_shack-a-lack

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Re: The Math Lovers Club v. 3.1416
« Reply #201 on: August 04, 2014, 03:43:50 AM »
So i've heard about The Curta Calculator but never seen one or really gave it any deep thought on how complicated it really is. Here's a nice little video demononstration:

https://www.youtube.com/watch?v=P0cGjC62XRQ

A genious invention!

Here's another video:

https://www.youtube.com/watch?v=ZDn_DDsBWws

and a simulation:

https://www.curta.de/kr34/curta_simulator_en.htm
« Last Edit: August 04, 2014, 04:09:33 AM by MrBoom_shack-a-lack »
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Offline Onno

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Re: The Math Lovers Club v. 3.1416
« Reply #202 on: August 04, 2014, 05:40:56 AM »
That's really cool.

Offline Kotowboy

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Re: The Math Lovers Club v. 3.1416
« Reply #203 on: August 04, 2014, 04:27:43 PM »
I love Math.






Even more than I love Physic.


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Offline Orbert

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Re: The Math Lovers Club v. 3.1416
« Reply #204 on: August 04, 2014, 04:49:53 PM »
Never thought about it that way.

I suppose Brits say "maths" because it's short for "mathematics" which is plural.  Americans just say "math" because it's shorter.

But "physics" is short for "physical science" which is singular, so "physic" would be consistent.

But that sounds dumb so we say "physics".  Also, American English is rarely consistent.

What do Brits say for "physical science"?

Offline Kotowboy

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Re: The Math Lovers Club v. 3.1416
« Reply #205 on: August 04, 2014, 04:52:29 PM »
I don't even know what that is :P

Offline Sir GuitarCozmo

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Re: The Math Lovers Club v. 3.1416
« Reply #206 on: October 01, 2014, 01:50:14 PM »
Okay, math people, I have to check Jr's algebra quizzes to see what he missed and why he missed them.  This was one of the questions and I'm struggling with the proper way to solve it:

One weight class at a wrestling match has wrestlers that weigh between 152 pounds and 160 pounds, inclusive. Write an absolute value inequality describing the acceptable weight in this class.

Help?

Offline rumborak

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Re: The Math Lovers Club v. 3.1416
« Reply #207 on: October 01, 2014, 02:19:41 PM »
Isn't the answer just....

152lbs <= x <= 160lbs

?
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Offline Sir GuitarCozmo

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Re: The Math Lovers Club v. 3.1416
« Reply #208 on: October 01, 2014, 02:22:49 PM »
I would assume so.  He'd put the following:

160≥|x|≥152

Which is essentially the same thing.  It was marked as incorrect.

Offline rumborak

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Re: The Math Lovers Club v. 3.1416
« Reply #209 on: October 01, 2014, 02:25:04 PM »
It's not quite the same thing, since it would allow for negative weights, which makes no sense. I would flag that as false as a teacher too, since Jr clearly just plugged the "|..|" in there because the problem statement had the words "absolute value" in it.
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