Mathematics

12:28 AM

off topic - complex analysis. What is $2^i$ where $i$ is the square root of $-1$? In particular, how can one show that it has absolute value $2$?

pjs36

Can you show that? I know that $i^i$ has infinitely many values, all real, and thus of varying sizes

The Substitute

Wolfram claims $2^i$ has absolute value 2, and a step in my text claimed $2^{x+iy}$ has absolute value $2^x$.

Stan Shunpike

@TedShifrin I have an unburstable bubble :P This is lots of fun.

Largely cuz I'm learning a lot along the way

JMoravitz

@TheSubstitute $2^i = e^{\ln(2^i)} = e^{i\ln 2}$

Ted Shifrin

Well, @Stan, I'm glad to hear it. I don't want to say it's good when it's not. :)

The Substitute

12:42 AM

@JMoravitz I don't see why the rightmost expression has magnitude 2

Stan Shunpike

@TedShifrin I wouldn't want you to. The point is to learn, make mistakes, and get better.

JMoravitz

@TheSubstitute continuing (since I haven't seen the lightbulb of realization go off yet), $e^{i\ln 2} = 1\cdot e^{i\ln 2}$. This is then the complex number with $r=1$ and $\ln 2 = \theta$, or equivalently we can see this as $(\cos(\ln 2) + i\sin(\ln 2))$

@TheSubstitute thats because it doesn't have magnitude two., it has magnitude one

Ted Shifrin

It doesn't, @TheSubstitute. But, @JMoravitz, remember that you need all the possible values of $\ln 2$. So you get $e^{i(\ln 2 + 2\pi i k)}$.

JMoravitz

Fair enough, I get lazy and use Log instead of log too often i suppose.

user147690

@Balarka "Any quotient of a ring by a maximal ideal is a simple ring. In particular, a field is a simple ring" - Wiki. But I need to understand the quotient of a ring first

The Substitute

12:45 AM

@jm324354, @JMoravitz thanks for clarification!

Clarinetist

Hello Math SErs

Starting tomorrow afternoon I will no longer be an actuary!!!!!!!!!!!!!!!!!

Ted Shifrin

We'll still call you Sir Actuary Clarinetist just to bug you, @Clarinet.

Clarinetist

LOL @TedShifrin

JMoravitz

I'm not familiar with all of the best runtime algorithms for various situations. Can anyone tell me if a more efficient algorithm exists for this?

0

A: What's the least number of combinations you need to determine who the most efficient members are?

I will assume the following: You are able to keep a log of productivity and don't forget information once it is learned You are only able to test groups of three for productivity, not individuals Individual productivity of each applepicker remains constant each day regardless of who they are p...

user147690

@Clarinetist Do actuaries make a ridiculous amount of money where you live?

Ted Shifrin

12:56 AM

hi @AlexC

JMoravitz

Sir Actuary @Clarinetist, what will you be doing next instead?

user147690

Hey @TedS, how is life?

Ted Shifrin

:) @JMoravitz

Mike Miller

morning

Clarinetist

@AlexClark I make less than the median income in this suburb of Des Moines, Iowa (I make $67k/year). My impression is that it depends on the company

Ted Shifrin

12:57 AM

Getting a bit frazzling, @AlexC, but I'll endure :P

I'm not saying goodnight again, @MikeM.

Clarinetist

@JMoravitz Lol, I will be working for Epic Systems. Chances are at least some of you have heard of that place

user147690

@TedShifrin Oh in general? Or because of us haha?

Clarinetist

@AlexClark Considering that your pay is mainly based on your exams, it is a ridiculous amount of money

columbus8myhw

@TheSubstitute wolframalpha.com/input/?i=%7C2%5Ei%7C

Ted Shifrin

No, not you personally, @AlexC, although I'd love to blame you :D

columbus8myhw

12:58 AM

It has a magnitude of 1

user147690

@TedShifrin Hahahaha

Ted Shifrin

Only the principal value, @columbus8myhw

user147690

@Clarinetist Something like this? payscale.com/research/AU/Job=Actuary/Salary

Mike Miller

Well, alright @Ted

Clarinetist

@AlexClark That's assuming you pass all of your exams (all 10ish of them)

@AlexClark I am stopping at 5.

Not interested in studying life insurance regulations.

user147690

1:00 AM

@Clarinetist Noone is I am sure, they are just interesting in earning more money ;)

Ted Shifrin

I think some really are interested, @AlexC.

Mike Miller

Different people have different tastes.

I have friends who have a hell of a time with excel.

user147690

Oh really? Wow that is a surprise

Ted Shifrin

Well, I've enjoyed mastering LaTeX for writing books ... :P

user147690

(not the excel part: I enjoy excel myself)

Clarinetist

1:01 AM

@AlexClark True, but I think this whole money rat race has driven me nuts. Hence another reason for me to get out

Mike Miller

:P

Clarinetist

I'm looking to get away from Excel since I've used it daily for the last 9 months...

Ted Shifrin

Absolutely, @Clarinetist. You should enjoy what you do for work.

Well, you will be doing all sorts of SAS and R programming, probably.

Clarinetist

@TedShifrin Yep, of course :) Those will be in my first two M.S. classes

user147690

Does Artin cover rings? I can't recall(and I suspect not)

Ted Shifrin

1:02 AM

Of course, @AlexC.

Mike Miller

@AlexClark Surely there's some subject you've studied and not enjoyed in university. Numerous majors in that subject will be able to say they love it. This is analagous.

Ted Shifrin

Rings, modules, and field theory are the latter half of the book.

Clarinetist

@MikeMiller You don't really learn what an actuary is until you've worked as one. The major has nothing to do with the actual job.

user147690

@MikeMiller True, but the high salary jobs that require you to learn about regulations are a little different in my expectations

user147690

@MikeMiller But yes, I found operations research immensely boring unfortunately

user147690

1:04 AM

@TedShifrin Okay thanks

user147690

@TedS Balarka said Artin's algebra is the best algebra text he has found. What do you think, or no opinion?

Clarinetist

@AlexClark They are quite different and no act sci major learns that stuff at a university.

user147690

@Clarinetist Where do you live again?

Clarinetist

@AlexClark Des Moines, Iowa

user147690

@Clarinetist I thought you were in Australia for some reason

Clarinetist

1:06 AM

Lol nope

user147690

@Clarinetist Sydney, I wonder who lives there, I know Benlim is Australian

user147690

Ahhhh

user147690

The Artist

Clarinetist

@AlexClark I know I've met an Aussie (is that what you call them?) on this site

@AlexClark But yes, 6 figures is quite common when you hit management

user147690

@Clarinetist In Australia 6 figures is quite common for lecturers in math

Clarinetist

1:08 AM

@AlexClark Dang, definitely not the case in the U.S.

user147690

@Clarinetist Yeah I was talking to Ted about that

Clarinetist

@AlexClark I make more than a lot of my professors.

Mike Miller

@Clarinetist: I'm claiming nothing about the job or the major or whatever. Just that there are undoubtedly people who enjoy it, and that this should not be surprising.

Clarinetist

Point taken

user147690

@MikeMiller Are there any jobs you think noone enjoys?

Mike Miller

1:09 AM

Retail.

Clarinetist

Janitorial

user147690

@MikeMiller Retail? I think there are people who like retail, in fact I know someone who does

user147690

lmao

user147690

@Clarinetist I have a friend who does janitorial and he enjoys talking to the client(assuming house cleaning counts)

Clarinetist

Interesting

user147690

1:10 AM

But I suppose it isn't the job he enjoys, just something he can do on the job(that isn't work)

pjs36

I've wanted to get a job being a janitor at a university - the plan being to "Good Will Hunting" those unsuspecting undergrads, and butt in when they're talking math

2

Clarinetist

I'm hoping to have normal human interaction where I will be relocating...

user147690

@pjs36 Hahaha, that would be amazing

Clarinetist

If I weren't living with my gf, I would be insane by now

Transcript for

$Mathematics$ Mathematics