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Different ways to prove that the square root of any prime number is irrational by Adly Assaf - Wed, 17 Dec 2014 01:02:18 EST ID:XuUSwld1 No.14534 Ignore Report Reply Quick Reply
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And I'm not satisfied with the indirect proof:
x^(1/2) = a/b | If 'x' is prime and both 'a' and 'b' are integers
x = (a^2) / (b^2)
(b^2) *x = a^2| Therefore 'a' is a factor of 'x' and...
(b^2) *x = (x^2)(c^2)
(b^2) =x(c^2)|.... 'b' is also a factor of 'x'
I don't think this is enough proof to go off of and say that 'x^(1/2)' is irrational, but I'm coming down off my coffee buzz right now and I wanna see what /math/ thinks while I brew the next pot.
Phoebe Wablingwere - Wed, 17 Dec 2014 03:39:19 EST ID:uPru0qmD No.14535 Ignore Report Quick Reply
You missing the key part: GCD(a,b)=1 therefore if x|a and x|b then x|GCD(a,b), a contradiction
Charles Murdford - Thu, 15 Jan 2015 19:56:16 EST ID:h2IBC+4I No.14564 Ignore Report Quick Reply
Little late. I won't type out all the details but a wonderful proof of this goes like:

Let p be prime, GCD (a,b)=1, and p=(a/b)^(2) b neq 0. So


Now consider the prime decomposition of a^(2). There has to be an even number of primes (a=p_(1)...p_(n) so aa=p_(1)...p_(n) which means there are 2n primes in the decomposition). Now look at the left side. A similar argument shows b^(2) has an even number of primes in it's prime decomposition, but p is also prime. So the left side of the equality has an odd number of primes in the prime decomposition and the right has an even. This contradicts the fund. theorem of arith. as the prime decomposition must be unique which means they have to have the same number of primes in their decompositions.
Charles Murdford - Thu, 15 Jan 2015 19:56:59 EST ID:h2IBC+4I No.14565 Ignore Report Quick Reply
made a mistake meant to say aa=p_(1)...p_(n)p_(1)...p_(n)
Fuck Chundlechod - Fri, 13 Feb 2015 00:01:12 EST ID:lx6v5XWF No.14605 Ignore Report Quick Reply
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This one's from The Book!

math question by jim - Thu, 22 Jan 2015 14:43:35 EST ID:yDDqWeTL No.14571 Ignore Report Reply Quick Reply
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hi. for a calculus assignment i have i have completed all but this final question:

A stereo manufacturer determines that in order to sell x units of a new stereo, its price per unit must be p = 1000 − x. It also determines that the total cost of producing x units is given by C(x) = 3000 − 20x.
a. Find the total revenue equation, R(x).
b. Find the total profit equation, P(x).
c.How many units must the company produce and sell to maximize profit.
d. Find the max profit

not very familiar with finances in relation to functions and my prof never touched on it nor is it in my textbook! any input / solutions with explanations would be ideal.. thanks
Ian Bockleridge - Thu, 29 Jan 2015 20:29:03 EST ID:mfk1g/VQ No.14587 Ignore Report Quick Reply
a) Revenue is the total amount money earned after selling x stereos. Each stereo costs p(x), so R(x) = x*p(x) = 1000x-x^2

b) Profit is the total amount of money earned minus the total cost of production; P(x) = R(x) - C(x) = 980x - x^2 - 3000

c) To know this answer, you must find out at which x does the function P(x) maximize. First, we find out dP/dx (or P'(x), I don't know what notation you use):
dP/dx = -2x + 980

When P is at a max, dP/dx = 0 (just trust me on this, I cba to explain it fully. It's in every 11/12th grade mathbook ever made); 0 = -2x + 980 > x = 490

d) Just substitute x for 490 in the profit equation: P(490) = 237 100 $
Shitting Sullerchutch - Sat, 07 Feb 2015 16:03:40 EST ID:cMHknuu4 No.14598 Ignore Report Quick Reply

I' m a pretty big math newbie. But shouldn't you want to determine whether dP/dx = 0, is a minima or maxima?
Rebecca Bicklestock - Sat, 07 Feb 2015 16:31:37 EST ID:tX1aaDR5 No.14599 Ignore Report Quick Reply
Since your profit eq is of the form -ax^2 + bx -c, then we know that the parabola opens DOWN (just graph a generic -x^2 to see this). So finding the point at which the slope = 0 is akin to finding the max. You should write this reasoning as part of the answer
Rebecca Bicklestock - Sat, 07 Feb 2015 16:33:19 EST ID:tX1aaDR5 No.14600 Ignore Report Quick Reply
Actually, its probably faster to just show it's the max by picking a point to the left of it, and to the right. Showing a generic graph seems like a lot of work compared toj ust picking points

algebra word problems by Walter Pettinglurk - Wed, 04 Feb 2015 18:07:09 EST ID:tkQOitI7 No.14593 Ignore Report Reply Quick Reply
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hey /math/,

Anyone have any good sites/resources for many algebra (high school level) word problems. I have a public service sector exam next month and althiough I did Calc 1 and 2 years ago in uni I find myself rusty with word problems.

Hugh Collerfoot - Thu, 05 Feb 2015 22:11:17 EST ID:Gj+82UIb No.14594 Ignore Report Quick Reply
Find a torrent of this or buy it http://www.amazon.ca/Solve-Word-Problems-Algebra-Edition/dp/0071343075

Frequency Analysis of Bit Stream by Emma Gandleforth - Thu, 11 Dec 2014 17:27:12 EST ID:A69r/eB1 No.14518 Ignore Report Reply Quick Reply
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I'm working on a project in knot theory, but my question is concerning coding schemes. When I transverse the knot, I keep track of each crossing I come across in a bit: if I go over, I set a bit to 1, if I go under, I set it to 0. So I have various strings of various lengths that might look like 000110, 101010101, 11111111, 011, 001100110011 etc.

But now, I've been asked to rank these various strings in terms of their "alternating"ness. For example, 1010101 will be the highest ranking, followed by 001100110011 and 111000111000111. Lowest ranking would PROBABLY be those with no visible pattern 0110101010101111101001. I kind of need to implement this in a program.

So my question is, is there some algorithmic process or mathematical value that can measure how close a bit stream adheres to the desired alternating pattern? My thoughts at first would be to approach this as a frequency analysis problem, but I'm open to any ideas.

tldr: can anyone point me to some references or share some wisdom concerning frequency analysis of a bit steam. Something that detects when a bit changes from one value to the next.
1 posts omitted. Click Reply to view.
Edwin Blenkinwell - Sun, 14 Dec 2014 10:44:08 EST ID:hudlvJsh No.14521 Ignore Report Quick Reply
What you code do:
For a bit string X
replace all 00 in X with 0
replace all 11 in X with 1
The then greater length of X the greater "alternating"ness
You can of course also normalize this by dividing by the original length of X
Ian Sittingstid - Sun, 14 Dec 2014 16:44:15 EST ID:nc9XL7V5 No.14522 Ignore Report Quick Reply
You could look into using hamming distance, which i think is what the post above me was talking about.

Alternatively you could look for occurrences of a sub-string (Your pattern) in the string, possibly using reg-ex's for this.

If your looking for like, any arbitrary pattern, a state machine would be your best bet i think.

I'm not sure what exactly your asking for here man, so i hope this helps
Betsy Pabberdurk - Mon, 26 Jan 2015 10:05:42 EST ID:zIqIyS2A No.14581 Ignore Report Quick Reply
Reminds me of Kolmogorov Complexity
Betsy Guvingspear - Mon, 26 Jan 2015 13:51:36 EST ID:JDIWTmrz No.14582 Ignore Report Quick Reply
>So my question is, is there some algorithmic process or mathematical value that can measure how close a bit stream adheres to the desired alternating pattern

That's just a Discrete Fourier Series. Read/skim through an EE book on Linear Systems and Signals and/or DSP.

Frederick Tillingwell - Tue, 27 Jan 2015 23:26:55 EST ID:EOD4uY1O No.14583 Ignore Report Quick Reply
It sounds like you want to calculate the length of the smallest substring that can be repeated to create the string, and rank streams by this. Of course this will consider something like 01010010101 to have the same "alternatingness" as 0001110010, I'm not sure if that's what you want. It's easy to come up with an algorithm for this that's quadratic in the length of the string. Here's an implementation in c++:

int main()
string s,prefix="";
for(int i = 0; i < s.length(); i++)
int j = i+1;
for(j; j<s.length(); j++)

Comment too long. Click here to view the full text.

mathematics?!?! by billyjoel - Tue, 13 Jan 2015 00:40:58 EST ID:29R5cpQe No.14559 Ignore Report Reply Quick Reply
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Nigel Bladdleville - Tue, 13 Jan 2015 01:21:14 EST ID:zyLGA8ah No.14560 Ignore Report Quick Reply
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You learned how to solve algebraic equations in algebra.
You will learn how to solve equations that contain derivatives of functions in differential equations.
Molly Blerringsore - Mon, 19 Jan 2015 02:38:13 EST ID:7MP0s8P6 No.14569 Ignore Report Quick Reply
weird ass equations that relate a value and the value's own rate of change.
Nigger Dubberdet - Fri, 23 Jan 2015 15:02:12 EST ID:OlFjx/Q0 No.14572 Ignore Report Quick Reply
It's a functional equation in which there are differentials.

A functional equation is an equation, in which the unknowns are functions, instead of numbers like in algebraic equations.
Solving an algebraic equation means finding a number (numbers) that satisfy given algebraic equation.
Solving a functional equation means finding a function (functions) that satisfy given functional equation.

Generally functional equations are very hard to solve. There is no general solution to such equations. Subset of those equations, differential equations, are particularly useful, and thus intensively researched. There are general ways to solve some rather simple classes of DE, but not all of them (like the infamous Navier-Stokes equations)
Phoebe Genderstitch - Fri, 23 Jan 2015 17:07:04 EST ID:E00AZouD No.14574 Ignore Report Quick Reply
Sometimes when you have a problem, you can describe it using an algebraic equation and this will give you at least one numerical value to answer your problem. It should allow you to at least narrow down your solution-search to a certain type of number.
Other times when you have a problem, you can describe it using a differential equation and this will give you at least one type of relationship between numerical values (aka functions) that will allow you to answer your problem. It should allow you to at least narrow down your solution-search to a certain type of characteristic relationship (function).

Some problems are simple and the solution will be a number. Other problems are more complex and the solution is a whole bunch of numbers that all share a certain relationship with one another.

Number one by David Barddale - Thu, 23 Oct 2014 18:57:56 EST ID:lnIBho4U No.14435 Ignore Report Reply Quick Reply
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1 is weird man.

If the basis for the value of one is wrong, all of math is pretty much fucked up right?

Also I wonder how aliens count things. Like, would they look at our system of counting things and be like wtf why is this so overcomplicated.
3 posts and 1 images omitted. Click Reply to view.
Beatrice Hebblekut - Sun, 04 Jan 2015 15:56:14 EST ID:81s39pKV No.14550 Ignore Report Quick Reply
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Why 12 or 16? Seems like that would be more complicated. Anyway binary is probably more universal. Only bitches need to count past 1.
Rebecca Dublingwater - Tue, 13 Jan 2015 01:29:26 EST ID:b1uzauJy No.14561 Ignore Report Quick Reply
Rebecca Poshhall - Sun, 18 Jan 2015 00:50:52 EST ID:6XbVXz0U No.14566 Ignore Report Quick Reply
I read some of Russel's writing on the subject and I still have a hard time wrapping my head around the concept that numbers themselves are sets (or classes, as he calls them).
Jarvis Hummerbick - Sun, 18 Jan 2015 10:34:32 EST ID:IYIYaVNy No.14567 Ignore Report Quick Reply
THink of them like segments on the number line. You can have a segment going from 0 to 1. THat's 1, and it contains the 0 (empty) set. A segment going from 0 to 2 contains 0, 1 and 2, and so on. A segment that does not include 0 wouldn't exist in this system.
Molly Blerringsore - Mon, 19 Jan 2015 02:36:01 EST ID:7MP0s8P6 No.14568 Ignore Report Quick Reply
I mean, like, one is just like an idea, man.

Average & Effective value by Electro M. Echanics - Mon, 12 Jan 2015 07:37:40 EST ID:Y56yfAG4 No.14557 Ignore Report Reply Quick Reply
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Somebody here who can calculate the average value and the effective (True RMS) value of this function?
I would be Very Thankful.
Electro M. Echanics - Mon, 12 Jan 2015 07:41:40 EST ID:Y56yfAG4 No.14558 Ignore Report Quick Reply
This might help: http://meettechniek.info/compendium/average-effective.html
Electro M. Echanics - Wed, 14 Jan 2015 08:44:45 EST ID:Y56yfAG4 No.14563 Ignore Report Quick Reply
Nvm. Already got it !

Math Problem by Frederick Niggerhall - Wed, 10 Dec 2014 12:46:28 EST ID:J8biWsPj No.14509 Ignore Report Reply Quick Reply
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Hi guys, I'm hoping I can get some math tips from you all. My girlfriend is a math major, and tells me that she's been having a lot of sex dreams about math recently. Sometimes, I'll find a calculator under the sheets. I'm not really a math person, so I'm not sure what to make of this or how to respond. Any tips? Thanks guys.
1 posts omitted. Click Reply to view.
Doris Puvingsutch - Thu, 18 Dec 2014 01:04:40 EST ID:Hs5ANTy/ No.14538 Ignore Report Quick Reply
Once upon a time (1/t), pretty little Polly Nomial was strolling across a field of vectors when she came to the edge of a singularly large matrix.

Now Polly was convergent and her mother had made it an absolute condition that she must never enter such an array without her brackets on. Polly, however, who had changed her variables that morning and was feeling particularly badly behaved, ignored this condition on the grounds that it was insufficient, and made her way in amongst the complex elements.

Rows and columns enveloped her on all sides. Tangents approached her surface. She became tensor and tensor. Suddenly two branches of a hyperbola touched her at a single point. She oscillated violently, lost all sense of direction, and went completely divergent. As she reached a turning point she tripped over a square root that was protruding from the erf, and she plunged headlong down a steep gradient. When she was differentiated once more, she found herself, apparently alone, in a non-Euclidean space.

She was being watched, however. That smooth operator, Curly Pi, was lurking inner product. As he numerically analyzed her, his eyes devoured her curvilinear coordinates, and a singular expression crossed his face. Was she still convergent, he wondered. He decided to integrate improperly at once.

Hearing a common fraction behind her, Polly rotated and saw Curly approaching her with his power series expanding. She could see by his degenerate conic that he was up to no good.

"What a symmetric little polynomial you are," he said. "I can see that your angles have lots of secs."

"Oh sir," she protested, "keep away from me. I haven't got my brackets on."

"Calm yourself, my dear", said our suave operator. "Your fears are purely imaginary."
Comment too long. Click here to view the full text.
Clara Blackfoot - Sun, 28 Dec 2014 10:32:31 EST ID:Ezs3wk1S No.14547 Ignore Report Quick Reply
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I liked it.
Lillian Nunderworth - Fri, 02 Jan 2015 00:24:58 EST ID:1f/Knshx No.14548 Ignore Report Quick Reply

I died at l'hospital.
John Crisslekon - Wed, 07 Jan 2015 01:09:39 EST ID:oEhGbHUR No.14554 Ignore Report Quick Reply
Golden post. lim x → 10 x/10
James Grandcocke - Sun, 11 Jan 2015 08:47:33 EST ID:oEhGbHUR No.14556 Ignore Report Quick Reply
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Here's my favorite math joke.

A Cauchy sequence is walking through town, when it sees on a wall a poster advertising a night club. "No limit night on Friday" it says. The sequence is all psyched for it, cause it's been a while since he last went clubbing, and this looked like the perfect occasion. So the sequence quickly goes back to it's place to put on it's best clothes and a nice cologne before heading to the club.
But then, when it is about to get in, the bouncer stops him and says :
Sorry, it's complete.

I just realised it may not work as well in English as it does in French. If it's the case and you're frustrated, here's a quickie.

Logarithm and Sinus wake up after a huge party. Sinus has the worst hangover ever, while Logarithm is fresh as a rose. Seeing the awful face his friend has, Logarithm says Man you really don't know your limits, don't you ?

Question about real numbers by Doris Blimmerladge - Mon, 15 Dec 2014 11:40:37 EST ID:akf5zfsA No.14524 Ignore Report Reply Quick Reply
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Is there a function that can project the entire set of real numbers onto an arbitrarily sized interval within the real numbers?
2 posts omitted. Click Reply to view.
Cedric Crebbercocke - Tue, 16 Dec 2014 10:09:36 EST ID:xrV+VzTJ No.14530 Ignore Report Quick Reply
Ah thanks, that's exactly what I meant
Isabella Blidgeville - Tue, 16 Dec 2014 13:07:43 EST ID:sPd/0oB/ No.14531 Ignore Report Quick Reply
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Beatrice Wommergold - Tue, 16 Dec 2014 15:53:58 EST ID:uPru0qmD No.14533 Ignore Report Quick Reply
Hyperbolic tangent :
tanh(x)=(e^x-e^-x)/(e^x+e^-x) maps R->(-1,1)
atanh(x)=1/2 ln((1+x)/(1-x)) maps (-1,1)->R
a*tanh(x)+b maps R->(-a+b,a+b)
atanh((x-b)/a) maps (-a+b,a+b)->R

The nicest functions you're going to find
Esther Fabberhall - Tue, 23 Dec 2014 20:47:35 EST ID:K8qJv5EF No.14542 Ignore Report Quick Reply
^This guy's post is correct if you're looking for continuous bijections. If you're looking for just a continuous map from the reals to [a,b], you can just choose f(x) = [(b-a)/2]sin(x) + (b+a)/2
Thomas Bangerham - Fri, 26 Dec 2014 18:20:04 EST ID:SlKfpVpP No.14546 Ignore Report Quick Reply
another interesting question is whether you can project an arbitrarily sized interval within the real numbers onto the set of real numbers

answer is yes

also you can map a line of length 1 onto a cube of volume 1 etc.

Majoring in Math by Cornelius Sollerwone - Tue, 02 Sep 2014 22:17:23 EST ID:kQQi+WA1 No.14343 Ignore Report Reply Quick Reply
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I want to know are good options for me career wise if I major in math. I just finished my first term and I don't really know what I'm doing. All I know is I enjoy math. The only thing I've had recommended to me is to become an engineer. I'm not great with electronics, computers, or mechanics. I think I could handle physics since that seems like just more applied math. I need college advice. I have a career advising appointment in a couple weeks but I would appreciate your advice!
Cornelius Brebbleford - Thu, 04 Sep 2014 00:46:14 EST ID:kQQi+WA1 No.14347 Ignore Report Quick Reply
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bumping for math majors
Nell Drennerdock - Sat, 06 Sep 2014 21:16:28 EST ID:Dk8yywxc No.14350 Ignore Report Quick Reply

I'm a math major but I don't expect to get a job from pure math. I do it because I enjoy it and find beauty in the subject. As far as getting a job, I'm double majoring in computer science so I can program and shit.

But there aren't many careers in pure math other than being a researcher, actuary, or teacher. Otherwise you will have to get some kind of certification. And yes, physics is just a specific subbranch of mathematics. All the time in my upper level classes I meet physics majors trying to understand exactly what it is they're learning about.

If you like proofs, be a math major. If you want a fulfilling pasttime that will develop you as a person, be a math major. A math major will make you stand out if you pair it with anything else, people assume mathematics = intelligence so it will get you to the top of many lists if you have other skills.

tl;dr math won't give you a career by itself but paired with something else it supercharges it and makes you even more awesome in the eyes of employers
Archie Worthingfield - Sun, 07 Sep 2014 18:17:12 EST ID:xvgqavvT No.14352 Ignore Report Quick Reply
Functional programming. since you need to think like a mathematician to do it. Designing algorithms is another high demand job, especially in the finance/trading industry. Artificial Intelligence is all based of real analysis (proofs) so another field you can go into. Any stats job for the government like an environment agency, lot's of options.
Cedric Hollertudge - Fri, 19 Dec 2014 05:04:22 EST ID:lx6v5XWF No.14540 Ignore Report Quick Reply
Analytics and machine learning is in very high demand right now, and is where a large part of the field of CS in industry is heading, due to the big data problem.

These are very math heavy. I'd recommend getting into computational math.
Learn C. Learn Python. See if you can find some open source projects and make some contributions.

Programs can be very proof-like, in my own experience.
Sophie Turveyhood - Fri, 19 Dec 2014 15:50:10 EST ID:4kDzPiCs No.14541 Ignore Report Quick Reply
If you want a career in math you really have to get a PhD. That said, mathematician is regularly listed as one of the best, if not the best, job to have by many metrics. Grad school for math is always paid for. Schools will actually pay you a stipend to go there, even if you're not a top student.

Don't listen to people saying you can't get a job doing math. It has very high growth and almost no one wants to do it.

Maths tutoring by Hugh Pupperford - Sun, 14 Dec 2014 17:18:22 EST ID:8T5tyzEs No.14523 Ignore Report Reply Quick Reply
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I wanna make some money on the side but by doing little work. I'm a maths undergrad so I was thinking of doing tutoring online. Anyone done this kind of thing before? How did you go about it? How much should I charge?
Cedric Hollertudge - Fri, 19 Dec 2014 04:56:04 EST ID:lx6v5XWF No.14539 Ignore Report Quick Reply
Your skill has probably taken years of work, so you should charge something above double minimum. I've charged $20 before, and $30 is not unreasonable.

I did my tutoring at a community college, and while I was a student, there were numerous tutors who weren't. You can see if any local CCs have openings.

can you help me? by Phoebe Wankinwater - Wed, 17 Dec 2014 15:56:58 EST ID:K92q/1nw No.14537 Ignore Report Reply Quick Reply
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Hey guys, can anyone help with the following question? I am really stuck with it (and not through lack of trying, believe me)

A microphone has a polar pattern described as e = 1 + 1.5 * cos(angle).
Its on-axis sensitivity is given as -40dBV/Pa.
A sound source is such that it produces 75dB SPL at the microphone diaphragm.
What is the microphone output in miliVolts if the source angle is 90 degrees to the right of the microphone.

V(angle) / V(on axis) = (1+1.5 * cos(angle)) / (1+1.5 * cos(0))

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