Advanced Mathematics Question/Answer thread

I've heard of derivatives, but I'm not aware of "derivates".

Say, friend, can you put the following into reduced row echelon order

[math] \displaystyle

\begin{bmatrix}

i & 2i & \pi i & 82 \\
42 & e & \sum\limits_{n=0}^{5} n & \frac{1}{10} \\
4 & 3 & 2 & 22 \\

\end{bmatrix}

[/math]

?

hm gee i wonder

Is this supposed to imply something about sucking dick?

Is the human penis an open or closed surface in topology?

wyzant.com/resources/lessons/math/calculus/derivative_proofs/sinx

you couldve just googled

Isn't it obvious given they are inverse?

In what sense are these two functions "inverses" of one another?

Oh, another one. Find A.

Alright, so I've got a SICP related question:

One of the exercises in the book requires you to prove that Fib(n) is the closest integer to φn/√5, φ of course being the golden ratio (1 + √5)/ 2. To do this, the book gives you the hint that you need to prove that Fib(n) = (φn - ψn) / √5 where ψ = (1 - √5) / 2.

How would I know to do that if the book didn't give me the hint?

damn this is not a problem this is just boring af

Also i've just passed my math mock competitve exam and there was also a "recude row echelon order" over-annoying problem

Here is the solution.
billthelizard.com/2009/12/sicp-exercise-113-fibonacci-and-golden.html

Additionally, you may find this useful:
billthelizard.com/2009/10/sicp-challenge.html

I'll use this as a reference after I reach a working solution to each problem to get a better understanding.

Thanks user.

nvm i got cos and csc mixed up.

by the way , its was part of a bigger problem :
Given
u(n+3)=-u(n+2)+5u(n+1) -3u(n) ,
u0=0 u(1)=0 , u(2)=1
Find u(n)

Indeed, I wouldn't recommend looking at the solutions until you've put in great effort to solve them/want to check your work. No problem.

I'm guessing either it is countable or the same cardinality as the real line.

Does anyone have experience with Satisfiability modulo theories?

I'm trying to decipher the notation.

I don't understand how to read

bE
bvE
mE

Can someone make sense of it?

and I thought Veeky Forums was full of smart people

c'mon

Idk if this is too easy for this thread or not, but I was hoping Veeky Forums could help me with my hw.

pic related

Can only be proved in special cases, what would you expect; It's a millenium prize problem.

TELL ME ABOUT GALOIS THEORY HOW DO I GET GUD

>tfw just failed a Real Analysis II class
>tfw can't graduate for another semester

Jesus Christ just end me.

Find the area of the whole circle. Divide by 4. Find the area of one of the 4 squares. Subtract 1/4 the area of the circle from the area of the square. Find the area of the smaller circle. Go from there.

too advanced

work harder

Analysis is just meme math anyway I don't give a shit anymore.

I recommend:
Tao Te Ching,
Littlewood's Three Principles, and
Bressoud's "A Radical Approach to Real Analysis." Peace, epsilon, convergence.

Nope. Take for example TS^4.

Got an analysis II final on Wednesday, been slugging and coasting by.

What's the possibility of getting an A on the final? We studied Limits, derivative, Taylor & power series, & integration chapters.

suppose I have a polynomial P(x) irreducible over Q and is solvable in radical
denote K as the splitting field of P(x) over Q
how can I construct an extension L over Q such that
1) Gal(L/Q) is a solvable group
2) K is a subfield of L, and K,L are distinct

yo what is a dee over dicks?

Can anyone take a stab at what this notation means I almost think the expression bE where E represents an expression/variable that can be replaced with: true, false, b, ~b, ~bE, bE1 or bE2 etc... but I am certainly not sure.

dude maths is useless in life
study cs

yo when am i gonna y=mx-b in my life

Oh okay, thank you. I see it now. How about this thing?

[math]

\displaystyle

\int_{0}^{1} \int_{0}^{1} \int_{0}^{1} ( \sin x \cos x \tan x ) dxdydz

[/math]

?

Also what does everyone think of the notion that "p implies q" is the same thing as " 'not-p' or q"? sounds kinda dumb and counterintuitive to me. After all, if something false implies something that is true, then that defies reasonability as a true statement.

triple integral of the same variable??? wtf lol.
literally integrate that 3 times. I sinxcosxtanx can be rewritten as sin^2x

this is literally just sin^2(x) dx from 0 to 1

never, now go pave my driveway or fill my car with gas

Okay. How about

[math]

\displaystyle \int_{0}^{1} \int_{0}^{1} \int_{0}^{1} ( \sin x + \cos \phi + \tan x ) d \phi dydz

[/math]

?

still need an answer on the implies thing too.

...

i understand the mechanics, but not the intuition behind tilted density sampling

anyone that did some work in statistics/sampling theory help out?

>No Pre-Calculus, Calculus I-III, Differential Equations or elementary Linear Algebra questions allowed.

So that excludes all engineers right?

The Taylor series are themselves created from the derivatives though.

signal processing \ information theory can be breddy based

for your logic question just do the logic tables m8 it is the same thing

and do you not know triple integration or something?

the answer to that integral is sin(x) - sin(1) + tan(x)

what is x?

>meme math
just stop

How do I into control theory?

PID controllers and state space analysis lad

math meme ?

I was asking for a book recommendation.

The syntax is defined in BNF notation. (possibly extended BNF) Apparently, the author assumed the reader would be familiar with it.

ogata - modern control engineering is what we used.

it uses MATLAB too for some bits which I like because I'm an EE and it's basically our bread and butter.

Hey guys,
Just a moron-tier engineering student here with a question regarding Stokes' Theorem:

Shouldn't the terminals of integration be 0-->a? Or have I missed something?

>terminals
and yup, looks like an error.

also
>no calc III

sorry for posting that shit-tier math problem bro, won't happen again

Why didn't you just post it in the stupid questions thread?

Your reply exceeded my expectations, thank you! Indeed the author makes many such assumptions, as I've never heard of BNF before.

How would you grind through the grammar?

For the Boolean expression type I'd assume you could convert the "b" in bE as follows

bE := (true)E, (false)E, bE (not sure about the b by itself?), ~bE, bE1 or bE2 and so on... and then you can replace the Es with either bE again, bvE or mE.......

is this correct?

Also, for the mE can you make sense what the lambda (x1,...,xk).bvE is?

looks like something from lambda calculus with lambda is binding x1,...,xk in the head and bvE is the argument for the formula.

Anyways, any good online resources to get some basic background in BNF or SMT?

BNF is a standard method to express syntax in formal language theory or computer science in general. I think wikipedia should be able to provide enough information on the format. The basic idea is that you define "tokens" (in your pic "bE", "bvE" and "mE"), for which you give a list of replacement option separated by "|". Those replacements are combinations of literals (e.g. "true") and other tokens, which allows you to construct and parse the language recursively.

I can't make much sense about the example you're giving, but the idea is to replace the entire "bE" part. Perhaps this clarifies something. If we want to create an "bE", start with that token and replace it by e.g. "bE1 v bE2". Now we can replace those new tokens (the numbers are only there to show the tokens need not have the same value) such that we get e.g. "true v false", which then is a valid instance of "bE". I think the author means that "bE" stands for boolean expression, "bvE" for bit vector expression and "mE" for memory expression. A bit clunky notation, imo.

The lambda part does seem to indicate binding from the lambda calculus. I suppose that is one way to formalise "memory".

I don't have any knowledge on the topic of SMT at all, but it looks interesting. Can you tell me where your image in is from?

There is a formula for a projection operator that uses a contour integral like so:

[math] P_{k} = \frac{1}{2\pi i}\oint_{|\lambda-\lambda_k|=\delta}(\lambda I-A)^{-1}d\lambda. [/math]

where A is a self-adjoint operator. For simplicity, let's work in finite dimensions. Where can I find a proof that the target subspace dimension equals the number of eigenvalues within the contour?

>bE ::= true | ....
bE is a boolean expression
Boolean expressions can either be true, false, a boolean variable, negations of a boolean expression, a clause of two boolean expressions, a conjunction of two boolean expressions, the equivalence of two boolean expressions, ...

bvE = bitvectorExpression which can either be a bit vector constant or a bit vector variable or ..., mE = memoryExpression ...

i only know the math topics listed by op, so what do i learn next?

complex analysis or functional analysis

There's a lot of unanswered questions in this thread, why aren't you guys posting on math.se or mathoverflow?

I gave up. My question didn't receive any answers there.

Posting on Veeky Forums is easier. I don't need a username.

Bounty/more attractive title/more popular tags?

Just post as an unregistered guest with a fake email.

This user is at work. Will respond after

I want to see atom

I have tried everything. I'm certainly sure that there are people, who the answer, but deliberately ignore. Meanwhile, the question is well appreciated (it got 10 votes)

How long ago was the question posted? I mean, if someone could answer such a well appreciated question, it's basically free rep.

A lot. Over two weeks. After some time, questions simply fall into abyss and never get answered.

Still at work. I want to post my questions :/

Yeah that won't be seen again... want to give it a sneaky edit to bump it back to the top?

How prove?
[math]\mathbb{R} = \mathbb{Q}\sphericalangle \diamondsuit \multimap \infty [/math]

pretty obvious from the formula for the n-th term?

i have taken math classes in 3 different countries, read hundreds of papers and textbooks in various languages, and never have i seen this clusterfuck of notation

explain yourself

I tried. I don't think it helps

IUT

Is e transcendental or just irrational?

...

kek

The proof is left to the reader

Not directly a math question, but a logistical question about synthesizing advanced math:

I spent the past six months studying a certain area of advanced mathematics, learning all the proofs through and through, even re-writing every proof from my own memory/understanding after learning them.

And now I can scarcely remember a damn thing.

It is so fucking frustrating. I feel like, relative to mathematics, I must be downright mentally retarded with respect to memory. I don't know how I'll continue as a phd student if I can scarcely remember a single goddamn proof.

Is this common, or am I exceptionally retarded? Regardless, what do I do about this?

Thank you.

Not directly a math question, but a logistical question about synthesizing advanced math:

I spent the past six months studying a certain area of advanced mathematics, learning all the proofs through and through, even re-writing every proof from my own memory/understanding after learning them.

And now I can scarcely remember a damn thing.

It is so fucking frustrating. I feel like, relative to mathematicians, I must be downright mentally retarded with respect to memory. I don't know how I'll continue as a phd student if I can scarcely remember a single goddamn proof.

Is this common, or am I exceptionally retarded? Regardless, what do I do about this?

Thank you.

Just skim your notes. It will all come back quickly.

+1'ing this, hope someone answers this.

was for ; I edited a typo.

Thanks. I hope so.

I also regularly forget what variables stand for halfway through a proof.

I was a drug addict throughout my undergraduate years, yet somehow got into a top-tier grad program. But I almost know for a fact that I did irreparable brain damage during my drug binges. I feel like I'm riding on the coat-tails of my former intellect, and now I'm a husk of that.

You have no idea how much I hate myself all the time for this. I don't know if I'm even capable of getting a PhD anymore.

To any user who hasn't methodically fucked up his own self and life: take a moment to be grateful.

>1+1 = 2, find x
Help pls

The solution set is the solution set to a system of linear equations -- namely, the empty system.

So simply put the empty matrix into row-echelon form to solve for x.

Basic linear algebra.