/sci/ - Science & Math

brainlet alert

haven't done a proof in forever so I don't really know where to start with this one, base case is easy enough but I don't know exactly what I'm aiming for with the inductive step

I don't necessarily want an answer, just need some help knowing what to do

>>9433584
Funny, I just saw that picture for the first time the other day.

Anyone have the instructor solutions to Calculus by Spivak?

Why do people say shit schools teach Java in CS101?
How true is it?
I'm already insecure about going to a "meh" school

>>9433734
desu if your school doesn't teach haskell in your CS101 course then your CS program is shite

>>9433740
Definitely going to contend this. Functional programing is a must in modern CS education. Java is 10+ years old as a valid educational language.

>>9433734
If you have more than one class on intro programming, it's shit.
If you have dedicated classes to OOP, web dev, or GUIs; it's shit.
If you're not required to take Computer Architecture, Operating System Theory, and Compilers; it's shit
If you're not required to take Calculus, Linear Algebra, Proofs, (Calculus based) Probability, (Calculus based) Statistics, Combinatorics & Graph Theory, or took watered down versions in the CS department; it's shit.
If you're not required to take Programming Paradigms, Type and Programming Language Theory, Formal Languages & Automata, Computability Theory, and Complexity Theory; it's shit.
If you're don't at least do one of Networking, Databases, or Distributed Computing; it's shit.
If you don't have a capstone project to graduate, it's shit.

What exact steps do you need to take to solve this? I feel like an idiot.

>>9433968
https://en.wikipedia.org/wiki/Quadratic_formula

>>9433969
Thanks. I have no idea how I keep forgetting about this.

>>9433969
Alternatively:

x^2 - x = 20
x(x-1) = 20

What number times one less than itself equals 20?

>>9425339
>you can't multiply any matrix by a 1x1 matrix

Sure you can:

A [a] = aA

>>9433935
>capstone project
>not thesis
brainlet

>>9433536
>Why is LSD even illegal?

"I think it's interesting the two drugs that are legal, alcohol and cigarettes, two drugs that do absolutely nothing for you at all, are legal, and the drugs that might open your mind up to realize how badly you're being fucked every day of your life? Those drugs are against the law. He-heh, coincidence? See, I'm glad mushrooms are against the law, 'cause I took 'em one time, and you know what happened to me? I laid in a field of green grass for four hours going, "My God! I love everything." Yeah, Now, if that isn't a hazard to our country... how are we gonna justify arms dealing if we know we're all one?!"

-Bill Hicks

Whats an example of a left-distributive operation (with regards to another) that is not right-distributive?

>>9434274
matrix multiplication

>>9434281
With regards to addition you mean? Thats both left and right distributive

>>9434096
an even more fun example is this, a simple projection operator onto the vector x,

[eqn]P=\frac{xx^\top}{x^\top x}[/eqn]

Go ahead and check that it satisfies
[eqn]P^2=P[/eqn]

>>9434274
Consider maps from R to R. Let the two operations be * = pullback or function composition and × = usual multiplication.

>>9433935
My school checks off most of that list.
When you say "it's shit" do you mean it's shit intellectually or does it seriously hurt job prospects?
I just wanna take care of my mom ffs

>>9433968
Anon, subtract 20 and factor using a +4 and -5

Say i have a heat distribution within a sphere modelled as u(r,t). Does "the temperature distribution in the centre is continuous" simply mean that u(0,t)_r = 0?
(_r means differentiate with respect to r)

I understand how to solve exponents when you multiply/divide bases but how the hell do you solve it when they are added or subtracted without using logs? Thank you in advance

>>9434591
>I understand how to solve exponents when you multiply/divide bases but how the hell do you solve it when they are added or subtracted without using logs?
Why wouldn't you use logs?

>>9434600
Logs aren't taught till the next grade so I'm assuming there's a way to solve this without it.

T. brainlet trying to relearn math 10 years after high school

>>9434613
>Logs aren't taught till the next grade so I'm assuming there's a way to solve this without it.
There isn't.

>>9434614
This was on an old grade 10 test. I guess the teacher is retarded then?

>>9434614
>There isn't.
Proof?

>>9434591
You can solve by intuitive analysis.
Play with it a little.

In the quadratic 12 - x - 6x^2, the terms are going to be factors of 12 (1, 2, 3, 4, 6, 12) on the left and 6 (1, 2, 3, 6) on the right. We can disregard the even factor options of 12 (2, 6) on the left because the x coefficient (-1) is odd. After this, I have to mentally shuffle round the right factors and order or signs till I find the right factors.

Question: after common-sense considerations like the above, how can I find the solutions apart from basically trial and error?

>>9434641
Use the quadratic formula?

>>9434632
>"""solve""" by ""intuitive"" analysis
That's not what "solve" means.

>>9434664
Is there a way to do what I described without using the formula?

>>9434591
-64=2^(x+2)-2(x+3)
-64=2^x*2^2-2^x*2^3
-64=2^x(2^2-2^3)
-64=2^x(-4)
-64/-4=2^x
16=2^x
x=4

>>9434730
He/she said without using logs

>>9434733
Trial and error then. Or he could go fucking retard mode and solve it by bissection.

>>9434684
If you are certain that the roots are rational numbers, you can assume that the quadratic can be factored as (ax + b)(cx + d) where a b c d are integers so that bd = 12, ac = -6, ad + bc = -1, from this third equation, you can see that b and d are coprime and similarly a and c are coprime. This can further reduce the search cases. You could also try reducing the equation modulo some number or use the intermediate value theorem to estimate the location of the roots. I don't think there's any general algorithm to find roots in this manner.

What is the abscence of abscence? If I can't answer this, they won't let me cross the loval bridge.

>>9434591
Yeah just factor out a 2^x from the right side,

[eqn]-64 = 2^x * 2^2 - 2^x 2^3[/eqn]
[eqn]-64 = 2^x ( 4-8)[/eqn]
[eqn]-64 = 2^x * (-4)[/eqn]
[eqn]16 = 2^x[/eqn]
now rewrite 16 as a power of 2,
[eqn]2^4 = 2^x[/eqn]
clearly x=4

also, get rekt kids:
>>9434600
>>9434614

>>9435385
>clearly x=4
He/she said without using logs.

prove [math]\sum_{n=1}^\infty \frac{sin(nt)}{n} =
\frac{\pi - t}{2}.[/math]
This came up on the 5th equality here:http://sos440.tistory.com/141

Somebody already has a solution on stackexchange (https://math.stackexchange.com/questions/566856/is-sum-n-1-infty-frac-sinnxn-continuous)) but I don't follow (is that fourier transform on the first equality? I don't follow)

>Show that
[eqn]\frac{-1 + i \sqrt{3}}{2}[/eqn]
>is a cube root of 1
So I just computed it and showed the steps, is that what this is asking for? I feel like it's asking for some kind of property of complex numbers as an answer.

>>9433901
It's a meme... don't respond to this bait

>>9434096
Scalar multiplication and matrix multiplication are two very different operations. What you are doing is scalar multiplication with a 1x1 matrix and calling it matrix multiplication.

>>9435654
[math]1 = e^{2\pi i}[/math]
[math]1^\frac{1}{3} = e^\frac{2 \pi i}{3}[/math]
[math]e^\frac{2 \pi i}{3} = cos(\frac{2 \pi}{3}) + i sin(\frac{2 \pi}{3}) = \frac{-1}{2} + i\frac{\sqrt(3)}{2}[/math]

Let me know if any of those steps didn't make sense.

>>9435667
At what point should my brain automatically switch to those identities, or am I already fucked?

>>9435676
Well the i in the expression is a pretty big giveaway that you might want to use complex analysis to show it. So my answer to your first question is "as soon as you see an i in the expression".

As for whether you're fucked or not, just do more of these problems and you won't be.

>>9435654
>So I just computed it and showed the steps, is that what this is asking for?
Yes.

>>9435667
>>Scalar multiplication and matrix multiplication are two very different operations. What you are doing is scalar multiplication with a 1x1 matrix and calling it matrix multiplication.

I didn't say it was matrix multiplication. The point is just that there isn't much of a difference between 1x1 matrices and scalars; abusing a little notation never hurt anyone.

>>9435877
Matrices requires a choice of basis (at least in the context of vector spaces), scalars exist irregardless of any basis being chosen

>>9435877
>there isn't much of a difference between 1x1 matrices and scalars

Don't worry anon, you will have your friends to support you!

>>9435877
>abusing a little notation never hurt anyone.
That's not what "abusing notation" means, retard.

>>9433584
Can anyone tell me just how much mathematics is used within Chemistry IRL? My major requires a Calculus I class, but will we actually use this IRL within labs or is it just to 'weed out' those who can't critically think?

How do I prove that the composition of two nonparallel Lorentz boosts isn't a Lorentz boost?

>>9433584
Is the cardinality of the set of all neighborhoods of a point greater than continuum in the standard metric space on R (i.e. d(x,y) = abs(x-y) )?

>>9435984
Science is pretty much all differential equations, so yeah you certainly need calculus.

Why is the current the same at the top and bottom of this circuit? Would it be split at the node after R1?

>>9436926
because of the grounding

>>9436926
because vout doesn't go anywhere

>>9436926
V_out is a node used to read/sense the voltage at that point. This structure is a Voltage Divider, as using precise values for the resistances will allow you to set a precise value of V_out in terms of V_in

Ideally, any device that senses/reads the voltage at a point (ref. to ground) does not itself draw current, so no current would flow out of the line labeled V_out.

>>9436158
contradiction

>>9436930
>>9436931
>>9436946
Sorry, I still don't get it. Thanks for trying, though.

>>9436954
Vout leads to nowhere, it cannot do any work there and it is an open circuit
so the whole current goes to ground

>>9433734

>>9436732
If by neighborhood you mean any set containing an open set around the point, then yes. Just form the union of each subset of R with an interval around the point.

>>9436988
> Just form the union of each subset of R with an interval around the point.
Uhh yeah, that's how you prove it by definition. The problem is I tried to use the Schröder–Bernstein theorem, it's easy to find an injection N(a) -> P(R) (N(a) being the set in question associated with the point 'a') , but I can't figure out what is P(R)->N(a) supposed to be. All the subsets of R in N are open sets with the cardinality of the continuum, what am I supposed to do with the finite and countable subsets of R?

Where can i learn about Lebesgue integrals? Khan academy doesn't have anything on them

>>9436926
The same reason why birds don't die when standing on high-power lines. In order for electrons (current) to flow, there must be a voltage difference to "motivate" them. That V_out wire is entirely on the same voltage, so there is no voltage difference.

>>9437008
>All the subsets of R in N are open sets
So you're restricting the neighborhoods to be open sets? If so then the answer to you question is no. Because there are only 2^N open sets.

>>9437023
>2^N
I mean 2 ^ \aleph_0 of course

>>9437018
There are some introductory lectures here
https://www.youtube.com/playlist?list=PLPH7f_7ZlzxQVx5jRjbfRGEzWY_upS5K6

>>9437023
What if I don't?

>>9437034
If you don't, then you can find an injection from P(R - I) to N(a) where I is an interval around a by mapping the set A to A \cup I

>>9437041
I think I got it. Thanks.

>>9436978
>C++
Is this the 20th century?

>>9437099
Any HLPL other than C/C++ is either babby coding or esoteric shit closer to math. Studying it as the first programming language gives you a good foundation. Nothing is too difficult after C++, except for the aforementioned esoteric shit like Lisp.

>>9437127
C and C++ are low level programming languages nowadays, and as such unsuitable if you want to learn high level programming (which is 99% of the programming one will ever do unless they are in a specific subfield like performance optimization or microcontroller programming, but that's too specific for CS). And for learning low-level programming, there's no reason why to use the bloated monstrosity that C++ is when C exists

>>9437152
Most software is still written in C/C++. C# and Python are pretty popular but still not on the same level. And Java... Well, frankly I don't remember the last time I used a Java program.

>>9437099
>>>/g/ is that way.

>>9437152
>C and C++ are low level programming languages nowadays

Stop being retarded. Low level programming is AMD64, ARM, MIPS, PPC

>>9437018
https://www.amazon.com/Integral-Measure-Derivative-Approach-Mathematics/dp/0486635198

Good examples to take a video of Newton's First Law?

I tried to download all the protein coding genes in the human genome from ensembl biomart, unspliced transcript form
it's 874 mb of compressed fasta and still counting
1: am I retarded?
2: will the unspliced transcript form return multiple copies of each gene but different transcripts?

>>9436954
Try this.

I don't know if it's because I'm a brainlet or there is a massive grade inflation problem but at the end of the semester I'm always embarrassed to come to the grade threads because the best I can do is Bs and 1 A maybe. How do I get all A's next semester in EE?

[math]1 + 1[/math]

>>9437414
[math]
1+1 = 1 \cup \{1\} = \{\emptyset\} \cup \{\{\emptyset\}\} = \{\emptyset, \{\emptyset\}\}=2
[/math]

It's the last night before the exam.
How do I make myself stop feverishly cramming and just accept that I will have to go through the embarrassment of handing in an empty sheet of paper and try again in a couple of weeks?

>>9437496
You could cheat and memorize all the answers in your brain ;^)

Is it possible to somehow coat neodymium magnet with titanium nitride?

Let X be a random vector from (omega, A, P) to (R^d, Bor(R^d)) and let C be its covariance matrix
How do i prove that the following result is true for all t in R^d ?

E ( < X-EX, t>^2 ) = < CX,t>


< , > is the dot product.

>>9437496
>night before the exam
>early January
If you were autistic enough to take winter classes then you deserve it.

>>9437514
I could, but not in the next 5 hours. There are 80-something questions, and most require at least 30 mins to understand the answer. I can answer a few, but I can't memorize the proof of Gödel's incompleteness theorems for shit. It requires a lot of reading I don't have time for.

>>9437535
> everyone on 4chan is an American, and the higher education system in every country in the world is exactly the same

>>9437533
Did you copy that correctly?
I think you must mean <Ct,t> for the right side of the equation for things to have any chance of handling scalar multiples of t.

>>9437559
>>9437533

yeah sorry, that's <Ct, t>

>>9437566
Then it's pretty straightforward if you use matrix-vector notation and expand things using linearity of expectation..

The critical point is that
<X - EX , t>^2 is t'(X - EX)'(X-EX)t
where t' is transpose(t).
Then use the fact that, for a random matrix A, and constant vector b, E(b'Ab) = b'(EA)b.

>>9437539
>living in a shithole country

>>9437589
Well, it's not like I got to choose.

>>9434339
If you just care about money it's going to be painful and embarrassing for you and you're never going to do well at it.

Your best prospect is finding a sinecure and hoping that no one really cares about how much you fuck up or how little you actually do.

Just bought Swakowski's Calculus with Analytic Geometry, 2nd revised ed. from Goodwill, how good of a text is it?

Usually I buy other mathematics books that I come across so I have larger problem sets to choose from whenever I need to go back over a topic and not forget it, just in case the answers for problems I already went over are still stuck in my head.

>>9437755
>Just bought Swakowski's Calculus with Analytic Geometry, 2nd revised ed. from Goodwill, how good of a text is it?
Why don't you read it and find out?

>>9437756

I'm about to. I was mainly looking for an overview of quality compared to some more modern texts or maybe a range from Stewarts to Spivaks perhaps.

I'll let you all know how it goes, though and what I think compared to the dozen or so other books I've gone through.

can anyone help me prove this? its a big-Omega question, I know it can be more CS but Im having trouble with the math parts.

I know that big-omega states that
f(n) >= C * g(n) for all n >= k
such that C and k are constants >= 1

for any two random values of k or C I choose the equation does not work, like if I chose
C = 1
and k = 5

log5(n) >= ( C ) * ( log2(n) ) for all n >= 5
and lets say n = 5:
log5(5) >= ( C ) * ( log2(5) ) for all n >= 5
1 >= 2.321 which is false

and for any values it comes out as false, is there a more formal way to derive C or K for this? thanks

>>9437883
fuck wrong pic, meant to post this

also, how do you write log subscript in a post?

>>9437883
>>9437903
Your definition of big O is backwards.

>>9437920
my questions is solving big Omega, these are my understandsing of each definition:L
[my attempt at correct notation too:]

BigO:
$f(n) >= C_1 * g(n) for all n <= k$
for C >= 1 and k >= 1

BigΩ:
$f(n) >= C_1 * g(n) for all n >= k$
for C >= 1 and k >= 1

>>9437883
You misunderstand the definition. It doesn't apply for EACH k and C, but for SOME k and C.

Is pic related correct?

If so it would mean, that the sum of two different numbers, that are both either greater or smaller than 0, is equal to zero.
Would that not be a contradiction (which would mean that i is neither greater nor smaller nor equal to 0)?

Am I simply retarded?

No matter what I put into my ti-84 plus' solver (for example, 0=x-1) it returns x=5. What is wrong with it?

>>9437929
show us the input field

>>9437927
oh ok, so would the statement be proven true if it is true for only one case?

like lets say I chose C = 1 and k = 1
log5(n) >= ( C ) * ( log2(n) ) for all n >= k
becomes
log5(n) >= ( 1 ) * ( log2(n) ) for all n >= 1
lets chose n = 1
log5(1) >= ( 1 ) * ( log2(1) ) for all n >= 1
0 >= 0 which is true

would showing that be enough to prove it is BigOmega, since the statement is true for my chosen C and K even though it is not true when n > 1? like I chose 1 above and it worked, but for anything above 1 it does not work

lets chose n = 3
log5(3) >= ( 3 ) * ( log2(3) ) for all n >= 1
.682 >= 3 ( 1.584 )
.682 >= 4.75 NOT true

>>9437937
>oh ok, so would the statement be proven true if it is true for only one case?
Yes, that's correct. Remember when you're switching bases with a logarithm, all you're doing is dividing by the log of the new base. Therefore, the two will be constant multiples of each other for all n in the domain, so it makes sense they're the same computational order.

>would showing that be enough to prove it is BigOmega, since the statement is true for my chosen C and K even though it is not true when n > 1?
That's fine. Just try to keep straight what you're saying when you claim g(n) is of order f(n). All you mean is that f(n) provides an upper bound on the size of g(n) as n approaches infinity (greater than k). The multiplicative constant can be changed to whatever works; it does not effect the general shape of the function, only the scale of it.

>>9437928
The relations '<' and '>' are not defined in general on the field of complex numbers, for a variety of reasons. For example, if we said i > 0, or if we said i < 0, either way we get -1 = i*i > 0.

>>9437959
Just wanted to clarify this by saying it will NEVER only be the case for one set of C and k. Of course, once you find the minimum value of k, any value you choose greater than that minimum will also be valid. The same goes for C; multiplying g(n) by a smaller value will only decrease the value of |C*g(n)| while keeping the inequality valid.

>>9437937
Since you're talking about CS, I assume you are interested in Knuth's big-Omega.
[math]
f(n) = \Omega(g(n)) \iff \exists C>0 \ \exists k \ \forall n>k \ f(n) \geq C \cdot g(n)
[/math]
C and k must be chosen such that for any n grater than k the statement is true.

> would showing that be enough to prove it is BigOmega, since the statement is true for my chosen C and K even though it is not true when n > 1?
By definition it would not.
In your case, C = log5(2) is a good C because
log2(n) = log2(5) * log5(n).

>>9436953
Please elaborate.

can something be A and not be A at the same time?

>>9438003
If the context changes, yes. See: 0/0

>>9438005
But 0 is the additive identity of a field, it doesn't have a multiplicative inverse, so "0/0" doesn't make any sense.

I'm having to use latex for the first time, and I cannot for the fucking life of me get this shitty fucking bmatrx to stay on the same line as some other equations. I need to clearly show that the matrix is equal to its equation form, but the stupid fucking thing keeps forcing a newline between them

>>9438003
>can something be A and not be A
yes, just assume that both A and not A hold. or your logic might be inconsistent, then everything is both true and false.
>at the same time?
this isn't defined in most logics.

>>9437987
Can I choose C = log5(2) ? I thought that C and K had to be a integer > 0.

>>9438003
If the set of axioms you're using is inconsistent, then yes.

>>9438026
They don't. You're working with real-valued functions, why would you demand a coefficient to be integer?

>>9437934

>>9437903
That's not big O you retarded CS monkey.

>>9437883
>>9437903
log5(n)=log2(n)*log5(2) so log5(n)∈Θ(log2(n))
since Θ(f)=Ω(f)∩O(f), log5(n)∈Ω(log2(n))

>>9437926
1. You don't need C>1. Just C>0
2. State what is in big Θ/Ω/O of what for fuck's sake!
3. It's less than or equal and n>=k for big O

BigO:
f∈O(g)
iff (∃N,C>0)(∀n>N) f(n) <= C*g(n)
iff limit(n→∞) f(n)/g(n) < ∞

BigΩ:
f∈Ω(g)
iff (∃N,C>0)(∀n>N) f(n) >= C*g(n)
iff limit(n→∞) g(n)/f(n) < ∞

BigΘ:
f∈Θ(g)
iff f∈Ω(g) and f∈O(g)
iff limit(n→∞) f(n)/g(n) = C s.t. C ≠ 0 and C ≠ ∞

>>9437920
That's not big O you retarded CS monkey.

>>9437883
>>9437903
log5(n)=log2(n)*log5(2) so log5(n)∈Θ(log2(n))
since Θ(f)=Ω(f)∩O(f), log5(n)∈Ω(log2(n))

>>9437926
1. You don't need C>1. Just C>0
2. State what is in big Θ/Ω/O of what for fuck's sake!
3. It's less than or equal and n>=k for big O

BigO:
f∈O(g)
iff (∃N,C>0)(∀n>N) f(n) <= C*g(n)
iff limit(n→∞) f(n)/g(n) < ∞

BigΩ:
f∈Ω(g)
iff (∃N,C>0)(∀n>N) f(n) >= C*g(n)
iff limit(n→∞) g(n)/f(n) < ∞

BigΘ:
f∈Θ(g)
iff f∈Ω(g) and f∈O(g)
iff limit(n→∞) f(n)/g(n) = C s.t. C ≠ 0 and C ≠ ∞

>>9437934
Should have just gotten a better model and said fuck it probably

>>9438056
where did I say it was Big-Oh? my image shows it as being big-Omega, and I state it as Big-Omega in my original post. Is my definition for Big-Omega wrong?

>>9438064
try this faggy video, should work
https://www.youtube.com/watch?v=6fHKfcR51X8

Is it ambitious to apply for top 20 PhD programs (in the US) from undergrad if I will only have about 1 semester of actual research experience? 1 rec letter from the professor I'm doing the research with, 1 from a professor in a lab class (made to be like real lab experience), and 1 from some sr/grad level related course. My GPA/GRE are 3.9/4.0 and 90th+ percentile for each section of GRE. I plan on aiming for a PhD anyways for a industry/govt lab (EE/lasers/optics) job so doing an MS first would just feel bad for all the money I would be in debt for.

>>9438061
So for solving big Ω I could choose my C = .1? that way the RHS would always be less than the LHS

How do I prove this:

If P is an orthogonal projection in a Hilbert space, then all λ in C different from 0 and 1 are regular values of P.

?

I am stuck.

Can someone explain to me what is happening here? So I subtract 4 times the second line from the first line. How exactly do I get -t here?

>>9438248
I mean, this can't be that hard right? What the actual fuck. Am I actually retarded? This is just one simple fucking rearranging step in a completely unrelated math problem. I assume my lecturer didn't specify what is happening here because everyone already knows.
Man I really just want to die. I have only a few weeks until the exam and forget what is actually being asked, I can't even do high school math.

>>9438248
Yeah you just replace row 1 with row 1 minus 4 times row 2. Have to account for 3 - 4*(t-9)/(t-12) and so simple algebra you have to make 3 be( 3t -36)/(t-12) so the denominators are the same

>>9438306
>3 - 4*(t-9)/(t-12)
Yea I understand that much.

>simple algebra you have to make 3 be( 3t -36)/(t-12) so the denominators are the same
What? I don't get it. Where does the 3 actually go?

>>9438234
define "regular value"

>>9438073
>try this faggy video
Why the homophobia?

>>9438318
To add/subtract fractions they need to be of the same denominator. To make 3/1 -> (3t-36)/(t-12) you need to multiply it by (t-12)/(t-12) as it is equal to 1 so the number is still conserved as 3

>>9438321
λ is a regular value of a linear operator T:H-->H whenever:
Ker(T-λI)={0}
Cl(Im(T-λI))=H
(T-λΙ)^(-1) is bounded

>>9438336
>Ker(T-λI)={0}
Trivial to show for lambda not 0 or 1

>Cl(Im(T-λI))=H
>(T-λΙ)^(-1) is bounded
Shouldn't be hard to show

>>9438332
Thank you, I finally got it.
It really isn't so hard, struggling with that surely is a sign of deficiency. Man I am really fed up with all this.

Here's a stupid question: Does any feel like they shouldn't be at the level they are? I'm about to graduate but for some reason I feel like I shouldn't be allowed too. Like there is too much I can't remember or don't quite understand enough. I've struggled the past two years and my marks are good but I feel like a fraud or something. I know this isn't therapy but does any other undergrad feel like this? I feel legitimately stupid and undeserving of academic success.

>>9438346
Just keep practicing. Rome wasnt built in a day, but they were laying bricks every hour

>>9438366
Just reread this. Sounds more like a an /adv/ problem. Will move there. Sorry.

what causes Homosexuality

>>9438369
Good strategy to make us answer you. Anyway, all of undergrad is building a base of familiarity. No undergrad education will fully prepare you for a truly difficult graduate program for example, but that's simply a challenge that you work at when you get to it. Keep reading more about your subject and you'll be surprised by how much you've actually retained.

>>9438394
Being gay, usually.

How does evolution work?

If I place a ground in the middle of a circuit will it act as a short circuit?

>>9438461
In general a ground symbol means 2 things:
1) this node is connected to every other node with a ground symbol
2) this node should be considered 0 volts and all other node voltages referenced against this one

>>9438461
Yes if before the load, no if after. however you will liven up all your earths

>>9438234
nvm found it:
https://math.stackexchange.com/questions/1369461/orthogonal-projection-in-complex-hilbert-space

are there any physicists on this board who arent larping?

>>9436158
Pls respond, I know the set of Lorentz boosts isn't a group, since it requires the addition of rotations to be closed. However, I don't know how to prove this. Does it suffice to show that the resultant matrix of two successive boosts isn't symmetric, and thus not a boost in itself?

>>9438423
I think something about environmental pressures on a species will cause them to evolve to better survive it. So like if it is cold out then species will probably evolve fur, beard, or other shit to protect itself from hypothermia, etc, and mate with similar members maybe it gets so cold that the ones without sufficient protection will even begin dying off and speed up the process towards a more cold protected species. Basically species and their bodies evolve over time to increase their offsprings chances of survival and reproduction as the rest may just go extinct. Faster members of a species can escape prey for longer/have a better chance of survival? Probably going to live long enough to reproduce. Over periods of time all these seemingly small factors can accumulate and create new species and is not necessarily a sequential thing. Just because dogs may have evolved from wolves, doesn't mean that the wolf line ends, it just means a group of wolves changed enough over time to make them different enough to be a new species.

There are probably numerous factors that go into how things evolve such as climate, food sources, energy (evolvution aint free). Also there can be genetic mutations (I think blue/green eyes, different skin colours, and lighter hairs in humans are examples but some might not be) which can spread throughout species and become common if desirable enough. I pulled all of this out of my ass from what I understand about 7 years past high school biology as an EE so don't take anything as definitive or correct.

>>9438603
>are there any physicists on this board
Yes. I've watched a lot of Neil deGrasse Tyson.

>>9438603
To what level? I'm in the Applied Physics specialization for my EE PhD 1st year. Not really a physicist, but I am researching on laser/optical technologies in a pretty good lab. Most people here for physics will be a student still (probably high school - PhD level, probably some fuckers that are in middle school though from some of the shitposts I've seen.) There might be some professors, researchers, or other actual working physicists lurking these parts though.

Where is all the hype around Gödel's incompleteness theorems coming from?
It's just a theorem about the Peano axioms. The existence of God? What?

So when amateur astronomers discover stars/comets/etc...

How in the FUCK do they know if it's been discovered before or not?

Is that even how it works? I swear I've heard of stars being discovered.

t. actual dumb cunt

>taking Calculus I over the summer

Everyone is telling me I'm crazy for taking it over the summer because of how fast it will go. I'm thinking I will be able to perform better because 100% of my focus will be on one subject vs spread among 4 subjects.

>>9438394
Fapping to traps.

>>9438863
The essence of Gödel's theorems is that any sufficiently expressive formal system must be incomplete, i.e. there are true statements which are unprovable within that system.

>>9439296
> any sufficiently expressive formal system must be incomplete
Last time I checked Gödel's theorems only applied to recursively axiomatizable (no fucking idea how to say that in English properly, the terminology hell is killing me) formal theories T, such that PA ⊂ T, where PA are the Peano axioms. That's not exactly "any sufficiently expressive formal system".
> there are true statements which are improvable within that system
An improvable statement is just that - improvable, it can't be called "true".

>>9439296
>Gödel's theorems
I know these apply to axiomatic systems (so that the axioms are contained in a set), but what about a category of axioms?

How would you define responsible sourcing?

Does this only affect the suplier of a raw product, or is it the whole chain of production

>>9439338
The category of axioms is a small category since its class of objects is in bijection with [math]\mathrm{Ext}^1_{\mathbb{Z}}(\mathbb{Q}, \mathbb{Z})[/math]. This was first shown by Grothendieck and later shown independently by Gödel.

I am trying to color shapes in a way that each colored shape is only connected to another colored shape at a single point and that there are no two adjacent shapes with the same color.
What are the rules that determine when this is possible and when it is not? The triangle in the lower right doesn't seem to allow coloring in such a way. What's the reason?

>>9439360
You might want to read about graph colorings, since you can consider the equivalent problem of coloring the vertices of the dual graph instead of coloring faces of those shapes

https://en.wikipedia.org/wiki/Graph_coloring

>>9439360
This sort of thing is usually called "map coloring", where you want to assign colors to regions such that no two regions that share a common border are of the same color. (Single points are OK.)

In these terms, it looks like you are trying to color a map with two colors: in the first two diagrams, blue and white, in the third diagram, black and green. We can call this a 2-coloring.

A planar map without any holes in it (regions to be left uncolored) can be 2-colored iff it doesn't have any points that are on the border of an odd number (at least 3) of regions.

>>9439364
>>9439392
Thanks, I'll read up on it.

how can I estimate the energy used in a single stroke of an air pump in joules (like for bikes)?

>>9439643
Take a guess on what the pressure in your tire is, assume it's constant over the stroke, then apply [math]W=pV[/math].

>>9439660
Thanks

t.noob

Hello friends,

Can someone explain why low frequency EM waves are able to reach Earth's surface, but higher energy waves (like gamma) are blocked despite their greater penetrating power?

>>9439161
The issue here isn't if you can focus on it, it's that the course will be rushed, probably multiple topics on the same day, so if you start struggling then there might not be time to clarify things. But if you think you can focus on it outside of class, then go ahead.

>>9433584
Which site has the most accurate depiction of fictional powerlevel discussion?

translates to: calculate the differential of these formulas.

Am I literally supposed to take a gradient of them or am I missing something? Turning a skalarfunction into a vector seems wrong here.

>>9439704
earth's atmosphere is basically a low-pass filter

Can someone please help me identify the structures in and around the vascular bundle of Tropaeolum majus? Where is the phloem?

>>9439957
and this is a better view of the bundle

>>9439920
Pretty much. I hope you fully understand what a differential is.
[math]
df(\vec{a}) = \sum_{i = 1}^n {\frac{\partial f}{\partial x_i}(\vec{a})dx_i} = \nabla f(\vec{a}) \cdot d \vec{x}
[/math]

>>9439971
I wonder if I can do this
[math]
\begin{displaymath}
df(\vec{a}) = \sum_{i = 1}^n {\frac{\partial f}{\partial x_i}(\vec{a})dx_i} = \nabla f(\vec{a}) \cdot d \vec{x}
\end{displaymath}
[/math]

>>9439971
it's the rate of change of a given function, so yeah I guess the vector makes sense here, but where exactly do you pull that dx to the end there? The way I learned to calculate gradients was like this

[eqn]
\nabla f(x,y,z) = (df/dx,df/dy,df/dz)
[/eqn]

>>9440007
... So you don't understand what the differential is.

>>9438104
I don't think so. You have a great GPA and applying to top programs is a crapshoot, anyway. You could apply top 50, though. No reason to apply to only top programs.

>>9440007
If a function is differentiable at point a, the following is true.
[math]
f(\vec{a} + \vec{h}) = f(\vec{a}) + (df(\vec{a}))(\vec{h}) + o(|| \vec{h} ||) \ \ \vec{h} \rightarrow (0,...,0)
[/math]
Where df(a) is a linear map.
You don't really need to know what the gradient is to find the differential of a function. In this case, it just makes the formulae shorter. You just need to multiply the gradient by vector dx (which sometimes looks like (dx, dy, dz, ...), it really depends on how you name your variables)
Generally, every point A has its own differential df(A), which is why the differential has two kinds of parameters: regular "x", "y", "z", etc. - the coordinates of the point A, and "dx", "dy", "dz", etc. - the arguments for the linear map df(A). So in the end (df(A))(dx) is a number.

>>9440016
Why don't you explain it then?
>>9440007
The way I understand it is as the basis of a tangent space on a manifold.
With dx, dy, dz being the basis and grad(f) being the components.

You have an orthogonal matrix A, so all of its eigenvalues have norm 1. How would we describe what would happen to any vector x under the transformation Ax? I know its norm would be unaffected but I don't really know what else to describe.

>>9440061
> How would we describe what would happen to any vector x under the transformation Ax?
You get the coordinates of x in a different orthonormal basis.

Why is the answer to question 17, m+1?

>>9440082
Empty set.

>>9440079
thank you, and just to verify my process on this problem if [math]AA^T=I[/math] does that necessarily mean that A is orthogonal? Or does it only work the other way around, if A is orthogonal then [math]AA^T=I[/math] ?

>>9440104
Actually nevermind I don't even need that, I'm just being retarded
[math]Av=\lambda v[/math]
[math]|| Av|| ^2=||\lambda v|| ^2[/math]
[math]v^TA^TAv = |\lambda |^2||v|| ^2[/math]
Since A is square, [math]A^TA=AA^T[/math]
[math]v^Tv=|\lambda |^2||v|| ^2[/math]
[math]||v|| ^2= |\lambda |^2||v|| ^2[/math]
Thus the eigenvalues have norm of 1.

>>9440104
Well, that's the definition, so it works both way of course.

>>9434580
Not necessarily. You can have a constant nonzero temperature over the entire sphere modulated by varying temperatures, and the center of the sphere would be that constant temperature. You could take it to be zero, however, by taking that as your baseline.

>>9440050
>>9440052
thanks, I learned something!

>>9440052
Read this
http://www.math.caltech.edu/~dinakar/08-Ma1cAnalytical-Notes-chap.2.pdf
Especially
"Definition",
"Jacobian matrix at a",
"Theorem 1(c)"

You'll be able to solve your excercise after.

>>9440052
>>9440171
read here as well

>>9440052
>>9440171
read here as well:
https://math.stackexchange.com/questions/1566376/derivation-of-the-multivariate-chain-rule

>>9440061
Read Axler's book.
By the way, S is initially defined there as "for all v in V: ||Sv||=||v||"

>>9440089
are you saying that's the answer? because the book says its m+1

>>9440439
Fine, I'll elaborate.
{X in P(A) : |X| <= 1 }
That is, every subset of A with 1 OR FEWER elements. Obviously, the cardinality of this set is at least m, because for every x in A there is a subset {x} in P(A) that meets the requirement above. But the empty set is also a subset of A, and its cardinality is 0, which is less than 1 and in meets the requirement, too. Which means in addition to {x} for every x in A, the empty set also belong to {X in P(A) : |X| <= 1 }.
Thus the cardinality this that set is m + 1.

>>9440460
* Thus the cardinality OF that set is m + 1.

is it possible to make a garment (particularly a jacket or a cloak) that can hide you from thermal imaging? i know that throwing a space blanket over yourself will work, but only for a short while and you have to anticipate when to put it over yourself. is there a buffer material to put between yourself and the blanket that will stop it from warming up?

>>9440729
Yes its possible.
There was a talk about this at C3 few years back but I cant seem to find it.
If you have time dig through their archive.

>https://media.ccc.de/b/congress

>>9433584
my retarded ass decided to follow the anon guide to mathematics avalialbe on sci wikia not realizing link to stewarts book contains whole 3 volumes in one pdf, while the guide wanted you to take volume one before Spivak. My interest so far was learing single variable calc sufficiently so I wanted to continue to Spivak and then study other subjects (currently SWITCHING major TO CS from a meme degree). I ended up doing pretty much all chapters 1-15 (also really pushed myself since the time estimated for volume one was one week, I did theese chapters in around 2 weeks but in atotally autistic way). I plan on doing more advanced maths course material because it's intresting to me anyways but wanted to do the rest later. So would you on my place finish Stewart or leave it for now on and go with Spivak and then study maths less rigourously for some time?

>>9440790
I really dislike Stewart's approach to calculus. I'd advise dropping it and sticking with Spivak.

>>9440795
thanks

How do I learn index notation for linear algebra? Shit don't make no sense.

>>9440790
>my retarded ass decided to follow the anon guide to mathematics avalialbe on sci wikia
Why?

>>9440828
>How do I learn index notation for linear algebra?
What do you mean by "index notation"?

>>9440902
Just an example.

Quantum electrodynamic theory, is it saying that a photon can affect the trajectory of an electron if fired at it? Can a photon fired at a certain frequency displace electrons from an object?
Tell me why i'm retarded, please.

Luigi got a certain number of tables from his friend, if he uses them as single tables with 4 chairs each he is 6 chairs short; if he uses them as double tables with 6 chairs each he has 4 extra chairs. How many tables are there?
>I know the answer is 10
>I know this is grade fuckin 5
>I don't know the algebraic approach
Anyone willing to help?

Can a planet like Jupiter orbit a small white dwarf? Star, not human ofc.

when calculating the work done to a box being pushed horizontally by an angled force, the equation is work=f×distance×cos(angle)

where does the cos(angle) come from?

>>9441129
The angled force?

I'm a brainlet too.

>>9441079
photoelectric effect?
t. iq89
>>9441113
I'm assuming a double table is putting two tables together. The left hand side gives the 4 chairs per table leaves you six unfilled. The right hand side gives the 6 chairs per 2 tables with 4 chairs unused.
[math]4x-4=3x+6[/math]

>>9441113
Every time you combine 2 tables, you gain 2 chairs. so we need to go from -6 to +4 in steps of 2. Thats 5 steps = combining 2 tables 5times = 10 tables

I want to think more clearly. To sharpen my mind and structure what I know.
How do I do this?
Is there a good book for logic? Do you guys have a link?
Any recommendations?

>>9441120
I would assume so. I think our sun would become a white dwarf but would have to expand first. So the inner planets would be swallowed and the gas giants would stay around, nothing to stop them from orbiting?
>>9441129
pic related, work is the dot product of force and distance, otherwise the component of force in the direction of travel. The cosine comes from the fact you have to split the component of the force parallel to the direction.

>>9441166
>I would assume so. I think our sun would become a white dwarf but would have to expand first. So the inner planets would be swallowed and the gas giants would stay around, nothing to stop them from orbiting?

I know white dwarfs are very small, but idk if they're like small and light or small and supermassive, aren't white dwarfs sometimes smaller than planets? How could a planet orbit around it if so?

>>9441162
>How do I do this?
>Is there a good book for logic?
You probably want to do math, not logic.

>>9441166
cos question noob here

so is it true then that there is also a vertical component of work which would f×distance×sin(angle) but since theres no distance, the work is 0?

is the same true for a z axis? would you have to switch to a 3d coordinate system for a z axis?

>>9438180
Yes, anything not 0.

How does mathologer do his animations of transforming formulas, like in this video, starting from 2:50?
https://www.youtube.com/watch?v=YuIIjLr6vUA

>>9441173
It's not volume that matters. The gravitational field is because of an object's mass. A white dwarf is made from the very dense collapsed cores of dead medium stars. In fact it's become electron degenerate matter, where the only thing holding it up from collapse is the Pauli Exclusion Principle between electrons. They average just over half the mass of the sun, so yes objects can orbit them.

>>9441189
>so is it true then that there is also a vertical component of work which would f×distance×sin(angle) but since theres no distance, the work is 0?
Yeah, only the parallel component really changes the energy of the object. Suppose you pushed a block on a frictionless surface for some distance, except you're pushing downwards at an angle. The component downwards simply contributes to the "weight" of the object and the normal force, whereas the parallel component gives you the final energy. It'd be the same if you pushed with a force equal to the cosine component directly horizontal for the same distance.
>is the same true for a z axis? would you have to switch to a 3d coordinate system for a z axis?
Yes, this is where dot product comes in handy

>>9441201
Oh, nice! Thanks for answering, I just wasn't sure.

>>9441174
But I want to think clearly for everything, not just for math.
I want to actually infer things from facts, and know why I know what I know, and be able to express it.

>>9438608
Lorentz boosts = Lorentz transforms - rotation

Just use determinate. Let L and K be nonzero boosts
det(L)=γ^2+β^2γ^2= [1+β^2]/[1-β^2]
det(LK)= [1+β^2]/[1-β^2] * [1+B^2]/[1-B^2]
=[1+β^2+B^2+β^2B^2]/[1-β^2-B^2+β^2B^2]

This must equal [1+b^2]/[1-b^2] for some other Lorentz boost. Therefore b^2 = β^2+B^2 + β^2B^2 = β^2+B^2 - β^2B^2 so β^2B^2 = 0 ...

>>9440082
>|X| = 0
[math]X = \emptyset \\
\mathscr{P}(\emptyset) = \{\emptyset\} [/math]
>|X| = 1
[math]X = \{\emptyset\} \\
\mathscr{P}(\{\emptyset\}) = \{\emptyset, \{\emptyset \}\} [/math]

>>9441231
the fuck

For a spin 1/2 system with an eigenket |Sz = h/2>,

why is <--|Sz> = 0?

where <--| is the spin down bra

>>9440082
All singletons of elements of A + the empty set. = m+1.

In general
[math] | \{ X \in \mathscr{P}(A) : |X| \leq k ~{\rm and}~ |A|=n \} | = \sum_{j=0}^{k}{ {n}\choose{j} } [/math]

>>9441252

Nevermind I got it.

I even sort of answer it in my question by saying Sz is an eigenket and not an operator.

>>9440790
follow the anon guide to mathematics avalialbe on sci wikia not realizing link to stewarts book contains whole 3 volumes in one pdf

What are you talking about? What link?

>>9440923
https://en.wikipedia.org/wiki/Einstein_notation

>>9441162
http://4chan-science.wikia.com/wiki/Mathematics#Set_Theory.2C_Mathematical_Logic.2C_and_MetaMathematics

>>9440790
>SWITCHING major TO CS from a meme degree

CS is the meme degree. You're better off majoring in anything else, even religious studies.

If youre a professor and you catch a group of students cheating, what would you do?

Half my physics class cheated on a major project last semester. My prof didnt rat on anyone but he did lower their grades an entire letter

>>9441366
>If youre a professor and you catch a group of students cheating, what would you do?
Punish them as severely as is permitted under department regulations.

>>9440043
Thanks. I guess I will just apply anyways. Some of the top 20 schools im applying to have MS options too which I think I have a better shot at. I plan to apply for about 6 or 7 top 20 and 3 or 4 top 40ish. After that I wont really have the money to apply for anymore.

>>9441366
I mean, if I was a professor then I would be trying to figure out if my teaching style is fundamentally flawed or if it's just really bad luck with a bunch of rotten apples.

>>9441388
>took a picture because formatting it on 4chan is too hard
Literally takes less than 90 seconds you lazy bum
[math]\underline{\rm{ Position ~ of ~ Particle}}: \vec{r}(t)=(1-2t)\vec{i}+\frac{t^3}{3}\vec{j}+t^2\vec{k}, ~t\geq 0 [/math]
[math]\underline{\rm{ Find ~ distance ~ traveled ~ by ~particle}} ~ \rm{between ~ point ~ \underline{P(1,0,0)} ~ and ~ \underline{Q(-5,9,9)}} [/math]

>>9441366
>If you're a professor and you catch a group of students cheating, what would you do?

Fail and report them to the dean.

>Half my physics class cheated on a major project last semester. My prof didnt rat on anyone but he did lower their grades an entire letter

Cheated how?

I want to prove that the eigenvectors corresponding to different eigenvalues of an orthogonal matrix are orthogonal. I don't really know how to go about starting this, any help would be appreciated

>>9441481
Let [math]A\vec{a} = \alpha \vec{a}, ~ A\vec{b} = \beta \vec{b}, ~ \alpha \neq \beta [/math].
What is [math]\vec{b}{}^T A \vec{a} [/math]?

>>9441481
>I want to prove that the eigenvectors corresponding to different eigenvalues of an orthogonal matrix are orthogonal.
Why?

>>9436926
>Would it be split at the node after R1?
It would, when you connect some load to Vout (something, that draws current, like a resistance, but not only).
People new to electronics often forget about it and treat it literally like a voltage divider when they want to eg. convert the voltage of their voltage source without any buffering, and are surprised that the Vout falls almost to 0 when they turn their load on.

That being said, you can still use it like that, and it's a valid thing to do in some appliances. The trick is to supply large enough current Is (current coming from voltage source) compared to the current IL (load current) so the voltage drop at Vout is acceptably small. You can do that by picking small enough R1 and R2 resistors and making sure your voltage source can handle the current.
Eg. say we have an ideal 10V voltage source that can supply any amount of current Is. We want the Vout to be at 5V with +/-10% acceptable margin, and we know the load draws 100mA at most. What is the value of current Is (and in consequence, the R1 and R2 that set that current) that has to flow through R1 (and partially R2) for Vo to meet the specifications? Try doing it on your own and test it in some circuit simulator.
Spoiler: the voltage has to be divided in half, so R1=R2, and from that you can calculate that the R1 and R2 have to be both 10 ohm resistors and Is =550mA.
That's a lot of current and it might seem to be a waste, as it has to flow all the time and waste ~5W of power for nothing, but it's also a cheap way of doing it and in some cases it's viable. But in this case it wouldn't be so cheap as those would need to be quite chunky resistors to dissipate 2~3W each.
But there's even a more important reason to remember this - anything you connect to Vout will always draw some current. Even high impedance buffers or any other two-ports will always act as some kind of a small load and that has to be taken into account to e.g. establish your margins

>>9441495
It's a proof left to the reader in my numerical linear algebra class notes
>>9441491
The only thing popping out to me is to replace [math]A \vec{a}[/math] with [math]\alpha \vec{a}[/math] but I don't think that's what's intended because it doesn't feel useful. I'm a bit of a brainlet on this kind of problem

>>9441498
it is probably best for me to try to figure this out based on your hint I think, I will try harder and come back if I cannot figure out a solution.

>>9441497
and bellow is the link to the simulation of that example:
http://www.falstad.com/circuit/circuitjs.html?cct=$+1+0.000005+10.20027730826997+50+5+50%0Ar+224+160+224+240+0+10%0Ar+224+240+224+336+0+10%0AR+224+160+144+160+0+0+40+10+0+0+0.5%0Ag+224+336+224+384+0%0Aw+224+240+320+240+0%0Ai+320+240+320+336+0+0.1%0Ag+320+336+320+384+0%0AO+320+240+384+240+1%0Ax+344+324+397+327+4+24+Load%0Ax+184+208+207+211+4+18+R1%0Ax+183+292+206+295+4+18+R2%0Ax+182+151+196+154+4+18+Is%0Ax+280+225+295+228+4+18+IL%0Ax+333+223+369+226+4+18+Vout%0Ax+131+147+156+150+4+18+Vin%0Ax+183+350+218+353+4+18+Is-IL%0A

>>9441491
I didn't follow your hint but I think I found a different way of showing it.
Using your example, we want to show [math]\vec{a}^T\vec{b}=0[/math]
[math]\vec{a}^TI\vec{b}[/math]
[math]\vec{a}^TQ^TQ\vec{b}[/math]
[math](Q\vec{a})^TQ\vec{b}[/math]
[math]\alpha\vec{a}^T\beta\vec{b}[/math]
[math]\alpha\beta\vec{a}^T\vec{b}=\vec{a}^T\vec{b}[/math]
This is only possible if [math]\alpha\beta=1[/math] or [math]\vec{a}^T\vec{b}=0[/math]; since [math]\alpha[/math] and [math]\beta[/math] are distinct eigenvalues with norm 1, one of them is at least not 1 so the latter must be true and thus the eigenvectors are orthogonal.

>>9441526
I fucked up the editing and notation on this but I think it's clear

>>9441526
>>9441527
oh I guess I should consider the eigenvalues could be complex, I'll just replace it all with complex transpose

I have a group:
>A, B, C, D, E, F, G, H, I
>9 separates

Each week, these must be organised into one group of five and one group of four.

I have the following constraints:
>B and I must always be together
>D and E must always be together
>A, B, and C can each be together, but not all three in one group
>The groups must be as differently arranged as possible each week

Is it possible to achieve this such that each letter is in the same group as another letter an equal number of times after X weeks? What value is X?

I'm not great at maths so I'm trying to figure it out manually, but I'm hitting difficulties.

[math]\vec{b}{}^T A \vec{a} \\
= \vec{b}{}^T (A \vec{a}) = \alpha \vec{b}{}^T \vec{a} \\
= (\vec{b}{}^T A) \vec{a} = (A^T \vec{b})^T \vec{a} = = (A^{-1} \vec{b})^T \vec{a} = \frac{1}{\beta} \vec{b}{}^T \vec{a} \\
\alpha \beta = 1 [/math]

>α=i, β=-i
>what now?

[math] \pmatrix{ \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta} [/math]
has eigenvalues i and -1 with eigenvectors
[math] \pmatrix{1 \\i} ~ and ~ \pmatrix{1 \\-i} [/math]
Which are not orthogonal (with a real inner product)....

So you either misread "an orthogonal matrix" and meant a symmetric matrix (unlikely) OR an orthogonal matrix with real entries therefore being unitary as well. Then T is replaced with * and you have [math] \alpha \overline {\beta} = 1 [/math]

>>9441617
>*has eigenvalues [math]e^{i\theta}[/math] and [math]e^{-i\theta}[/math] with eigenvectors

>>9441617
>>9441620
We were just given that [math]AA^T=I[/math]. I'm guessing it's the latter therefore

>>9441617
>>9441620
thank you for your helping me in understanding this, my linear algebra background is a bit lacking (I'm doing a special program for data science since I just got out of conscription)

>>9435394
You don't need to know about logs to realise if a^b = a^x then x=b

>>9441662
>You don't need to know about logs to realise if a^b = a^x then x=b
But that implication is actually false.

>>9441662
No, x=b modulo [math]2 \pi i [/math]

>>9441551
>Is it possible to achieve this such that each letter is in the same group as another letter an equal number of times
No. There always exists a pair (B,x) that has been in the same group less times than (B,I).

>The groups must be as differently arranged as possible each week
You have to define this formally, preferably as some metric [math]d(a,b)\geq0[/math] that is to be maximized, where a and b are some partitions into groups.

Most likely the easiest approach is to consider the set of all partitions into groups of said sizes, i.e., [math]S=\{s\in\{0,1\}^9:\Sigma_i s_i=4\}[/math]. Clearly [math]|S|=9C4=126[/math]. Then take out elements according to the constraints and compute [math]d(a,b)[/math] for every remaining [math]a,b\in S[/math] and pick the maximal pair(s).

>>9441481

[math]f:\mathbb{R}\to\mathbb{R}[/math] defined by
[eqn]f(x) = \begin{cases}
2-x & x \leq 1 \\ (x-2)^{2} & 1<x<4 \\ 8-x & x\geq 4
\end{cases} [/eqn]
How the HECK do I evaluate [math]f[A][/math], where [math]A = [0,2] [/math]. I understand for discrete sets but this it putting my neurons to the breaking point. It would be the set such that [math](0\leq f(x) \leq 1) \cup (1<f(x)\leq 2)[/math], r-right?

How to solve this?

I've done (x'i+1x)^-1 and (x'i+1)y

But stuck on how to get the required form

>>9441796
https://proofwiki.org/wiki/Image_of_Union_under_Mapping

Can anyone help me understand addition of angular momenta (qm)? I get adding l_1 + l_2 and getting the subsequent m spectrum, but why would you say L=|l_1-l_2|? Thanks in advance and please don't be mean

>>9441427
Copied each other's code in a programming class for the midterm. The prof knew bc they all made the same mistake

what's [math]\mathbb{R}\setminus (0,\infty)[/math]

>>9441876
is it [math]\mathbb{R}_{x\leq 0}[/math]

>>9441813
so is [math]f[[0,1]]\cup f[[0,2]][/math] a sufficient answer?

>>9441885
[math]f[(0,2]][/math]*

>>9441885
answer is [math][0,4)[/math]

why aren't you smart folks putting us dumb folks out of our misery?

>>9441900
If you sit near ant colony and talk with them,will they respond?
The answer is no,so nobody cares about you people and you are ignored en mass.

>>9441905
in english please

>>9441796
m8 just look at the graph

what element of [math]\mathscr{P}(\mathbb{R})[/math] does it map to over [0, 2]? answer is [0, 2]

>>9441908
i don't understand

Why are ceramics harder than metals?
Why are they more brittle too?
Is there a relationship between hardness and brittleness at the higher end of the hardness scale (diamonds etc).

>>9441919
that blue line is a set of the form [math]\left\{(x, f(x)) \in \mathbb{R}^2 : x \in [0, 5]\right\}[/math]

now grab all the points in that set that have a number between 0 and 2 in the first coordinate and take the union of all (the singleton sets containing) their second coordinates. what do you get?

Is there any undergrad physics workbook book with exercises and commented solutions to them?
I'm not a smart guy. I can't solve a three level questions from Young book alone. There is a lot of gimmicks to solve them that I don't know but I want to learn.

Pls help me and don't bully

>>9441885
[math]
[0,2]=[0,1] \cup (1,2] \\
f([0,2])=f([0,1] \cup (1,2]) = f([0,1]) \cup f((1,2]) \\
f([0,1])=[1,2] \\
f((1,2])=[0,1) \\
f([0,2])=[1,2] \cup [0,1) = [0,2]
[/math]

>>9441936
over-complicating it

>>9441931
>>9441936
should be able to learn from these thanks.

>>9441947
read some of this too if you haven't already https://en.wikipedia.org/wiki/Image_(mathematics)

>>9433584
Does anyone have the scoop on the engineering scene at the university of Florida ? Which engineering majors are backed up and what is a critical course gpa worthy of applying with? I’d like to do mechanical engineering. I’m three courses away from eligibility.

>>9441943
How?
The only thing redundant is the first line
And lines 3 and 4 need justification which I skipped.

What is a non-specific interaction ? And then what is a specific interaction...

Corrently writing a term paper in astronomy (high school) on the relationship between galaxy classifications and color.
So in my work I decided to plot the b-v color index against the Hubble type of some galaxies from a VIZIER catalog and try to find the correlation between them. What else do you suggest for me to do?

can someone link the wiki with recommended books?

How do I get rid of "image 1.jpg" beneath the image? :L

>>9433584
Reminder that Erdos was so autistic that when he attempted to care for people in their time of need, he instead drove them and people who knew them to suicide.

>Hoffman reports the following anecdote, which displays Erdős's single-minded devotion to his friends and mathematics. In the late 1960s, the young mathematician Jon Folkman was diagnosed as having advanced brain cancer. During Folkman's hospitalization, he was visited repeatedly by Ronald Graham and Paul Erdős. After his brain surgery, Folkman was despairing that he had lost his mathematical skills. As soon as Folkman received Graham and Erdős at the hospital, Erdős challenged Folkman with mathematical problems, helping to rebuild his confidence.[1]

>Hoffman notes that Folkman's recovery was short-lived. Notwithstanding his ability to solve the problems posed by Erdős, Folkman purchased a gun and killed himself. Folkman's supervisor at RAND, Delbert Ray Fulkerson, blamed himself for failing to notice suicidal behaviors in Folkman. Years later Fulkerson also killed himself.

https://en.wikipedia.org/wiki/The_Man_Who_Loved_Only_Numbers#Erd%C5%91s's_nursing_of_Jon_Folkman

When determining the representations of raising/lowering operators in a given Lie algebra; should the raising/lowering operators always be able to be written as a linear (hermitian) combination of generators? I'm analyzing the B2 algebra and my root representations satisfy both the transitions between eigenstates and neccesary commutation relation perfectly but can't be written as a sum of generators.

>>9442318
\caption{Your text}

>>9442318
Either caption after includegraphics or no space in the image name

>>9442338
basically /sci/ in a nutshell
>YOU SHOULD BE ABLE TO SOLVE THIS

How do i solve this physics question?

A person sprints 100 meters in 10.8 seconds.
Constant acceleration the first 2 seconds.
Constant speed from then on.

What is his speed after 2 seconds?

>>9440082
What book is this?

>>9442403
The solution is pretty straightforward.
[math]
S = \frac{a{t_1}^2}{2} + v{t_2} = \frac{a{t_1}^2}{2} + a{t_1}{t_2}
[/math]
t1 = 2, t2 = 8.8

We have a cost function [math]\frac{1}{2} \sum_{i} ||y^{(i)} - Wx^{(i)}|| ^2[/math], where each individual [math]y^{(i)}[/math] and [math]x^{(i)}[/math] is a known vector of some length. We want to minimize this with respect to W, which is throwing me for a loop.

I rewrote the norm as [math]||y||^2-2x^TW^Ty+x^TW^TWx[/math] and tried taking the gradient. The hint on the problem gives the derivatives with respect to W of [math]tr(WA)[/math] and [math]tr(WAW^T)[/math], but I wasn't coming across those in my initial attempt. Any ideas how to get started ?

>>9442403
split into 2 sections. t from 0 to 2 then from 2 to 10.8

t= total time, x is distance, v1 is velocity at t=2

x1=vi*vi*t + (1/2)*(v1-vi)*t*t=2*v1
x2=v1*(t-t1)=8.8*v1
x=x1+x2= [put the above equations in]=100
solve for v1

sorry for the mess. im a phonefag

>>9442515
learn how to use the math tag retard

>>9442403

100 = d1 + d2

10.8 = 2 + t

t = 8.8 seconds

d1 = 0.5a(2)^2 *initial velocity 0, from the equation d = v(i)t + 0.5at^2*

d2 = v(8.8) *this v is the velocity after 2 seconds of acceleration*

however, this v also equals a*t, which happens to be a*2 since we accelerate for 2 seconds


grand equation:


100 = 0.5a(2)^2 + a(2)(8.8)

100 = 2a + 17.6a

100 = 19.6a

a = 5.102 m/s^2

therefore, v = 10.204 m/s


check:

first 2 seconds:

d1 = 0.5(5.102)(2)^2 = 10.204 meters


last 8.8 seconds:

d2 = 10.204(8.8) = 89.7952

d1 + d2 = 10.204 + 89.7952 = 100 meters rounded

>>9434274
You could just take any ring and alter the multiplication to
[math] a \circ b = (1+a)b [/math].
The result is left-distributive (check it!) but not right-distributive.

>>9442480
>>9442518
>>9442560

Thanks! Did not expect serious answers. Pleasantly surprised.

Hey /sci/, help me out a bit. Does the ideal gas law change when I assume more than 3 degrees of freedom?

If I derive it via collisions in a l3-sized cube, I get a change of impulse per particle of
2mv_i
with frequency
v_i / l
along each axis. Yields a force of 2mv_i^2 / l per axis, a force of 2mv^2/l in total and a pressure of 2mv^2 / 6l^3, all per particle. Assuming E to be the average kinetic energy, that yields:
P = 2NE / 3V

Now for 3 degrees of freedom we have E = (3/2)kT and we get the well-known PV = NkT.

So for 5 degrees of freedom, I'd get PV = (5/3)kT ?

>>9442700
Yes. Google specific heat capacities.

>>9442564
>(check it!)
Do it yourself. I'm not your slave!

why is pressure proportional to the square of the particles' velocity rather than directly proportional

>>9442403
Let [math] x(t),x'(t),x''(t) [/math] denote the distance, speed and acceleration respectively after t seconds have passed.
We have:
[math]
x''(t)= \begin{cases} a, &0 \leq t \leq 2 \\ 0, & 2<t \leq 10.8 \end{cases} \text{, where a is constant}\\
x'(t)=x'(0)+\int_{0}^{t} x''(u) du \\
x(t)=x(0)+\int_{0}^{t} x'(u) du \\
x(10.8)-x(0)=100
[/math]

When [math] 0 \leq t \leq 2 [/math] we have
[math]
x'(t) = x'(0) + \int_{0}^{t} x''(u) = x'(0) + a t
[/math]
and when [math] 2 < t \leq 10.8 [/math] we have
[math]
x'(t) = x'(0) + \int_{0}^{t} x''(u) du = x'(0) + \int_{0}^{2} x''(u) du + \int_{2}^{t} x''(u) du = x'(0)+2a+0 = x'(0)+2a
[/math]

Now,
[math]
x(0)+100 = \int_{0}^{10.8}x'(u) du = \int_{0}^{2}x'(u) du + \int_{2}^{10.8}x'(u) du = \int_{0}^{2}(x'(0)+au) du + \int_{2}^{10.8}(x'(0)+2a) du = 2(a+x'(0)) + 8.8(2a+x'(0)) = 19.6a+10.8x'(0) \implies \\
x'(0)=\frac{x(0)+100-19.6a}{10.8}
[/math]

We can obviously assume that x(0)=0 so we get
[math]
x'(0)=\frac{100-19.6a}{10.8}
[/math]

>>9442754
>using x prime not x dot
fag

Is the proof that every cyclic group is abelian below correct? There seems to be something odd about it.

Let a be the generator of the group. Define the elements[math]x=a^m[/math] and [math]y=a^n[/math]. Then [math]xy=a^ma^n =
a^{m+n} = a^na^m[/math]. Hence, G is abelian. C.Q.D?

>>9442786
>Let a be the generator of the group. Define the elementsx=am and y=an. Then xy=aman=am+n=anam. Hence, G is abelian. C.Q.D?
No, you only showed two elements (a^m and a^n) commute.

>>9442786
There's nothing odd about it. It's correct.

>>9442787
That's what every element of the group looks like.

>>9442791
>It's correct.
No it's not, see >>9442787

>>9442799
Are you retarded or what?

>>9442801
>Are you retarded or what?
What do you mean?

>>9442786
Yes, it's correct. Since your group is cyclic, every element is of the form [math]a^n[/math] for some [math]n \in \mathbb{Z}[/math] where [math]a[/math] is your generator.

>>9441872
If the code was just a minor part of some lab analysis, the professor probably would care too much.

NEW
>>9442805

>>9442791
>nothing odd about it

I don't know, I guess it's the fact that we're assuming [math]a^{m+n} = a^{n+m}[/math], which seems to implicitly assume the commutativity of the group. Am I being silly?

>>9442813
>I guess it's the fact that we're assuming am+n=an+m, which seems to implicitly assume the commutativity of the group.
That equality doesn't rely on commutativity of the group, only commutativity of addition of natural numbers.

>>9442823
>natural numbers.
/integers

>>9442813
It assumes the associativity of the group, not the commutativity.

>>9441876
-|R|

>>9441925
>Why are they more brittle too?
Sea of electrons

>>9442826
>It assumes the associativity of the group
How so?

>>9442813
>Am I being silly?
Yes.
You have to understand that all that [math] a^n [/math] means is [math] \underbrace{a\cdots a}_\text{n times} [/math]
So,
[math] a^m a^n = \underbrace{a\cdots a}_\text{m times} \underbrace{a\cdots a}_\text{n times} = \underbrace{a\cdots a}_\text{n+m times} = \underbrace{a\cdots a}_\text{n times} \underbrace{a\cdots a}_\text{m times} = a^n a^m[/math]

>>9442833
>You have to understand that all that an means is a⋯an times
Only true for positive n.

>>9442754
why did you use a instead of v
nice try tho brainlet

>>9442836
Well, if one one of them is negative then you can rearrange them again since a and a^{-1} commute.

>>9442833
Yeah, clear as day. I'm just over analysing this thing.
>>9442836
I don't think we consider negative numbers when talking about generators of cyclic groups.

>>9442868
>I don't think we consider negative numbers when talking about generators of cyclic groups.
We do, he is right, I forgot that case.
Consider the integers for example.

>>9442868
>I don't think we consider negative numbers when talking about generators of cyclic groups.
Then your proof only applied to half of the cyclic group. You need to show that all elements commute with each other.

>>9442874
>We do, he is right, I forgot that case.
I'm not a "he".

>>9442877
Who cares, bitch.

>>9442875
>""half"" of the cyclic group
Unrigorous garbage.

>>9442874
Totally forgot about the integers.
>>9442856
That should settle then.

>>9442881
>Unrigorous garbage.
What do you mean?

>>9442754
> tries to show off his knowledge of basic analytical mechanics
> denotes differentiation with a prime instead of a dot
There was an attempt.

>>9433992
this

use number theory to solve equations desu
>solving x(x-3)(x+2) = 70 using cubic general solutions

Does anyone know a good book about the history and philosophy of science?
>Pls not the L.W.H.H. one