/sci/ - Science & Math

How do i prove that 1+1=2

>>8784491
>How do i prove that 1+1=2
axiomatically

>>8784491
read Principia

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

>>8784494
thanks

Are there any psychological differences that arise when comparing populations who read left-to-right (i.e. English) compared to right-to-left (i.e. Japanese, Arabic)?

>>8784697
Why do you post this anime picture in every thread?

Stupid question thread. Im allowed to ask. You have to answer me.

>>8784699
I have many questions, few pictures.

>>8784697
people tend to be right handed
right to left people tend to write right to left
when they write they tend to smudge more.

this also happens with lefties in the West

>atan2
>a comma
>ends in a period
I feel like something may have been written wrong when some Wikipedia editor copied this formula for calculating hue form a book.
Problem is, everything else I can find is based off of the Wikipedia article.

>>8784903
learn to read brainlet

literally the sentence before that section
>where, atan2 is a two-argument inverse tangent.

https://en.wikipedia.org/wiki/Atan2

K>=S>=1.

Where should I start at proving this? I'm supposed to use generating functions.

OK, this is probably a really dumb question, but I've always wondered this.

If the definition of work/energy in physics is force through a distance, how come my arms get tired when I hold a weight above my head? I'm applying a force to it, to stop it falling down, but I'm actually not imparting any work/energy onto it.

So why do I get tired/warm/etc. which would be signs of work being done?

>>8785072
The energy of the weight does not change, but it takes energy to keep the weight in it's state.

>>8784484
How can I prove the Riemann hypothesis and bench 700 lbs at the same time

>tfw 19 and organic chemistry is raping my ass

How relevant is this shit as a retail or hospital pharmacist? Is Organic II harder or just more coverage of the same topics?

>>8785072
The stuff you are holding is constantly moving downwards. Your arms cause an instantenous reactionary movement upwards, combined they are close to doing nothing at all, but the work done by your arms is real.

>>8784494
that's not real... right?

How do you do p-value testing for least squares method?

>>8784484
>Are nootropics a meme?
probably. I tried them and didn't notice any difference

What is the name for Sierpinski triangle for decimal?
How may I name it if I find something noone knows?
How do I find out if something is known or not?
Doesn't science keep an accurate register for everything?
How do I find a database where all abecedaria are kept?
If such things do not exist how do I create them? Let us create them!

>>8785178
Organic chemistry is the basis of all of Pharmacy. I am unsure what you are learning now, but understanding the structure of compounds is key to understanding how they work. In retail pharmacy you need that type of knowledge to understand interactions mostly. It also helps to understand things like stability. In the hospital pharmacy it is especially important to understand shit like solubility for IV-bags, because precipitation can kill people. An example my professors used is that adding 2 compounds into 1 IV bag is knowledge the pharmacist should have
tldr: Yes, it is important to know for stuff like product stability mostly and for more advanced Organic Chemistry, which is bonding of molecules in proteins and that type of thing. Spoiler: that is about the hardest thing you will learn

>>8785244
It is.
>PM has long been known for its typographical complexity. Famously, several hundred pages are required in PM to prove the validity of the proposition 1+1=2.
Math was a bit different before Gödel put an end to stuff like this. Even in all its futility, trying to achieve the fundamental goals of PM is quite romantic, and going that far makes me tip my imaginary fedora.

How to do refrain from guessing and checking math problems ? When i'm solving a integral for example i'm always thinking: ''this is probably wrong, lets just scribble something down and check how the professor solved it'' It's very hard to not do it this way as i have developed it as a way to not feel lost. I tend to get very surprised when i do things the correct way.

>>8784491
>>8784494
>PM

"It purports to reveal the fundamental basis for arithmetic. However, it is our everyday arithmetical practices such as counting which are fundamental; for if a persistent discrepancy arose between counting and Principia, this would be treated as evidence of an error in Principia (e.g., that Principia did not characterise numbers or addition correctly), not as evidence of an error in everyday counting."

"The calculating methods in Principia can only be used in practice with very small numbers. To calculate using large numbers (e.g., billions), the formulae would become too long, and some short-cut method would have to be used, which would no doubt rely on everyday techniques such as counting (or else on non-fundamental and hence questionable methods such as induction). So again Principia depends on everyday techniques, not vice versa."

>>8785524

Sounds like a self-esteem problem, not a math problem.

However, if you're actually incapable of solving integrals without checking, just isolate yourself from anything that will give you the solutions, such as the textbook, lecture notes, computer, calculator, and try to solve them on your own. See how many you can do, or get approximate answers for without "feeling" like you need to check. If you're still uneasy about that, think about other kinds of problems you don't need to check the answers to because you know how to solve them. What makes your method of solving them different from integrals? What is your reasoning? Can you apply the same reasoning to integrals?

In general, math is not a social activity and you shouldn't need to check other people's answers to "know" if yours is right. You should be able to verify it independently by deduction. That's kind of the whole point.

I need to calculate how many books each customer has bought and how many times each book has been bought, given this customer id and book that they bought, The language I am using is Prolog. Any help would be nice.

Well /sci/?

>>8785696
It would be amazing if i were able to see that my answers were wrong on my own related to finals etc.
I do enjoy solving integrals. They feel complex at my level and i feel smart when i'm able to solve them. Integrals feels different compared to other things. It's like a puzzle with many solutions that leads to the same answer.
Anyway, i will take your suggestion to hearth.

hey guys, i came across a really stupid problem but i couldn't solve it on my own...
i want to create a computer algorithm to solve a problem me and my friends came across by playing an online RPG.
but i have a math problem which is:

a player can throw 1 to 10 ten sided dices (1d10), lets say he throw 5 dices and get these results:

2, 5, 9, 10, 6

each 10 is one success, so lets remove it, (here comes the tricky part):

2, 5, 9, 6

now we need the optimal way to sum a pair of numbers to get another 10:
these are the possibilities to get another 10:
2 + 9; (*)
5+9;
6+9;

* being the optimal way, because removing the 2 numbers (one success):

5, 6 = 5 + 6
another success

i'm not sure you guys understood what i meant, my english is terrible.
But basically:
after checking for 10s and counting them, i need an optimized way to sum 2 numbers and check if they're >=10; if they're not then check the sum of 3+ numbers

Why has no one ever found a comet

Can I get some help with pic related?

I know I have to do some manipulation here in order to get the result of 200.

But I dont understand how, I already did everything. Once the switch is closed then the capacitor behaves as a short. So I merge 20k and 80k and get a voltage of ... 120?

Why is the answer 200?

>>8786011
v(0) is the cap fully charged so it has the same voltage as the cap being OC across the resistor.

Calculate the voltage and voltage divider:
[7.5*(70||80)]*[50/70]=200V

>>8784484
is the truncus symphaticus the same as the ganglions of the spinalnerve?

Do Magnets Work in Space With No Magnetic force taking place

>>8784484

My question has to do with the concept of dimension or "direction in space", more specifically, when considering a linear system as a system of equations compared to a linear combination of vectors.

I guess specifically what I'm curious about is, given an arbitrary linear system, why is the concept of direction in space sort of contained / stored in the variables when considering the system as linear equations, but then is stored in the vectors when considering the same system as a linear combination of vectors?

I know its sort of a strange question, so I'll phrase it using a more concrete yet still general example. Consider a linear system of three equations in three variables, where each equation is of the form (a_i)x + (b_i)y + (c_i)z = d_i. For convenience, and so that we may get some nice geometric intuition, suppose also they represent three distinct planes in R^3 (so we have linear independence). In the context of the system representing planes in space, it seems to me that dimension/direction is sort of "stored" in the variables x, y and z. Now this same system of 3 equations in 3 unknowns can also be expressed as a linear combination of vectors: x<a_1, b_1, c_1> + y<a_2, b_2, c_2> + z<a_3, b_3, c_3>. Here direction of course is stored in the vectors themselves; the three variables that stored direction in the context of linear equations now simply scale the vectors.

And it gets even more bizarre when you consider that, considering the system as linear equations of planes in R^3, we can express each plane as a vector equation by dotting any vector parallel to it with the normal and setting it equal to zero!

>>8786134
And I suppose I'm also curious as to how this relates to the system when considered as a matrix / linear transformation.

Any stats people in here ? >>8786106

>>8785072
The really good question!
This stands for useful and total work. You see, when car is moving it consumes gasoline and when it stands on the ground with working engine its still consume gas. So your muscles does.

What's the name of the theorem that states for all a and b in the Reals there exists an m such that ma>b

>>8786305
i've seen it called the archimedian principle:
https://en.wikipedia.org/wiki/Archimedean_property

So I'm supposed to prove this formula for vectors in pic related, and I can't find anything like it in the calculus books or the internet, does this ring a bell to any of you? I really need a hint :(

>>8786455
https://en.wikipedia.org/wiki/Dot_product#Geometric_definition

In regards to modular exponentiation by squaring and functions that implement it, why is it when the exponent is small, e.g. 2, it's slower than simply taking [math]x^2 mod (n)[/math]? This appears to hold true for exponents 3, 4, and maybe more.

Does anyone know how to prepare bacterial DNA for pcr? I'm an undergraduate and I'm trying to learn new methods.

I haven't had the chance to do much research into different methods because I'm out of my home country at the moment but the graduate student in my lab is seriously useless when it comes to learning new techniques.

TlDR: how do you extract DNA from bacterial colones for pcr.

Why is
10000/x + 15000/x^2 + 20000/x^3=40406 X=1.05
But
45000/x^6 = 40406 X=1.018
Why are they not the same?

>>8786488
Of course they are not the same since you add them together and not multiply them together. I am legit retarded. Anyhow how do I count?
10000/x + 15000/x^2 + 20000/x^3=40406

>>8784484
>Is [anything Joe Rogan has talked about] a meme
Always yes

The fuck am I doing wrong?

Bit confused, anyone want to elaborate?

For a) I wrote that L' = {b^n c | n >= 0} and the connection is that L' would be a subset and a possible substring of L

for b) I wrote L = {c, c^m b | m,n >=1} and the connection is that L' is not necessarily a direct substring of L, but still a possible subset of strings from L.

c) Would I draw a FSM (dfa/nfa) for L' ? So id how do I draw a dfa for a non specific language? L subset {b, c}*

So given the stochastic variable Y=X^2

The cumulative distribution
G(y) = P(X^2 \le y) = P(|X| \le sqrt(y) )

where do I go from here? I realize I suck at inequalities. My first thought was that X is less than sqrt(y) or X is less than -sqrt(y), but that does not sound right, as or becomes union with probabilities, and the union of ``less than sqrt(y)" and ``less than -sqrt(y)''

what are the steps in between the above that leads to:

P(-sqrty(y) \le X \le sqrt(y)) ?

Are knots just a sequences of infinitesimally small vectors?
Are categories just generalized groups?
Are groups just closure tests?
Are sets just containers?

Is it physically possible to completely remove all of the water in a toilet bowl using only a hairdryer?

>>8787031
Yes as long as you don't flush and refill the bowl.

>>8787031
>>8787041
it should evaporate if you just leave it there too, right?

I had a cup of water in my room that over the course of a few weeks or month/two, I forgot completely evaporated leaving only a bunch of gross looking dust left

>>8787013
>Are categories just generalized groups?
no, but groupoids might be interesting for you
https://en.wikipedia.org/wiki/Groupoid

>Are groups just closure tests?
no, groups measure symmetry

>>8787077
>groups measure symmetry

right, that's what I said, closure tests.

>>8787077
>partial function has one of the barbs missing from the arrow

that's cute

>>8787013
categories are generalized mathematical structures. That's their whole point, they generalise a bunch of different branches.

>>8787100
>generalized mathematical structure

IMHO categories aren't really general enough. I don't see what all the fuss is about.

>>8785178
orgo II was easier imo

>>8784484

I HATE THAT MOTHERFUCKER DELTE THIS

>>8786877
a)L' is empty, all words in L contain a
b)L' doesn't contain "c", since m,n>=1
c)Consider the language K={b,c}*
It is obviously regular. Intersection of regular languages is regular. L' is the intersection of L and K and therefore is regular.

>>8787112
Sorry, wouldn't b) be L' = {c^m b | m >= 1} ? Don't quite get why it L' cannot have any c's, since a^n c contains a's the entire subset should be omitted but c^m b should be fine ?

>>8786487
There are plenty of protocols online bro. Most require using detergent to lyse the cell, the separate the DNA, lots of centrifuging and heating, finally staining it with ethidium bromide. It's been years so I don't really remember, but this is something you can simply google.

Is this the correct antiderivative of 1/ (1 - sec(x))?

cot(x) + csc(x) - x?

Here's what I did:
∫dx/ (1 - sec(x))
∫[1 + sec(x) ] dx / [1 - sec^2(x)]
- ∫[1 + sec(x) ] dx / [tan^2 (x) ]
- ∫ cot^2(x) + cot * csc (x) dx
- ∫ (csc^2(x) -1) dx - ∫cot (x) * csc(x) dx
cot(x) - x + csc(x)

Why is burning 'fossil fuels' bad? People say it releases carbon but it had to be in the atmosphere before being absorbed by the biomass and compressed into coal. What is wrong with restoring the atmosphere? Life adapted before, it can adapt again. Let's bring back the Jurassic period.

>>8787242
I can't tell if you're being obtuse or not, but I'm going to give you the benefit of the doubt

The amount of CO2 and other noxious gases we're releasing is at an unprecedented pace/scale compared to what historically has happened before. organisms have been naturally selected to adapt to a specific environment, and man-made technological progress threatens to upset this balance. We are not giving the ecosystems/biomes enough time to adapt properly.

Think of it this way: You have a house by the shore. Sure, it may be a bit waterproof, but it won't be able to stand up to a tsunami.

There's also a bunch of related phenomena that comes with the burning of fossil fuels. You've probably heard of the greenhouse effect, which is the trapping of Earth's heat by the atmosphere. Without the GE, Earth would be at -30°C, so we do need some of the GE to keep us alive. However, due to the CO2, Methane, and other Greenhouse Gases, scientists and (sane) policy advisors predict a best-case scenario average increase in temperature of 2°C, which doesn't seem like a lot, but you have to keep in mind that this is an *average* change. Some areas will get warmer, and some will get colder, meaning more extreme temperatures in climates all around, which would absolutely destroy agrarian economies and developing nations, who bear much of the brunt of industrialization from other countries.

Hope my little harangue cleared some things up.

>>8787276
>I can't tell if you're being obtuse or not
Nope, just retarded. Thanks.

What were the first/earlier indications that the climate is changing?

>>8787283
>Nope, just retarded. Thanks.
Nah, man... Don't sweat it. I've just hung around here enough to the point I can't tell when someone's being ironic for the sake of being edgy sometimes.

I'd be happy to point you in the direction of useful climate change readings / policy stuff if you'd like

>>8787284
There have been signs for a long time, please just go to bed. Lets all get some rest.

>>8787290
I just wanted to know the first sign that spurred on all the research

And I just woke up, why would I go to bed?

>>8787299
>why would I go to bed?
Because you need to sleep more

don't quote me on this, but I think it was research in the Arctic that first may have tipped people off...

>From the late 1970s and through the 1980s, Exxon funded internal and university collaborations, broadly in line with the developing public scientific approach, and developed a reputation for expertise in atmospheric carbon dioxide.[1] Between the 1970s and 2015, Exxon and ExxonMobil researchers and academic collaborators published dozens of research papers generally supporting the "emerging consensus that fossil fuel emissions could pose risks for society" and exploring "the extent of the risks."
>In the late 1980s, Exxon became a leader in climate change denial.[27][28] Lee Raymond, Exxon and ExxonMobil chief executive officer from 1993 to 2006, was one of the most outspoken executives in the United States against regulation to curtail global warming,

>>8787305
The fact that the climate changes has been known for so long that it would be impossible to identify when this was first noted.

The thing about climate is that it takes significant effort to distinguish actual change from statistical noise (i.e. a run of consecutive warmer/colder-than-average years).

With regard to carbon-driven AGW, it's more a case of it starting with the observation that it "should" be happening (a consequence of the absorption spectrum of CO2 and the fact that we've spent the past century scouring the earth for sequestered carbon then putting it back into the atmosphere as fast as we can find it), then trying to analyse the extent to which this is apparent in the available data.

IIRC, the theoretical argument was first made around the middle of the 20th century. Since then, it's largely been a case of analysing weak indicators (tree rings, ice cores, etc) to compensate for the fact that systematic weather observations don't go back far enough to reliably separate trend from noise.

>>8784484
How do I prove that 0 is not actually a number?

>>8785012

The generating function of the left side should be written as a product of two generating functions (each containing just one of those binomial terms).

>>8786490
>how do I count?
>10000/x + 15000/x^2 + 20000/x^3=40406
Please help a retard that has forgotten basic math out. Why is it different from 45000/x^6?40406

Where can I find good courses about compsci like MIT OCW and (RIP) Berkeley's YT Channel?
No bully

Please help!

I'm dumb and don't understand statistics. I have a homework assignment due asap and I can't figure this one thing out, can you please see image related and quickly scribble down answers + work?? you'd be really helping a brother out....

>>8787735
You can divide by a number and get another number. When I divide by zero, my calculator says "not a number", therefore zero is not a number.

>>8786134
>I guess specifically what I'm curious about is, given an arbitrary linear system, why is the concept of direction in space sort of contained / stored in the variables when considering the system as linear equations, but then is stored in the vectors when considering the same system as a linear combination of vectors?

I dont really understand your question.
In both cases it is exactly the same, where is the difference?

You can restate the question to the solution of a system of linear equations to the linear combination of a vectorspace.
That means:
(a_1)x + (b_1)y = d_1
(a_2)x + (b_2)y = d_2


Can be trivially restated as:
(a_1,a_2)^T*x+(b_1,b_2)^T*y=(d_1,d_2)^T

Basically you are "taking the x out of each component of the vector".

The vectors in both cases represent the exact same thing.

>And I suppose I'm also curious as to how this relates to the system when considered as a matrix / linear transformation.
It is just the same. Roughly speaking each vector of a matrix represents a base vector in a vector space.

In that interpretation matrix vector multiplication becomes transforming the vector into another vector in a different vector space.

And solving a system of equations or asking whether a linear combination exists such that target vector is a part of the vector space, (which are the exact same thing) becomes the question whether the linear transformation contains the target vector in its image.


I am sorry if I am not answering your question, but I dont really understand where exactly your question it.

>>8788035
Wait... what don't you understand about this? This seems pretty self-explanatory to me (simply plug in X, solve for Y)

>>8788035
Just put 2 instead of x and solve for y^

>>8788069
I can't do that, my calculator only says "divide by zero error"...

I should get a better calculator

>>8788069
> When I divide by zero, my calculator says "not a number", therefore zero is not a number.

The standard viewpoint is this:

Zero is a number. But the division operator is restricted so that division by zero is undefined.

In other words, instead of restricting the number, they just restrict the operator.

They could have thrown out zero if they had wanted. But they considered it a more elegant solution to just restrict the division operator.

I have a collection with x, y and class values in R
Is there an easy way to calculate means per class and the covariance matrix without splitting it in one collection per class?

Has anyone dealt with having to learn while exhausted? I've got narcolepsy and constantly feel like I'm dead even after I wake up from any amount of sleep. I feel like material just isn't being absorbed and internalized, my focus simply doesn't exist, and when I run into something I truly don't understand yet I end up feeling like I've got a fucking tumor in the front of my brain. If there's anything I can do to help even a little bit, I'd like to know.

>>8788279
red bull

>>8788298

I'm already on real stimulants, it doesn't really do anything except help me not fall asleep. I still feel exhausted and in a hellish silent-hill thick fog.

Is there some formula to find the exact angle if I have both x and y positions on the unit circle?

I know that if I take acos(x) or a asin(y) I will get an angle. But there will be two solutions. I need to find which one of the two is the correct one.

Doing some AI programming and need it to make the AI shoot in the correct direction

>>8788492
>I know that if I take acos(x) or a asin(y) I will get an angle. But there will be two solutions. I need to find which one of the two is the correct one.
Do both, compare the four solutions and use the two that are the same

>>8784484
Should I copy the teachers QED sign?
[eqn]\not \triangle[/eqn]

>>8785178
Orgo II focuses primarily on more in depth analysis of functional groups and their reactions, I can't really say it's necessarily harder since it covers stuff you've learned about already but in more depth

>>8788492
You might be able to use some identities to get things in terms of Tan, then you can use atan2 to fix the quadrant problems

I know nothing about set theory. Is solving problems like
S + {2, 7} = {x, y, z}, Solve for S(I realize this might be unsolvable, it's just an example)
Part of set theory? If so, what are the applications of problems like these?

>>8788809
define '+' for sets first

>>8788540
Yeah I ended up doing it like this. Was hoping for some more effecient solution but it'll do!

>>8788746
Hmm. Interesting. I'm not very good at Tan stuff. I'll try to look it up. Thanks!

As a guy who is weak at maths (lazy) how do I get better? I'm starting science undergrad next year so I want to be prepared? What are the best guides/textbooks? I'll be studying linear algebra and calculus in 1st semester so they're top priority

>>8788884
sorry i put the ? on second sentence by mistake

>>8788809
Besides
>>8788814
No, if I understood you correctly. Set theory is a lot about our axioms (ZFC) and logic. Nowadays (what I have seen so far, naming a few buzzwords) about non-materialistic set theories, large cardinals, advanced combinatorics and set-theoretic-concepts like forcing, ultrafilters etc.

Can a circle exist that has a whole number as perimeter and a whole number as a diameter?

>>8788915
No. If [math]\pi*x=[/math] a whole number for any value of [math]x[/math], then [math]\pi[/math] wouldn't be irrational. You can only turn a decimal into a whole number if it's a fraction, and the very definition of irrational numbers is "decimals that can't be expressed as fractions."

>>8788915
A rational number multiplied by a rational number is always irrational.

Pi is irrational, and how do you find the circumference? You multiply the diameter by pi, therefore either the radius or the circumference must be irrational, i.e. both can't be whole number.

>>8788915
no because pi = C/d and pi is irrational

>>8788930
>>8788939
>>8788940
Alright, and how do we know an irrational number is irrational and it doesn't just start to repeat after 2 trillion digits?

I am trying to wrap my head around the 'time moves slower when moving' part of relativity. I have no training in science, my university degree went in a completely diferent direction.

I take a super fast train going around earth. Or something of the sort, doesn't matter. A spaceship travelling at 200k km/h. When I come back home, are my friends the same people? Implying I have friends, of course. But I have a hard time understanding time not passing at the same speed everywhere, because time is where things happen.

What would it look like if we lived in hyperbolic space?

How would I find the curve [math]g(t)[/math] through [math](2,-1)[/math] whose tangent is parallel to the gradient of [math]f(x,y)=x^2 y^3[/math] for all [math]t[/math]? I've tried integrating [math](\frac{dx}{dt}=2xy^3, \frac{dy}{dt}=3x^2 y^2[/math] but I cant express [math]y[/math] as a function of [math]x[/math] so I don't know how to find the curve.

Can someone explain why this is true?

[math]p_k(n) = \sum_{i = 0}^{k} p_k(n - k)[/math]

Where p_k(n) is the partition function - splits n into k partitions.

Also is there a similar formula for o_k(n), where you can only use odd partitions?

>>8786305
its the defining property of an atchimedian ordered field

>>8789215
Sorry I meant

[math]p_k(n) = \sum_{i = 0}^{k} p_i(n - k)[/math]

>>8784484
Some confusion about gradients. I want to know I'm understanding them correctly.

Say you have a function z = f(x,y), which I am imagining as some surface floating above some domain in xy-plane.
Is it correct to say that (gradf)(a,b) is the direction in the xy plane of the maximum rate of change of the surface above the point (a,b)?
Is it also correct to say (gradf)(a,b) is perpendicular to the contour curve through the point (a,b)? Also, how does (gradf)(a,b) relate to this curve?

If the above are true, then let's say we rearrange the above function into another function g(x,y,z) = f(x,y) - z = 0. This describes a contour surface of some 4-D object, right?
So, what does (gradg)(a,b,c) mean? It would be a vector with 3 components, the first two being (gradf)(a,b) and third being -1. What does the -1 mean?

>>8789220
Wikipedia tells us

[math] p_k(n) = p_k(n − k) + p_{k−1}(n − 1) [/math]

From this, your formula follows, just by applying it again to [math] p_{k−1}(n − 1) [/math] and so on.

Reduces the problem to arguing for this recurrence relation.

>>8789237
Oh I see, just thought up of a combinatorial argument.

If you have k partitions, then you need k elements to start each off, then the other n - k can go in the k partitions. They could all go in one partition, they could be divided evenly, they could all be mixed around, which represents the summation.

Do you know of a similar formula for partitions made of odd partitions? Not sure if this will help but odd partitions = distinct partitions.

how do i find the moment of inertia for a cylinder rotating about an axis that not on the cylinder? for instance, if a cylinder is on the edge of a plate which is rotating?

>>8789258
Parallel axis theorem

What's a good book on nonlinear dynamics?

>>8789272
>kek at pic

Strogatz if you are into aplications

Best qft textbook?

>>8789293

>>8786877
This is math, but I have no idea what field this is. This is so confusing.

>>8789319
>I have no idea what field this is.
Formal languages/computability - subdomain of theoretical CS

>>8788279
Modafinil+adderall+caffeine 8:1:5 ratio.

>>8788915
Yes. Don't get excited though, it's the trivial case of C(0,0).

Are there any examples of spontaneous protein formation? Or can they only form with the aid of RNA?

>>8788950
The faster you move, the time particles have a harder time reaching you, so your personal time slows down.

How do I make a time machine?

I know this isn't supposed to be a homework thread, but how would I actually go about doing this?

As far as I can currently tell I have to do a path integral of the line element [math]dl[/math] (which in cylindrical coordinates is [math]ds \hat{s} + s d\phi \hat{\phi} + dz \hat{z}[/math] ), but how would I go about restricting it to the surface of the cone and then extremizing the resulting integral?

are there any sources on the internet where you can ask scientific and mathematical questions to accredited individuals and expect an answer in a reasonable time? I've got a physics question and it isn't homework.

>>8789594
You're on it right now. But you could try physics forums or stack exchange.

>>8789581
Why isn't this just a half circle?

>>8789554
You just need a cardboard box.

>>8789594
>>8789596
I tried asking this question before but nobody could give me an answer. It's most likely that I didn't fully explain the question. This might be confusing due to a poor explanation, but I'll try to clarify any questions you might have.

Let's say you have a Von Braun style circular space station like the attached pic. Those spokes stretching from the central area to the outer area are hollowed, and inside them are weights attached to cables. The cables are fixed to the hub, and are connected to pulleys. Essentially the spokes are elevator shafts, the weight is the elevator, and the cables can pull the weight. As the space station rotates the weights move to the outer rim as a default position.

Now for the sake of orientation, let's say that "up" in that attached photo is the 12:00 position of an analog clock. Down is 6:00, left is 9:00, right is 3:00. As the space station rotates, and each spoke approaches the 12:00 position, the cables in the spokes pull the weight towards the center of the hub, so that at the 12:00 position the weight is as close to the hub as it'll ever get. After the spoke passes the 12:00 position, the cable is given slack and the weight naturally moves away from the hub, towards the outer wall of the space station. At the 6:00 position the weight is the farthest away from the hub.

Would this centripetal force be powerful enough to propel the space station? I hope I made sense of this, I'm obviously not a scientist.

>>8788949
It is transcendental over the field of rationals, that is, there is no polynomial with rational coefficients such that [math]\pi[/math] would be its root. This has been shown. If it stabilized after some n digits, then it would be rational and we would have a polynomial [math]x-\pi[/math] having both rational coefficients ([math]1, \pi[/math]) and [math]\pi[/math] as its root, contradicting the transcendentality. Therefore, it must be irrational.

>>8789639
The answer to your question is no.

You probably already know of the famous example of a figure skater speeding up when they draw their arms inwards - that's because angular momentum [math]L[/math] is conserved, and drawing your arms (or in the case of your space station, elevator weights) inwards lowers the moment of inertia [math]I[/math], so that angular frequency [math]\omega[/math] increases.

Of course, in the case of your space station, the angular momentum starts at zero, so no amount of change in [math]I[/math] will lead to a change in [math]\omega[/math]. If you just want to think about it intuitively, just think that any "pushes" in an axial direction will never lead to forces in a completely different transverse direction.

You can test this yourself by sitting on a spinny chair and flailing your arms about, which I just did. I could not get a steady rotation to occur just my moving my arms in and out.

If you did want to rotate your space station, you would just have a single track running along the outer circumference, along which you would accelerate some mass in the opposite direction you want the spaceship to rotate.

>>8789660
the space station rotates using small engines like Von Braun suggested. the moving weights aren't meant to cause the space station to rotate, but to propel it forward.

>>8789599
I'm pretty sure it has something to do with the fact that the surface is curved, and they give an answer which is clearly not an equatorial semicircle

>>8789664
Internal forces cannot affect the total momentum of an object, so the answer is still no. You will require some external force to translate the whole station.

If you were to cut the cables each at 12 o clock and send your elevators flying off into space, then yes, the rest of the spaceship would move.

>>8788950
https://youtu.be/GguAN1_JouQ?list=PLsPUh22kYmNCLrXgf8e6nC_xEzxdx4nmY
This video will probably do a better job of explaining it than i can.

Trying to figure out the best way to analyze a set of data, my mind is fried after actually cleaning up it all and I feel like the answer is right in front of me but I can't figure it out

I'm trying to see if there's an effect between load, block number, and location on the result. So 3 IV on 1 DV, but what form of ANOVA would work best or should I be looking at the relationships separately and then analyzing the results of that?

>>8784484
Are there [reputable] math competitions that exist independently of one's grade? For instance, maybe one with age requirements as opposed to grade requirements, or one completely divorced from the educational system?

>>8789745
there's at least a dozen unsolved math problems with prize money attached to them (ranging from $500-$100000), but they're probably not the 'organized competition' you mean

>>8788950
I'm assuming that you've already accepted that light always moves at the speed of light, as seen by any one observer.

Say you have a clock built of two mirrors, spaced far apart so that a few photons bounce back and forth between them, and take exactly one second to do so. Each time the light hits the bottom mirror, a clock ticks forward by one second. The spacing is about 150,000,000 meters or so. If you're standing next to these mirrors, the clock will be ticking fine.

Now let's just take the entire assembly and move it so it's going sideways at some speed v. From a stationary position, light can only travel at c, but must move along a longer path length, so to us, the clock ticks slowly by the factor [math]1/\sqrt{1-v/c}[/math].

Two arbitrary groups have orders a and b respectively. Will the cartesian product of these groups ALWAYS have order ab?

>>8789831
obviously

>>8789850
say that to my face not online punk

I need help on a project euler problem...

In what combination of operators (+, -, *, /) will the numbers {1, 2, 5, 8} evaluate to the number 36?

I'm so unbearably close to coming up with the solution (literally an "off-by-one" error), I just need some extra help on this... I'm just stuck on how you could possibly get 36 from {1, 2, 5, 8}

>>8789933
cmon brainlet

36=6*6=(5+1)*(8-2)

>>8789935
Okay... So in RPN, that would be

5 1 + 8 2 - *

I'm asking this because I implemented a RPN calculator using stacks (evaluating two numbers and an operator and inserting it back in to the top of the stack) to get answers. I just realized that I might not be able to express ( (5+ 1) * (8 - 2) ) using my method

God damn it I hate designing algorithms that almost work but not quite because of a fatal flaw.

>>8784701
Few in number but diverse, nonetheless.

>>8788913
By "+", I meant sumset.

How the hell am I supposed to figure this out

What field of study in EE is the most math intensive? Also, is pure mathematics a stupid major?

>>8789968
then you're vaguely working around things like arithmetic (specifically additive) combinatorics
https://en.wikipedia.org/wiki/Arithmetic_combinatorics

(which isn't set theory)

>>8789969
PChem?

>>8790000
no, electricity/magnetism, just straight physics

also nice quads

>>8789969
Use the given velocity to find the current density, from there it should be pretty easy to us J to find the dipole moment

>>8785307
>How do I find a database where all abecedaria are kept?
https://libraryofbabel.info/search.html

Inside it, you could find the "cure of cancer", but you could also find a flawed version of it. Type any sentence.

>A set of functions are either linearly independent or they're linearly dependent
>exam question says to prove that three functions are LD
>use a wronskian to show that they're not LI
>get marked down for "proving it incorrectly"

Am I in the wrong here or is my prof just an autist?

>>8790062
Also forgot to add that I demonstrated one function was a scalar multiple of another.

What if I increase the strong force in the sun, but also increase the electromagnetic force relative to that?

Do I eventually run into a stumbling block where the temperature can no longer support fusion?

>>8784484
What are some good (preferably online) resources to learn discrete math?

My professor for the intro course next semester is apparently god awful so I'm trying to study it and grasp it before I attend the class, mainly because I'm really slow at understanding math and all I have working for me is an autismal obsession with getting a compsci degree.

thanks guys

>>8790062

We're you supposed to use a different technique?

You're supposed to use the technique being taught in class, to do otherwise defeats the purpose. The exam exists to show you have command of the material being presented, not some other method

>>8788884
>>8788888
my dude you know there's a wiki right?

By the way I'm also bad at math (for more reasons than just being lazy) and basically I've been improving by simply working my ass off,

i.e. reading the textbook and watching online tutorials and constantly practicing problems. I was getting Ds and low Cs in highschool but I've gotten nothing Bs and As now that i'm in college.

If you're actually interested in learning now that helps a lot to.

but I'm also this faggot
>>8790068

so I guess this method only went so far with me. Either that or I'm just scaring myself. Dem 30+ low ass reviews on rate my professor are scaring me man.

>>8790078
We were taught to use Wronskians but I believe that a property is that if it is equal to zero that it is not necessarily LD, which is why I took it one step further to show that one function was a multiple of another. He also showed us a method to prove LD using a graphing calculator but I've never used one and don't own one so I didn't really have a choice given the time constraint.

>>8790098

If the wronskian is equal to zero, then it's linearly dependent.

You probably overthought it and gave an unclear answer, and he docked you for that

>>8790116
What if the wronskian doesn't have a constant solution but has a variable that can be any real number? If you can find one value that makes W=0 then can you say the set is LD? I'm only asking because we never had such a case in our lectures and homework.

Help me please

>>8790148
what have you done so far?

>>8790150
I did (1/2)(2)-2 = -1, not sure though

Any ideas on this one?

>>8790162
plot some examples

>>8790166
Cheers for that, I did that and I realised that the answer is C. That's correct right?

>>8790172
For me it looks like it is contracting.

>>8790184
Ah cheers for that you legend! What do you think about this problem? I set 2=(1/2)x-2 and got x=0 as the new point, is that correct?

>>8790196
Woops I mean x=8

>>8790204
I am sorry, but I have honestly no Idea what the question even is.

Is there an add-on or a program that lets me see math on /sci/ ? I see people typing in long mathematical codes here all day, and i don't understand them unless i type it into wolfram etc.

>>8790260
Your browser should really be able to render latex.

[math]\sum[/math]

This should look like a sum symbol, and you shouldnt be able to see any text.

If you just see text you should really use a different browser.

you can also preview latex by clicking on the TEX symbol in the top left of the reply field.

>>8790271
I'm using chrome like the rest of the cool kids these days.

>>8784484
I plan to build my math skills

Here's the books I plan to work through

I am going to start with an

Algebra and Trigonometry (Stewart, Redlin, Watson)

Book of Proof or some other mathematical proofs book

Now should I do Stewart's Calculus Early Transcendentals, or Stewart's Single Variable Calculus

Then do I move on to Tom Apostol's 2 volume book or onto Spivak's? Or either.

Please feel free to suggest any books?

After calculus, should I move onto linear algebra?

>>8790272
Is it up todate?
Have you tried a different browser (maybe non-chromium based like firefox/IE/edge)?
Are you on windows?

This seems kinda weird.

>>8790280
Hello anon. I just tried to turn off my 4chan addon called appchan x. It gives me a few handy features. But it also fucks up the ''render latex'' as you calld it.
So that is indeed the problem. I can't stand default 4chan so i guess i will just have to leave it like this for now.
Thanks for helping.

>>8790283
I just tried appchan x, weirdly enough it rendered the Latex normally but on 4chan sites with latex the whole site flickered, making 4chan completely unusable.

Leaving it as it is is probably your best option if you dont care about Latex.

>>8790333
Yeah, thanks a lot. I will just turn it off whenever i feel the need to do so.

>>8788320
Do more

Can someone explain to me what the fuck is going on here with the implicit differentiation? These lecture slides don't explain it at all.

>>8789977
> is pure mathematics a stupid major?
You tell me

>>8789933
Another question: How do I get 44 from {1, 2, 5, 8}?
The closest I'm coming up with is (5+1) * 8 - 2 = 46

>>8790639
First term you differentiate, then apply the chain rule to get the dy/dx. Second term you apply the product rule and proceed in the same way as before. On the RHS you simply differentiate. Then you solve for dy/dx.

>>8790639
You're deriving with respect to x, but when there is a y variable in there, you take the derivative as usual but stick a dy/dx there. Try to get all the y's and their dy/dx on one side with the x's on the other, factor out the dy/dx, then divide by that giant term. Just as they did in the photo.

>>8790670
>>8790671
Alright thanks, I think I get it now.

Someone explain to me the mathematics behind why buying separate containers of both vanilla and chocolate ice-cream would be the economically better option than buying pic related.

>>8784484
Extremely stupid question incoming:
Analysis I, II and III as well as Linear Algebra I and II are the core of every math mayor, right?
Everything else is - more or less - an elective or depends on the univerity?

>Analysis?
The european equivalent to Calculus

>>8790716
you get two tubs of ice cream then

ayy boye,

find the sum of

1/2 + 1/6 + ... + 1/(n^2 + n)

testing for n = 1, 2, 3 shows that its n / (n + 1)

but i dont know how to necessarily prove it. I guess I can use induction but can i prove it any other way?

>>8790727
I'm not a math major but I think topology and probability are mandatory subjects if you're studying maths too

>>8790260
do you have JS disabled in your browser?
/sci/ uses some kinda js library to display latex

>>8790667
are you trying to brute-force this shit by hand?
isn't the point of the project euler questions "come up with an algorithm that solves this problem and then implement said algorithm in code"?

>>8790953
The proof par induction is rather easy.

>>8790953
With partial fraction expansion, just compute it. [math]H_n[/math] denotes the n-th harmonic number:
[eqn]
\begin{align}
\sum_{k=1}^{n}{\frac{1}{k^2+k}} &= \sum_{k=1}^{n}{\frac{1}{k}} - \sum_{k=1}^{n}{\frac{1}{k+1}} \\
&= H_{n+1} - \frac{1}{n+1} - (H_{n+1}-1) \\
&= 1-\frac{1}{n+1} \\
&= \frac{n}{n+1}
\end{align}
[/eqn]

>>8784491
Find an object
Get a second object
You now have 2 objects

>>8790671
>deriving

I need help to find a basis for the set of solutions of the given system of differential equation
I posted it on stackexchange so I'll just post the link

http://math.stackexchange.com/questions/2210754/find-a-basis-for-the-set-of-solutions-of-the-given-system-of-differential-equati

>>8791018

holy shit thanks bro

that first bit was smart.

Why is sigma such a cool notation?

>>8791486
because you are literally 14 years old

>>8788035
What's the ^ mean?

>>8791536
^=^

>>8791486

it sucks, that's why we suppress it in physics

>>8791536
[math]\hat{y}[/math] is an estimate for the value of [math]y[/math]

>>8791549
Isn't that because it's suppose to represent a problem and not a formula?

Can someone help me with the resonance structures for this? I'm in my first semester of organic and floundering. I'm not even sure what this is called. (Methyl somewhere) cyclopentadienyl anion? If that methyl group wasn't there it would be easy but, it's throwing me off.

Honest question. How do I become smarter/more informed in my field? I love to read, but textbooks put me to sleep. I love self-teaching and really want to improve my knowledge on my major (geology) but I just don't know where to begin

Hey guys is this thing solvable?

1000 <= (2(k+1))!

Trying to find k in this case.

>>8792398
well 1000/2=500
k+1 = 500
k = 499

I am reading pic in OP and it doesn't make sense to me. I understand the rules that satisfy the definition of an equivalence relation (reflexive, symmetric, transitive) but I do not understand what a partition of a set is. Can someone explain this to me in an understandable way with an example?

Also, I do not understand the book's examples.
It defines S={1,2,3,4,5,6,7,8}.

It says the partition of the set is P={{1,4,7}, {2,5,8}, {3,6}, {9}} This is mysterious to me. How did they get P from S? What relation are they using?

Also the book states: "Here is how to get a partition of S from a relation ~ on S: for every element a in S, the equivlance class of a (wrt ~) is the subset of S defined by:
[a]_~ := {b in S| b ~ a} -- can someone explain what this means?

I thought maybe ~ could be < in this situation but saying {1,4,7} < {2,5,8} etc makes no sense.

>>8787235
http://www.integral-calculator.com/#expr=%201%2F%20%281%20-%20sec%28x%29%29

>>8792438
>Can someone explain this to me in an understandable way with an example?
you partition a set S by cutting it up into some number of subsets so that every element of S is in exactly one of these subsets

>It says the partition of the set is P={{1,4,7}, {2,5,8}, {3,6}, {9}} This is mysterious to me. How did they get P from S? What relation are they using?
its just an arbitrary example

>"Here is how to get a partition of S from a relation ~ on S: for every element a in S, the equivlance class of a (wrt ~) is the subset of S defined by:
[a]_~ := {b in S| b ~ a} -- can someone explain what this means?
it means that equivalence relations define partitions, where the equivalence classes are the subsets the set has been partitioned into

>>8792438
>>8792454

>>It says the partition of the set is P={{1,4,7}, {2,5,8}, {3,6}, {9}} This is mysterious to me. How did they get P from S? What relation are they using?
and the relation is 1~4~7, 2~5~8, 3~6, or the set
{(1,1), (2,2), (3,3), (4,4), (5,5), (6,6), (7,7), (8,8), (9,9), (1,4), (4,1), (1,7), (7,1), (4,7), (7,4), (2,5), (5,2), (2,8), (8,2), (5,8), (8,5), (3,6),(6,3)}

>>8792438
>How did they get P from S? What relation are they using?
They're not using a relation. It's just an example of a partition.
Also, I'm not sure that last part make sense.
Consider a ~ b ~ c.
a ~ c by transitivity.
Then a is in [b]_~ and in [c]_~, which means the two equivalence classes are not disjoint, so they can't be parts of a partition.

>>8792478
>They're not using a relation. It's just an example of a partition.
wrong

equivalence relations are exactly partitions

>Then a is in [b]_~ and in [c]_~, which means the two equivalence classes are not disjoint, so they can't be parts of a partition.
wrong again, since b~c implies [b]_~=[c]_~

>>8792436
ignoring the factorial?

>>8792454
>>8792466
>>8792478

I'm really fucking confused on mutiple fronts.

So you're saying P={{1,4,7}, {2,5,8}, {3,6}, {9}} is a partition for {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6), (7,7), (8,8), (9,9), (1,4), (4,1), (1,7), (7,1), (4,7), (7,4), (2,5), (5,2), (2,8), (8,2), (5,8), (8,5), (3,6),(6,3)}?

If so, why do they define S={1,2,3,4,5,6,7,8}.

> it means that equivalence relations define partitions, where the equivalence classes are the subsets the set has been partitioned into

Can you break this down for me using the P and S in my example?

>>8792500
sounds tricky, I absolutely am

>>8792505
>So you're saying P={{1,4,7}, {2,5,8}, {3,6}, {9}} is a partition for {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6), (7,7), (8,8), (9,9), (1,4), (4,1), (1,7), (7,1), (4,7), (7,4), (2,5), (5,2), (2,8), (8,2), (5,8), (8,5), (3,6),(6,3)}?
no

P={{1,4,7}, {2,5,8}, {3,6}, {9}} is a partition of S={1,2,3,4,5,6,7,8}.
every partition gives an equivalence relation and vice versa, in this case that equivalence relation is
{(1,1), (2,2), (3,3), (4,4), (5,5), (6,6), (7,7), (8,8), (9,9), (1,4), (4,1), (1,7), (7,1), (4,7), (7,4), (2,5), (5,2), (2,8), (8,2), (5,8), (8,5), (3,6),(6,3)}?

>Can you break this down for me using the P and S in my example?
the equivalence relation is {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6), (7,7), (8,8), (9,9), (1,4), (4,1), (1,7), (7,1), (4,7), (7,4), (2,5), (5,2), (2,8), (8,2), (5,8), (8,5), (3,6),(6,3)}

the equivalence relation is defined by a~b if (a,b) is in this set, so we see that the equivalence class of 1 is {1,4,7}, the equivalence class of 2 is {2,5,8}, the equivalence class of 3 is {3,6}, and the equivalence class of 9 is {9}
this gives the partition {{1,4,7},{2,5,8}, {3,6}, {9}}

>>8792515
lol ok

>>8792398
1000<= (2(k+1))!
=(2k+2)!
=(2k+2)(2k+1)(2k)...(2)(1)
=2(k+1)(2k+1)2(k)...2(1)(1)
=2^(k+1)[(k+1)(2k+1)k(2k-1)(k-1)...(1)]
=2^(k+1)(k+1)![(2k+1)(2k-1)(2k-3)...(1)]

so if k=9 then 2^(k+1)=1024, so for any k>=9 you have 1000<= (2(k+1))!

similarly (k+1)! is greater than 1000 for k>=7, so for any k>=7 you have 1000<= (2(k+1))!

so you just need to check k=1,2,3,4,5,6 to see where the cutoff is (it's actually k>=3)

>>8792519
Thanks for the clarify in what you write.

>"equivalence relation is defined by a~b if (a,b) is in this set, so we see that the equivalence class of 1 is {1,4,7}, the equivalence class of 2 is {2,5,8}, the equivalence class of 3 is {3,6}, and the equivalence class of 9 is {9} this gives the partition {{1,4,7},{2,5,8}, {3,6}, {9}}"

Still confuses me. The book says:

equivlence class of a (wrt ~) is {b in S| b~a} which is different than your a~b definition? Can you explain the difference in definitions?

>the equivalence relation is defined by a~b if (a,b) is in this set, so we see that the equivalence class of 1 is {1,4,7},

So what are you doing here? Picking 1 and saying where does 1 occur in P? It occurs in the set {1,4,7}

Okay so in: {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6), (7,7), (8,8), (9,9), (1,4), (4,1), (1,7), (7,1), (4,7), (7,4), (2,5), (5,2), (2,8), (8,2), (5,8), (8,5), (3,6),(6,3)}

does (1,4) appear anywhere? (this is your a~b)? -- the anwer is yes it appears in the set! does (4,1) appear anywhere in the set? (is this the books b~a?) -- the answer is yes it appears! does (1,7) and (7,1) appear anywhere in the set? the answer is yes they both appear!

I'm kind of getting it but still fucking confused. Is there a better book to learn this shit?

i'm a noob and self-learning

>>8792540
man that makes no sense lol. im so fucked

>>8792540
anyone mind giving me a quick rundown on how factorials like this work?

>>8792545
for any relation R (not just equivalence relations) of a set S, you write a~b if (a,b) is in R

you then define equivalence classes for each element, you have equivalence classes [a]_~ for every a in S, defined by [a]_~ ={b in S| b~a }

when R is an equivalence relation you have [a]_~=[b]_~ whenever a~b

>So what are you doing here? Picking 1 and saying where does 1 occur in P? It occurs in the set {1,4,7}

[1]_~={b in S | b~1} = (in this case) {1, 4, 7} since (1,1), (1,4) and (1,7) are in the relation

>Is there a better book to learn this shit?
its pretty standard fare, just try to focus on doing the exercises. i think i first learned equivalence relations from the first chapter of Kolmogorov/Fomin's book 'introductory real analysis' which spends a bit more time on them than Aluffi does (more exercises too)

>>8792568
>[1]_~={b in S | b~1} = (in this case) {1, 4, 7} since (1,1), (1,4) and (1,7) are in the relation
err with the definition b~1 it's because (1,1), (4,1) and (7,1) are in the relation

>>8792568
ok, i'm new to math. I need a good 'first book' to go through with more explanation. if you say kolmogorov's text is better then i will read this over aluffi.

>>8790979
I'm not trying to brute force-it... I'm asking this because there's clearly something in my algorithm that's missing, and looking at the ways in which my algorithm doesn't work helps me understand how to improve it.

I have the bulk of the answer, I'm just missing a small, albeit crucial part

Is there anything I should do to prepare for taking rigorous Abstract Algebra and Real Analysis beyond getting an A in my proof-writing class (that's a pre-req)?

>>8792636
go find a book on abstract algebra and a book on real analysis and start reading and doing exercises

>>8792613
Probably your algorithm is grouping parentheses improperly: checking all combinations is too easy to mess up.

You should look at all (non-equivalent) ways to arrange parenthesis among four numbers; there aren't that many and it will help you make sure you aren't missing any of them.

>>8792647
Gotcha... I thought I was being a Clever Chloe by putting everything in RPN and assuming it would work

I might take a break from Project Euler until I make some projects and read SICP... Hopefully that will help me overcome the "wall" I'm hitting

>>8790127

The the set of functions are linearly indepdent whenever the determinant is not zero. Suppose your Wronskian gives you something like 2t^4, then it's obvious that it is linearly independent whenever t is NOT 0.

This sounds like a differential equations class; given a set of functions, if the solutions are only LD at t=0, but LI at all other t, it is safe to say that your solution set is LI in general.

Books seem fine, but your order is a bit messed up. My suggestion:

Algebra and Trig (book not really important, just find the one with best amazon reviews)

Precalculus, do it as quickly as possible, focus on functions, graphing, slopes.

Stewart's single variable calculus or early transcendentals, work up to and including taylor series.

Multivariable calculus next, use either Stewart again, or whatever, it's not too important.

Then, elementary (computational) linear algebra + Differential Equations.

NOW do the proof book, you will have the maturity to understand it's purpose

Then graduate onto abstract linear algebra (check the wiki) and do Spivak's.

From there, Abstract Algebra and baby Rudin.

>>8792268

This will resonate exactly as if the methyl group is not there.

Electrons can only push into sp2 orbitals (basically, only onto the carbons with pi bonds), the methyl carbon is a full sp3 orbital, so the electron pair will NOT push to the methyl, and it will push around the ring as if it were not there.

This ring is aromatic, btw. Not sure if you have to know that, but it is.

>>8792639

Alright, guess I'll just buy Baby Rudin a few months early and do it over the summer.

If x-y=2, aren't there an infinite number of things that x and y can be?

>>8792704
Nevermind, of course there is I'm retarded.

Hi /sci/.
I love school, but I'm really burned out right now.
I had to drop a silly humanities course and I think I'm depressed or something. I can't focus and get my fucking work done and it's driving me nuts. I live on fastfood and eggs. I don't exercise and I don't care. I don't even know why I'm in school to get an education because I'm not sure why I'm doing it, other than that I just like learning stuff.
What do I do? I sound like a whiny faggot but I'm having a hard time getting out of bed in the morning even.

>>8792682
are you replying to me (>>8792588)?

>>8792714

Hey dude.

So, I used to be like you. You're depressed, sounds pretty bad if you aren't getting up out of bed in the morning.

All I can say is, you have to nip this in the bud, and your anhedonia and lack of drive is a symptom of the depression, not the other way around. Make an effort to get in touch with the school counselling or a doctor, and see a psychiatrist. Get some therapy, get a little medication. You're not being a faggot, I've been there too and it sucks. Trust me, it's way better to deal with this and find enthusiasm and passion in what you're doing than it is to wallow in bed all day, fail 5 classes, get kicked out and wish you were dead. TRUST ME.

While you're dealing with this, take a light load. Minimum course load that's still full time. One hard class, two easy ones that are interesting.

>>8787793
You are not combining your terms properly. You need common denominators before you can add them all up. So you need to multiply the denominators until you get the variable with degree (highest exponent). That is, since x^3 is the variable with degree, then the denominator x needs to be multiplied by x^2 and the denominator x^2 needs to be multiplied by x to achieve this.

>>8792747
Thanks anon.
But don't depression meds make you lose any critical thinking ability? I'd almost rather be sad than dull.

>>8792754
just see a psychologist then and let him tell you about the options

honestly, just seek people out. a school counselor to talk to is a great start. any friends you have, contact them.

>>8792758
O...okay.

>>8792682
Nobody should be planning this fucking far in advance.

How do I go about solving problems like these?

So for sets, magnitude describes the number of elements within them. For numbers and vectors, magnitude describes distance from an origin. Is there logic behind why the term "magnitude" is used for both of these things, or is it just a recycled term?

>>8792786
no one says magnitude for sets, it's universally called cardinality
https://en.wikipedia.org/wiki/Cardinality

>>8792786
it's not a rigorous term, it just means size
for a vector space, the word "norm" is more specific. for sets, "cardinality".

1000 <= (k+1)!

can someone give me a step by step. i suck with factorials

>>8792897
1000=10^3=(2^3)(5^3)<=(2*3*4)(5*6*7)=7!=(6+1)!
so its true for k>=6

then just check k=1,2,3,4,5 brainlet

>>8792906
i don't get it

>>8792906
wait wait wait. where did =10^3 come from?

>>8792911
>>8792912
WHICH Of Me iS THE REAL ME

>>8792906
I don't understand the right side of the equation. what are you doing there.

>>8792912
1000=100*10=10*10*10=10^3

what is there to explain?

>>8792936
look you're gonna have to break this down step by step. ideally in a lot of simple steps.

>>8792948
Are you actually retarded senpai

>>8792955
can you explain the right side?

>>8792962
fuck off

>>8792955
no, just at least clarify what the first part meant

not seeing where the 3 comes from

Is there any animation of what a grid looks like as you gradually introduce negative curvature to it?

>>8792964
tell me you dummy

Is going back to University for a masters in aerospace engineering a mistake?

>>8793000
NOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIITTS

NOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOT

Idk why I fail to solve this, but I feel like a retard.

>>8793003
Okay good, I'm leaving an okay paying job and just don't want to graduate with no job and debt.

I want to know about the history of math. More specifically, cases similar to [math]i[/math] where an operation was undefined, but then it was found to behave consistently if you just pretended like it was defined. Are there many cases of this happening?

>>8784491
Isn't that axiomatic?

>>8792682
Were you referring to me I assume?

>>8790275

I thought precalc and algebra and trig books are the same

>>8792438
>that prose

Haha, what a pretentious explanation. What book are you reading? I love when authors write like they're talking to students who already know about the subject and they're, "merely reviewing the *rather* trivial elementary concepts."

He got to P from S by arbitrarily picking subsets of the powerset of S. Note that arbitrary doesn't mean "random" it means he the person is the arbiter rather than some function. You are doing set theory so you should get comfortable with these types of "choice """"functions"""""".

>{1, 4, 7} < {2, 5, 8} makes no sense

It shouldn't. Inequality is not defined for sets without cardinal grouping symbols, ex. it would need to be something of the form |{a, b}| < |{a, b, c}| to be defined. It is important to remember that set theory is a first order ~*language*~, which means you're just doing predicate logic, not math. Don't try to use the same intuition for math when working with sets, you're just going to get frustrated.

>>8784906
kek

>>8792682
>NOW do the proof book

Wrong. You need to learn to think in cases while you are learning to do baby algebra. That is the whole point of algebra is to reduce problems to a finite number of cases and eliminate disjuncts accordingly.

>precalculus, do it as quickly as possible

Also wrong. You should spend a significant amount of time thinking about limits as they are a fundamental concept in mathematics that are not just limited to exercises in your precalc book. You need to learn to think in limits, not just compute them. Limits are everywhere!

and

>linear algebra and multivariable after differential equations
>distinguishing between the "levels" of calc
>waiting that long to do rudin
>doing "abstract" algebra without any geometry to motivate it

Terrible advice.

>>8793151
>you're just doing predicate logic, not math.
What is math if not essentially predicate logic? It is just infeasable to do it when proving most statements, so we use meta-language. It's a bit like we use assembler in set theory and c++ otherwise.

>>8793131
No.

>>8793013
The integral from 0 to k of 2^x dx is equal to the integral from k to 2 2^x dx then solve for k?

>>8792775
Could anyone have a look at these problems?

>>8793013
>>8793208
nm f@m, I tried it and got k=5/2

>>8793191
>What is math if not essentially predicate logic?

It's tempting to think the world is made of nails when you're holding a hammer. This is just the impression you get from doing lots of proofs. You can prove statements about math with predicate logic. You can prove statements with propositional logic. You can also prove statements with diagrams. You can also prove statements by pointing at pictures and waving your hands. You can also prove statements by doing nothing. That doesn't mean math "is" a picture or math "is" a diagram or math "is" a proposition or that math "is" nothing. These things are useful, they are not mathematics itself.

>It is just infeasible to do it when proving most statements, so we use meta-language.

No, that's not why we use it. We use set theory for historical reasons and also because some people have a hardon for proving uniqueness and existence with braces.

>It's a bit like we use assembler in set theory and c++ otherwise

No. Set theory is by its own axioms not comparable with the way computers work and even if it was, it would not be considered a "low-level" language because it is already classified as a first-order logic which is an order above propositional logic, "zeroth-order logic," which is what computers are built out of and it would also be descriptive, not imperative like asm. If you are familiar with asm you should know this so I don't know why you're making the comparison.

>>8793351
k shouldn't be bigger that 2, however [math]\log_2{\frac{5}{2}}[/math] is the answer I got

>>8793430
Yeah I said nm because the k I was getting for anon's problem was incorrect when looking at the graph. I guess I just put in the wrong antiderivatives into wolframalpha but it looks solved now. Glad I was able to help out in an indirect way if he's still here.

>>8793400
No. You need a formal framework to do, what we commonly call, "math". Otherwise you doing it in a pre 19th century way. Of course you can prove statements with diagrams or by "pointing at pictures and waving your hands", but there must be an underlying (at least believed to be) sound and consistent formal language (and in "math", it usually is first order logic + set theory). Propositional logic is far too weak to do "real math" in it.
This discussion can go on forever, it depends on what is meant by the word "math".

>We use set theory for historical reasons...
No, it's not the only reason.

>...and also because some people have a hardon for proving uniqueness and existence with braces.
Yes, therefor we use meta-language (as said before).

> Set theory is by its own axioms not comparable with the way computers work
Yeh, of course I meant to take it literally.

how would a sport such as MMA be modelled by sports bettors? since there is no score to speak of.

Some sort of chess ranking model possible. not sure

>>8789537
Bumping question

I know this isn't my homework help, but no example in my book and on khan academy seems to work with this. What do I do, what am I missing?

>>8793973
forgot picture, partial fraction decomposition

I'm 22, got shitty grades in high school but decent test scores, and have worked various jobs including military service since graduation.

If I were to take 3 semesters of Math/Physics/Gen Ed., what are the chances that I can get into a decent state school for engineering?

>>8793996
>3 semesters of Math/Physics/Gen Ed
at a local university that is.

>Are nootropics a meme?

Other than prescription grade stimulants they are snake-oil.

Suppose that F(x) = f(g(x)) and g(3) = 5, g’(3) = 3, f’(3) = 1, f’(5) = 4. Find the value of F’(3).

I think it might be F'(3) = 4 , but there is no answer key, can someone make sure I'm not a retard

>>8794179
Nvm I got it sorry for wasting your time with my shitpost

>>8794179
chain rule
[math]F'(x) = \frac{d}{dx} f(g(x)) = g'(x) * f'(g(x))[/math]

[math]F'(3) = g'(3) * f'(g(3)) [/math]
then recall that [math]g'(3) = 3, g(3) = 5[/math]
[math]F'(3) = 3 * f'(5)[/math]
and we know that [math]f'(5) = 4[/math]
[math]F'(3) = 3 * 4[/math]

>>8784491
you have one apple in a basket
you add another apple into basket
have two apples in basket now

Hello what would happen if you Translated the RNA of tRNA?

>>8793151
Thanks for the response. I'm in mobile but the textbook is chapter 0. This is my first exposure to "real math" and the book is quite terrible for an introduction to mathematics.

Instead I picked up a discrete textbook and working through that. Thanks for your explanation.

>>8793973
>>8793978
your answer is going to look like [math]\frac{A}{x+1}+\frac{B}{x-1}+\frac{C}{(x-1)^2}[/math] if it's (x-1)^3 you add another fraction if it's (x-1)^n you keep following the pattern all the way to n

set up systems of linear equations like you probably already know, it's the same thing just a bit more complicated

How do you do these "Given a power series find the function" problems?

I've seen them when they aren't multiple choice too so trying all the answers isn't always an option

Are you just supposed to isolate this

[math]f^n(c)[/math]

from the taylor series formula

[math]\frac{f^n(c)}{n!}(x-c)^n[/math]

and then use your brain to figure it out? I can never do these

>>8794445
basically you are just supposed to memorise the power series for common shit like cosx, sinx, e^x
and then you can look at the series and recognise if it is made up of one of those

Why do set-related notations seem so long-winded and require constant restatement of definitions?

>>8794675
because you're a brainlet

provide examples of what you're talking about

BURNING QUESTION

I'm a first year undergrad student, and I've got my mind set on becoming a computer science major BUT I'm interested in mathematics, yet know practically nothing about the field.
The highest level of math I've taken was kind of a dumbed down version of calc1 for econ students, we basically only got up to learning about multivariable functions.
What are some ESSENTIAL READINGS for someone who's trying to get into mathematics?
Any advice going forward?

Can one get a bachelor's in business finance then get a master's degree in economics?

>>8794709
take the calc series and some other math classes then youll know math your welcum

Why not strap the whole falcon 9 on top of a large plane like Antonov and fire it once it reaches high altitude? pic related.

Falcon 9 weighs 550tons. An updated An-225 carries 250 tons (claimed). So they just need to build double that size and power more or less to carry the rocket by plane. It gets lift from wings without relying on purely rocket fuel.

guise please help

I'm studying to be a mech engineer. I'm taking lectures on formal languages on computer and shit.

Hell, I don't fucking know what the fuck an automata is, neither how can elaborate a fucking automata.

This kind of shit is for CS students, not engineers

pls halp, any good book about it?
I never programmed in my life

>>8794709
Hi anon, I'm in the same boat, only I'm still taking precalculus because reasons.
Anyway, I've found it very easy to just get the last-last-last edition of calculus books (make sure they're old, but still the highly technical type you need-calculus is calculus)
I have one from 1989 by an author called Gillet. It still has logarithm tables in it, so it's a bit of a throwback BUT the information inside is still relevant and good.
Because you said you took business calculus it sounds like you got took the one without trigonometry in it. You may benefit from brushing up on some trig if that's the case. Again, get an "outdated" textbook and just work through it when you can.
Good luck anon and happy studies.

is this a book worth getting for a complete pleb?