/sqt/ Stupid Questions Thread

[Anonymous No.9368782]

Previous: >>9357587

Anyone know lambda calculus?

true = [math]\lambda t. \lambda f. t[/math]
fls = [math]\lambda t. \lambda f. f[/math]
Reduce the following lambda term: tru a b

Suppose the logical and operator was defined as the following: and = [math]\lambda b. \lambda c. b c fls[/math]
Reduce the term: and tru tru.

[Anonymous No.9368785]

Is there a method for this or am I just supposed to 'see' it?

[Anonymous No.9368883]

>>9368785
Okay, I figured it out.
>try some guessing to get the form of a difference equation to describe the series
>create a system functional from the difference equation
>factorise into partial fractions
>turn each fraction into geometric series

[Anonymous No.9369190]

If you have m vectors in since vector space Rn, where m > n, how can you tell if m spans Rn?
So when you put the vectors into a system of equations and reduce it to row echelon form, how can you tell if the do or don't span?

[Anonymous No.9369202]

>>9368782
Can someone pls recommend an advanced book on R?

[Anonymous No.9369203]

>>9369190
sifting algorithm

[Anonymous No.9369339]

>>9368782
I'm a stats major and I have to take Calc II this Spring. I didn't do very well in my calc class, C+, granted I wasn't as motivated as a student as I am now. What sort of stuff should I be focusing on before I go into this class?

[Anonymous No.9369363]

>>9368782
>Reduce the term: and tru tru.
How? You haven't given any reduction rules.

[Anonymous No.9369373]

are the field "axioms" axioms or definitions?
i understand them being axioms for R, but in most cases you have to prove them right?

[Anonymous No.9369378]

>>9369373
>are the field "axioms" axioms or definitions?
The axioms are axioms. The field is defined by those axioms.

[Anonymous No.9369381]

>>9368785
You should start by noticing it's of the form [2^(n+1)-1]/2^n

[Anonymous No.9369413]

>>9369373
>but in most cases you have to prove them right?
you can be asked for instance to show that they hold true. The most you get in terms of "proof" based stuff is proving stuff like -(-x) = x .

[Anonymous No.9369429]

>>9369378
but they don't assert anything do they? what makes them axioms instead of properties of operations?

[Anonymous No.9369436]

>>9369429
don't question it, bad goy. -500 shekels have been withdrawn as punishment

[Anonymous No.9369439]

>>9369429
>but they don't assert anything do they?
The first one from your picture asserts associativity for addition of all elements, the second one asserts existence of 0, etc.

>what makes them axioms instead of properties of operations?
Some of them are properties of operations, but you need to start with some set of axioms otherwise you can't do any operations

[Anonymous No.9369452]

>>9369439
>you need to start with some set of axioms otherwise you can't do any operations
*well you can but you would just have strings of unsimplified addition/multiplication in the case of fields

[Anonymous No.9369459]

>>9369439
>asserts associativity for addition of all elements,
for all elements of what though? the field?
what difference is that to saying [math]\phi(a+b)=\phi(a)+\phi(b)[/math] is an axiom of homomorphisms?

[Anonymous No.9369476]

>>9369459
>for all elements of what though? the field?
Yes

>what difference is that to saying [math]\phi(a+b)=\phi(a)+\phi(b)[/math] is an axiom of homomorphisms?
Nothing.

[Anonymous No.9369517]

>>9369190
The reduced row echelon form has at most n non-zero rows. If it has exactly n non-zero rows, then the vectors form a basis for R^n

[Anonymous No.9369521]

>>9369373
A field is a model for these axioms. Anything which satisfies them is a field.
>in most cases you have to prove them right?
You have to prove that they hold for a particular construction if you want to call it a field.

[Anonymous No.9369524]

>>9369190
>>9369517
And that's an "if AND ONLY if"

[Anonymous No.9369550]

is nofap a meme?

[Anonymous No.9369564]

What fun stuff can I do with 3% hydrogen peroxide mixture?

[Anonymous No.9369568]

>>9369550
Not only that, it's literally cancerous. And yes, I mean literally.

[Anonymous No.9369573]

>>9369568
how come? isn't it true that it increases testosterone levels?

[Anonymous No.9369584]

>>9369573
he's trying to convince you that your prostate will automatically get cancer if you don't masturbate. You know just like every celibate monk in history and such. He's just fallen for stupid information, you probably have too. If you're really interested in if it's a meme or not, just do it yourself and see.

[Anonymous No.9369660]

>>9369550
I'm on week 3 and kissed a girl for the first time on it so I'd say no

[Anonymous No.9369678]

[Anonymous No.9369697]

How do you visualize division? I dont think i ever learned how to properly. Multiplication is easy. Multiplying x by y means taking x, making y rows of the quantity, then adding them all up (so of course it is repeated addition). How do you visualize this with division? Since it undoes multiplication it should be repeated subtraction but it isn't as clear when I try to visualize what's going on.
For instance dividing z by x, would it mean take z, make x rows of it, and subtract x-1 rows? But this doesn't seem like doing the exact opposite of multiplication.

[Anonymous No.9369711]

>>9369697
I actually had this same realization the other day too. I really don't know wtf division is. Perhaps x / y means:

Divide x into y rows of equal size, and count the number of items on one row

But that sounds kinda fucky

[Anonymous No.9369726]

>>9369573
>>9369584
https://www.harvardprostateknowledge.org/does-frequent-ejaculation-help-ward-off-prostate-cancer

[Anonymous No.9369854]

Can someone's blood type ever be changed? Either the letter or the rhesus factor?

[Anonymous No.9369887]

If you have a 3x3 homogeneous system of equations, and when in row echelon form one of the rows is all 0, leaving a 2x3 system, does that mean the column vectors are dependent?

[Anonymous No.9369894]

>>9369854
I changed mine so apparently it's possible. It was after I received severe brain damage though.

[Anonymous No.9369932]

Any idea of how I should start tackling this problem? Just need suggestions to get me in right direction

[Anonymous No.9369938]

>>9369932
it looks like a trig substitution question

[Anonymous No.9369955]

>>9369894
>I changed mine so apparently it's possible.
Letter or Rh or both?

[Anonymous No.9369974]

>>9369854
RH can change apparently for women during pregnancy, but only from - to + and only if the father has + (and the baby too)

[Anonymous No.9369978]

>>9369887
>leaving a 2x3 system
It's been a while since I've taken or even used linear algebra but iirc it doesn't become a 2×3 system. It remains a 3×3 system. I know that doesn't answer your question, sorry.

[Anonymous No.9369983]

>>9369887
>does that mean the column vectors are dependent?
Yes

[Anonymous No.9369998]

>>9369978
Yes, he's saying it's an 3x3 system with one row zero

[Anonymous No.9370025]

When is the electric potential maximum with respect to a magnetic field?

[Anonymous No.9370040]

>>9368782
I want to put in some time to learn calculus. How can I prevent myself from forgetting it in a couple years like what happened with most of what I learned in high school?

[Anonymous No.9370042]

>>9370040
>How can I prevent myself from forgetting it in a couple years like what happened with most of what I learned in high school?
"use it or lose it"

[Anonymous No.9370055]

>>9370042
That's true, I guess there's probably no way around that. If I never use it it will gradually slip away from me. I enjoy programming but the only thing that has pushed me to put in some serious hours learning is to understand physics engines.

Guess I can try to find some excuses to use and brush up on my calculus every few months.

[Anonymous No.9370083]

>>9369697
You can totally view division as repeated subtraction. To divide x by y, start with a group of x things, take away groups of y things (i.e. subtract y) until you run out (i.e. reach 0). How many times did you take away a group of y things? That's the value of x/y.

[Anonymous No.9370234]

>>9369887
Think about what row reduction is doing and what independent means.

[Anonymous No.9370238]

What is the equation relating mass per unit of area (kg/m^2) to tension per unit length (N/m) on a membrane? Specifically in the context of waves/acoustics.

[Anonymous No.9370427]

>>9369932
If y=sin(t).

[Anonymous No.9370448]

can someone explain what's going on

[Anonymous No.9370933]

>>9370083
This, except you might not reach 0 and be left with r < y things. Then r is the remainder. Integer multiplication has no inverse.

[Anonymous No.9370934]

>>9370933
That is, it has an inverse operation "/" such that (xy)/y = x but no unary inverse operation.

[Anonymous No.9371003]

>>9369697
1. dividing a line into equal parts.
2. rows and columns with a little bit left over.

[Anonymous No.9371026]

>>9370040
By rewriting, improving, correcting, and simplifying the material, aka "taking notes." Editing is the best way of learning. You have to understand it to clarify and simplify it. And you remember it because you thought about it and put it into your own words and way of understanding. Note: the best and hardest part of writing is deciding what to leave out.

[Anonymous No.9371115]

>>9371026
I know that, and you're right that will make me retain a whole lot more than the stuff I couldn't wait to pass exams and forget in high school. I'm just paranoid I'm going to put in a ton of time learning and forget it all in a few years.

No way around that I guess, 'use it or lose it' like the other guy said. Probably will start MIT open courseware tomorrow a bit.

My goal is to understand these tutorials:
http://fneuron-mc.myselph.de/gamePhysics/equalityConstraints.html
and implement them into my own physics engine.

I already created a basic demo: https://jsfiddle.net/htg7bn6p/ but anyone can do that. The hard part which has been researched a lot is systems of constraints. And I don't even know where to begin on that, whenever I look at open source physics engines or papers it's a lot of equations, 'Jacobians,' Euler, systems of equations and some calc stuff which I barely remember from high school.

[Anonymous No.9371539]

I'm reviewing high school math: is it smarter to go with a collection of specific books to each subject (algebra, trigonometry, euclidian geometry, solid geometry, analytical geometry etc) or go straight with a precalc book like Stitz-Zeager? I want to get to calc 1 as fast as possible with a solid math foundation

[Anonymous No.9371799]

No, not homework. I'm just too stupid for this right now. I have A1 and A2. How do I get Aq? If you can tell me, you do have permission to laugh at me.

[Anonymous No.9371976]

Should I study geometry? Is it important for future courses?
I remember some basic shit like area and volume, but thats all

[Anonymous No.9372251]

>>9371799
Α1+Α2

[Anonymous No.9372261]

>>9371799
Are A1, A2 and Aq lengths or vectors? As vectors, Aq=A1+A2. If they're lengths, first turn them into vectors:
[x y] = [A1 0] + [A2*cos(60) A2*sin(60)]
=> x=A1+A2*cos(60), y=A2*sin(60)
The length
Aq^2 = x^2+y^2
= (A1+A2*cos(60))^2+(A2*sin(60))^2
= A1^2 + 2*A1*A2*cos(60) + A2^2*cos^2(60) + A2^2*sin^2(60)
= A1^2 + 2*A1*A2*cos(60) + A2^2*(cos^2(60) + sin^2(60))
= A1^2 + 2*A1*A2*cos(60) + A2^2
= A1^2 + A1*A2 + A2^2

[Anonymous No.9372264]

>>9372261
=> Aq = sqrt(A1^2 + A1*A2 + A2^2)

[Anonymous No.9372765]

How would you find the closest k points to a given point p in a 2D space?

So if p = (0,8), and k = 5, so you need to find the 5 closest points to (0,8), what would be the best way to do this?

Bonus for any answer given as Java example implementation!

[Anonymous No.9372779]

>>9372765
There are no closest points other than the point itself.

[Anonymous No.9372784]

>>9372765

What do you mean? You can get arbitrarily close to the point so there are no closest points in that sense, which I'm sure you're aware of. Did I miss some lingo or something?

[Anonymous No.9372798]

>>9371799
>too stupid for this right now
>right now

[Anonymous No.9372799]

>>9372784
Probably described it poorly.
If you have say 14 points on a (x,y), such as pic related.
p represents the given point
The red points are the k closest points relative to p
The black points are other points

How would you find the k closest points relative to p, if all points are defined (i.e. have set coordinates in world space)?

[Anonymous No.9372805]

>>9372799
fuck forgot pic

[Anonymous No.9372825]

>>9372805
just manually calculate the distance between all of them with point p?

[Anonymous No.9372833]

>>9372825
As in brute force?
It'd work but when the number of points becomes larger then wouldn't you essentially be checking every point where only about 80% of them would be of any importance?
So if there were 10000 points, there may be about 100 that are of any importance, k of that 100 you'd actually want, so 9900 would be irrelevant to begin with.
Hypothetically speaking obviously, it could be different.

[Anonymous No.9372852]

>>9372833
You can split up your data it up in rectangles of equal size, then given a point you only have to check the rectangles closest to the point until you have enough points. But that's probably too complicated to be useful unless you actually have 100 000+ data points

[Anonymous No.9372862]

>>9372833
yeah i was talking about brute forcing.
Im not a cs guy but try to do something like check p's x and y coordinates and then do:
-check point A's x and y, do P's x - A's x, then add it to the a list, do this till you have 5 points, then let's say check point F's x and do F's x -P's x, if its lower than any of the elements in the list, replace it with the biggest one of there, then do it for all points, and do the same for Y coordinates, this is unreliable but should be faster, unreliable because you can have P is (5,5) and it will give you points like (6,200) as closest.
-Second way is brute forcing i guess, so do like the same thing but the same for x AND y, or x and y at same time...

[Anonymous No.9372892]

>>9372852
This anon is kinda right, but unreliable again, because if P is (5,5) then /16,5) is closer to P than (14,14) but you dont check it.. do like check every point that is in the rectangle x-10,x+10 and y-10,y+10 then if you dont get 5 points do it for a bigger rectangle, if you get to more than 5 check which is closer

[Anonymous No.9372969]

If we could naturally send and receive radio waves at a large frequency range, what modern electronics could this ability power (as in, supply external power where there previously was none)? Is there any technology that merely receiving long-range radio waves could power up?

[Anonymous No.9372979]

Can any eurobros post examples of their exams? I hear europeans saying their classes are tough as fuck and I just want to see how

[Anonymous No.9373121]

>>9372979
What subject?
Also, from where? Highschool? University?

[Anonymous No.9373151]

How to tell whether it's a shart or not without wiping?

[Anonymous No.9373186]

>>9372799
If the size of the set is small, just use selection sort, but stop after finding the first k points. I.e. find the closest point, find the second closest point, find the third closest point and so on. Requires O(n*k) comparisons.

For a large set of points, there are many possible optimisations. The simplest is to sort by distance squared to avoid the sqrt(). Beyond that, you'd preface selection sort with a one-pass radix sort (i.e. binning), so that you can quickly ignore all but the closest points.

[Anonymous No.9373189]

>>9368782
Has there ever been any obese contributors to science or mathematics?

[Anonymous No.9373197]

>>9373121
University. Anything math, physics, chemistry, biology, or EE related

[Anonymous No.9373202]

>>9372979
>>9373197

Europe is a clusterfuck of countries, all different from each other. Also it really depends on the professor.
I have a master degree in chemistry obtained in Italy, and I took very easy exams as well as very difficult ones.
I went in Sweden for 5 months and the situation, apparently, was pretty much the same.
So, to answer your question, you can't really compare. Probably those Europeans were just lazy, stupid or where just bitching.

But then again, I never saw American exams, except here on /Sci/, so can't really say.

[Anonymous No.9373205]

>>9373202
I just realized I contradicted myself, but the point still stand.

[Anonymous No.9373223]

>>9372979
>>9373197

Ehh, kinda broad but since you asked, here's an average second exam for the Introduction to functional analysis -course. You can take it after you've done the basic first year courses but most take it after the second year.

University of Helsinki, Finland.

[Anonymous No.9373296]

>>9373223

Managed to dig up some exams for Calculus 1. It's the first course you take, along with linear algebra and other basic shit.

Doubt it's any more difficult than in burgerland. If anything, I'd say it's probably easier.

[Anonymous No.9373525]

How do I prepare myself for calc II? Just watch the patrickJMT and 3blue1brown playlists? I remember an anon saying you need to know discrete math to have the proper context to understand calc II but I can't find the post on warosu at this point.

[Anonymous No.9373530]

>>9373525
>How do I prepare myself for calc II?
Just start reading whatever textbook you'll be using

[Anonymous No.9373546]

>>9373525
>I remember an anon saying you need to know discrete math to have the proper context to understand calc II but I can't find the post on warosu at this point.
also this isn't true

[Anonymous No.9373559]

>>9373546
Ok, but I often hear around here that calc II is sort of a mindfuck for a lot of people and that it seems completely "contextless" compared to previous math they've learned.

[Anonymous No.9373663]

What is [math]\int_{}{}idx[/math]?

[Anonymous No.9373665]

>>9373663
ix+c

[Anonymous No.9373671]

>>9373665
I guess what i meant to say was how do you extend integration into the imaginary field?

[Anonymous No.9373674]

>>9373671
https://en.wikipedia.org/wiki/Antiderivative_(complex_analysis)
https://en.wikipedia.org/wiki/Complex_analysis
https://en.wikipedia.org/wiki/Contour_integration

[Anonymous No.9373675]

>>9373671
same as in R^2??? my math is terrible but don't tell anyone

[Anonymous No.9373680]

To get into undergrad research do I legit just email the professors my resume and ask for a chance to meet with them irl? Should I email even if they dont explicity stste they are looking for undergraduate researchers?

[Anonymous No.9373685]

>>9373680
I think so, I have to do this myself but I literally have no qualifications so I don't think I'm gonna get it.

[Anonymous No.9373690]

>>9373680
>To get into undergrad research do I legit just email the professors my resume and ask for a chance to meet with them irl?
Yes, or just skip the email and start off face-to-face

>Should I email even if they dont explicity stste they are looking for undergraduate researchers?
Yes

[Anonymous No.9373702]

>>9373690
Okay thanks. I will probably just email though because professors offices and office hours are not known unless you are in a class of theirs

[Anonymous No.9373708]

>>9373690
Not him, but i wanna do this but im scared. Should I go into his office, introduce myself and ask him about research? What if he yells at me to get out of his office? Im a sophomore undergrad btw

[Anonymous No.9373713]

>>9373708
sure kid

[Anonymous No.9373718]

>>9373708
>Should I go into his office, introduce myself and ask him about research?
Yes (protip try professors you already know first) [also post-docs and PhD students may be open to getting you into research but they obviously won't be able to fund you like a professor can]

>What if he yells at me to get out of his office?
Leave and try the professor next door

[Anonymous No.9373719]

>>9373713
You don't sound very confident with that answer

[Anonymous No.9373722]

>>9373718
How do I meet professors? I'm not a brainlet so I never have to go into office hours

[Anonymous No.9373724]

>>9373719
how to delete? It was accidental

[Anonymous No.9373727]

>>9373680
you should go to office hours or ask after class, it's better.
email is fine. I wouldn't send my resume right away though, but do mention your interests and why contacted that particular prof

[Anonymous No.9373737]

>>9373722
talk to them in class. go into office hours and ask questions about cool shit

[Anonymous No.9373768]

>>9369660
Tell me how you did it anon? Unless you were already a normie in which case fuck off

[Anonymous No.9373769]

>>9368782
Is y' correct?
[math]

\\
\frac{d}{dx}(e^\frac{x}{y}) = \frac{d}{dx}(x-y)\\
\frac{d}{dx}(xy^{-1})e^{\frac{x}{y}} = 1-y'\\
(y^{-1}-xy^{-2}y')e^{\frac{x}{y}}=1-y'\\
y^{-1}e^{\frac{x}{y}}-xy^{-2}y'e^{\frac{x}{y}}=1-y'\\
y^{-1}e^{\frac{x}{y}}-1=xy^{-2}y'e^{\frac{x}{y}}-y'\\
y^{-1}e^{\frac{x}{y}}-1=y'(xy^{-2}e^{\frac{x}{y}}-1)\\
y'=\frac{y^{-1}e^{\frac{x}{y}}-1}{xy^{-2}e^{\frac{x}{y}}-1}

[/math]

[Anonymous No.9373771]

>>9368782
So I'm currently a math major undergrad in my junior year, but I just realized I fucking hate math and wanna do organic chemistry. But I haven't taken any chemistry since highschool.

Where should I start?

[Anonymous No.9373791]

>>9373769
>using regular derivatives for a multivariable function
>e^(x/y) = x - y

[Anonymous No.9373792]

>>9373791
Well yeah I'm trying to learn implicit differentiation.

[Anonymous No.9373794]

>>9373792
Well you're failing

[Anonymous No.9373812]

>>9373769
looks good
>>9373791
>>9373794
shut the fuck up you imbecile

[Anonymous No.9373817]

>>9373812
Thanks m8

[Anonymous No.9373835]

>>9372969
Bumping this. I'm tempted to write a short science-fiction story that has this idea among others.

[Anonymous No.9373837]

>>9372969
>>9373835
>I scream at my toaster to power it

[Anonymous No.9373841]

>>9373837
That would actually be kinda awesome. But no, that's not what I was thinking about, also I don't really know if you can harness radio waves to directly power anything, which is why I'm asking.

[Anonymous No.9373846]

>>9373841
https://www.google.com/search?client=ubuntu&channel=fs&q=can+you+use+radio+waves+as+power&ie=utf-8&oe=utf-8

[Anonymous No.9373897]

>>9373812
He's wrong though

[Anonymous No.9373902]

I want to start learning about audio engineering. Where should I start?

[Anonymous No.9373930]

>>9373897
Mind pointing out the errors? I'm learning this during my free time without a tutor. Any help will be appreciated.

[Anonymous No.9373931]

>>9373930
You clearly have no idea what you're doing so why would I waste my time trying to teach a brainlet?

[Anonymous No.9374001]

>>9371539
Just read a precalculus book. Simmons is nice and concise.

[Anonymous No.9374020]

>>9372833
Unless the points are presorted, you're going to have to scan them all regardless.

Tip: compare distance squared rather than distance and save yourself the square root operation
Tip: compare the distance^2 with (x-x0)^2 and if that's already bigger than the 5th nearest you can stop there and save 3 operation with the expense of an extra compare.

[Anonymous No.9374164]

Where the fuck do I start with teaching myself higher level math? How do I even go about it? I'm tired of being a brainlet and want to develop myself. I have basic highschool level knowledge of algebra, and rudimentary knowledge of derivation and integration (like formulae and implications). Where do I go from here?

[Anonymous No.9374185]

>>9374164
>higher level math
Are you implying you know "lower level math"? Nothing you mentioned can be considered math.

[Anonymous No.9374211]

>>9374185
Ok then, where do I start?

[Anonymous No.9374220]

>>9374211
That depends on your goals, what exactly do you want to learn?
Wanting to develop yourself is pretty vague and you won't stop being a brainlet without any major physical alterations to your brain if you are indeed a brainlet.

[Anonymous No.9374232]

>>9369854

Only if you get a bone marrow transplant.

[Anonymous No.9374235]

Has anyone ever published their undergraduate dissertation? How did you go about it?

Its in a decent field
>Muh Developmental Biology
and can't really find any relating literature on my subject.

However its been a few years since undergrad for me and haven't kept in touch with my supervisor (Not on good terms).

[Anonymous No.9374297]

>>9368785
>1^n

[Anonymous No.9374298]

can smbd explain how this shit is even legal?

[Anonymous No.9374299]

>>9374298
forgot pic

[Anonymous No.9374309]

>>9374299
got it, I guess I don't know the rules yet

[Anonymous No.9374310]

>>9373737
How do you do this without seeming like you are just brown nosing? I feel like any question I would ask is trivial and I could just google it instead of wasting his time.

[Anonymous No.9374312]

>>9373771
Just finish your math degree, you have 3 semesters left. Dont throw all that time and money away.

[Anonymous No.9374327]

>>9374211
Khan academy is unironically fine for learning everything they offer, its really guided so good for an intro to teaching yourself. I watched sal khan videos at x2 speed instead of going to lecture for calc 1, 2 and Linear Algebra and got high 90's, so its not like it doesn't teach you. I think they have multi variable calc too. Once you get those down you have the "core" fundamentals, and math really starts to branch out from there, see what branches interest you and go from there, you cant learn it all. Personal recommendation is discrete mathematics, especially Graph Theory, which you can get into with some basic Calc 2, diff eq, and linear algebra knowledge.

Some think stats is a fundamental, but while learning calc you should be exposed to the important parts anyway. I think you can get by without specifically spending time on it, unless that is what you want to dig deeper into.

[Anonymous No.9374342]

>>9374327
>Some think stats is a fundamental
Entire post disregarded.

[Anonymous No.9374345]

>>9374342
I mean calc stats, not "what are the chances 2 dice roll 7?". I have rarely needed anything beyond basic statistics in courses not directly tied to statistics, when I did it was one or two concepts I could have quickly learned and get back to what I was doing.

[Anonymous No.9374347]

>>9374327
>calc 1, 2 and Linear Algebra
>so its not like it doesn't teach you
What are you basing this on?
>Once you get those down you have the "core" fundamentals, and math really starts to branch out from there
Maybe if you are an eng*neer, but otherwise it's retardedly wrong.

[Anonymous No.9374353]

Vote for SENS and LEAF for P4A 2017!

http://www.projectforawesome.com/?charity=7RGRgIDG

[Anonymous No.9374380]

>>9374347
Are you saying it doesn't teach you? It covered everything we went over in all of my basic courses. It is completely fine to start with.

>Maybe if you are an eng*neer, but otherwise it's retardedly wrong.
Looking at the undergrad mathematics 4 year plan at my university the required courses are: Physics, calc 1, 2, multivariable, LA and diffeq, and sequences & series(which I guess I didn't mention but it is lightly touched on in calc 2). From there you chose a branch and take courses related to that branch. Those courses teach you the basic concepts that you will be using often in more advanced courses down the line. What would you consider to be the fundamentals?

Remember that the person I was replying to is wanting to teach themselves math and is currently sitting at a high school level of math. Not some aspiring mathematician.

[Anonymous No.9374418]

>>9373708
Why would the professor do that? They're people who love talking about what they do.

[Anonymous No.9374454]

>>9374380
>from there you choose a branch
what the fuck? from there you haven't taken a single math class. the fundamentals are real and complex analysis, linear and modern algebra, topology and geometry.

[Anonymous No.9374468]

>>9374310
then don't ask a trivial question, that's better than asking something dumb. just go to office hours, and say

"Hello Prof. X, can I come in?"
"So, I am very interested in [topic] and have been considering pursuing graduate school on it later on. I am very interested in obtaining undergraduate research experience, and I wanted to know if you knew any projects where I could do this. I ask you (specifically) because [...]."

[Anonymous No.9374480]

Dear sci, sorry for asking this ridiculous question...

If I have a two square centimeters, do I calculate (2*10^-3m)^2 = 4*10^-6,
or is it (2cm)^2 = 4 cm^2 (like ignoring the order of magnitude and inputting it afterwards).

I know if I have a square kilometer (10^3m)^2 its 10^6 m, but going the other way makes the number smaller. Sorry for being a total noob. I study humanities.

[Anonymous No.9374557]

>>9374380
>Physics, calc 1, 2, multivariable, LA and diffeq, and sequences & series(which I guess I didn't mention but it is lightly touched on in calc 2)
None of that is even remotely related to math.
>the undergrad mathematics 4 year plan at my university
Your university is fucking garbage.

[Anonymous No.9374562]

>>9369697
multiplication can be seen as finding the area of a rectangle and division can be seen as finding the length of a side of a rectangle given another side length and the area, or division can be seen as giving the size p of n groups if the number of items is m(m/n=p) or the number of groups n of size p if the number of items is m(m/p=n) (last two make most sense in integer division)

[Anonymous No.9374587]

>>9374480
first off a centimeter is 10^-2m. You could do (2*10^-2m)^2 to give the units in meters or you could just make the unit cm and convert to meters later either will work

[Anonymous No.9374600]

>>9372825
Just draw a circle around your point, so the correct amount of points fit into it.

[Anonymous No.9374617]

>>9372805
you can do a spacial partitioning to make your program faster than checking against all neighbors, grid partitioning is the easiest

[Anonymous No.9374620]

>>9374617
here are some other ideas from wikipedia https://en.wikipedia.org/wiki/Nearest_neighbor_search

[Anonymous No.9374637]

LaTeX problem: For some reason my hyphenation command is being ignored...

Any ideas appreciated :)

[Anonymous No.9374744]

>>9374557
Most of those are related to math. Don't be a tool.

[Anonymous No.9374789]

you guys don't mind if I test latex here right?(that counts as stupid question)
[math]\sum_{a^{a}}^{abcd}[/math]

[Anonymous No.9374793]

Whats (-1-(3)^1/2)^2?
(a+b)^2=a^2+2ab+b^2 but i cant figure it out by being negative help pls

[Anonymous No.9374798]

>>9369584
>lol don't research or listen to other people with lived experience
no, fuck off. you fucking repressed homosexual, nature hating, body hating loser. Jerking off is fine, porn is the problem and not talking to or having sex with women. Monks are disgusting and obviously the entire priestarchy has a pedo problem from celibacy/chastity.

[Anonymous No.9374807]

>>9372261
>/sci/ poster who calls others brainlets
doesn't know how to unicode

[Anonymous No.9374810]

>>9374798
>lived experience
can we ban this from the CDC report too?

[Anonymous No.9374897]

>>9374744
>Most of those are related to math.
Not even close.

[Anonymous No.9374915]

What's a good CAS for 3d-graphing / visualizing analytic functions?

[Anonymous No.9374919]

>>9374897
>Linear Algebra
>completely unrelated to math
Retarded

[Anonymous No.9374961]

>>9374919
If it has "matrices" (which it most likely does judging by the rest of your examples), it's not even linear algebra, just a twisted and dumbed down version of it for engineers.

[Anonymous No.9374974]

Do black holes orbit around anything?

How quickly do they move?

[Anonymous No.9374983]

>>9374961
You just confirmed yourself as an edgy autistic memelord

[Anonymous No.9375008]

>>9374983
>edgy autistic memelord
Fuck off to >>>/r/eddit/ if you refuse to accept this simple reality.

[Anonymous No.9375020]

>>9374961
Just FYI, mathematicians use matrices all the time. They exist because they can be useful and convenient.

[Anonymous No.9375021]

>>9375008
You're the one sperging out about engineers

[Anonymous No.9375026]

>>9374974
they can orbit around each other and gravity from everything else effects them because they have mass

they move as quickly as they're moving relative to other objects

[Anonymous No.9375051]

>>9375020
>mathematicians use matrices all the time
That's not really relevant. Mathematicians can do stuff outside of work as well.
>they can be useful and convenient
Perhaps for engineering purposes. Are you implying engineering is somehow mathematics?

[Anonymous No.9375061]

Is the fundamental theory of calculus supposed to be intuitive?
I mean I get it. I did good on my final.
But I don't see how the difference in the antiderivative of two particular points relates to the area under the curve itself.
Does it justwerk?

[Anonymous No.9375069]

If f'(x)=0 and f''(x)>0, then f(x) is a relative min, but why? Im not saying that it shouldnt be, i just dont see how we can relate f'(x) with f''(x)

[Anonymous No.9375070]

>>9375061
>theory of calculus
There's no such thing, calculus is dumbed down garbage for engineers. You're thinking of real analysis.

[Anonymous No.9375074]

>>9375070
>calculus is real analysis
maybe at amerifat community colleges

[Anonymous No.9375075]

>>9375061
The FTC is concerned with the function F(x) defined as follows: you pick a function f and starting point, say 0. Whenever I give you an x, you stay at 0 and then go all the way out to x, and then tell me how much area you've passed under the graph of f. As I move x a little bit, how much is the area under the graph of f changing? It changes by the area of a tiny little rectangle of height roughly f(x).

[Anonymous No.9375080]

>>9375075
Fuck, *start at zero. Phone posting sucks.

[Anonymous No.9375085]

>>9375074
Do you have reading comprehension problems? Calculus is the dumbed down "version" of real analysis.

[Anonymous No.9375087]

>>9375080
>Phone posting
>>>/r/eddit/

[Anonymous No.9375094]

>>9375087
Okay buddy. I'll take my actual mathematical conversation and leave y'all to shitpost about engineers.

[Anonymous No.9375102]

>>9375094
>admitting to phoneposting
Redditor trash is not welcome here. see >>9375087

[Anonymous No.9375103]

>>9375085
>Calculus is the dumbed down "version" of real analysis.
What do you mean? Calculus has nothing to do with real analysis

[Anonymous No.9375110]

>>9375103
Your question is logically incoherent, since you are assuming the existence of R.

[Anonymous No.9375120]

>>9375102
>>9375087
your weird

[Anonymous No.9375133]

Guys
is it gay to cuddle your homies to express you love them as friends?

[Anonymous No.9375135]

>>9375110
>you are assuming the existence of R.
Where did I do that?

[Anonymous No.9375193]

>>9374789
You can test latex with the tex preview (click on "TEX" in the upper left of the "reply" dialog)

[Anonymous No.9375330]

>>9375135
>I
I'm not an "I".

[Anonymous No.9375357]

>>9375061

The proof is pretty intuitive, but as a standalone the result isn't very intuitive. At least I don't think it is.

If you don't mind watching a loud pajeet for 15 minutes, this guy does a pretty good job explaining the intuition behind the proof.

https://www.youtube.com/watch?v=vf5f_SuZ6XE

[Anonymous No.9375359]

I am using R for basic statistics and I would like to know more about the following two claims I picked up:

- The linear model regression function lm() determines an intercept and a slope. The intercept is the same as the mean of the predictor, and is the same as a regression of the predictor to a vector of all 1's.

- Regression in N variables can be reduced to a regression N-1 variables, which means regression in N variables can be reduced to repeated regression in one variable.

Can someone point me in the right direction for these questions? Google brings up a lot of stuff but most of them are tutorials which avoid these questions.

[Anonymous No.9375360]

Can a girl be artifically made pregnant before her first menstrual cycle?

[Anonymous No.9375397]

>>9373546
>>9373559
I agree discrete math isn't necessary but it definitely can't hurt. For many students it is their first experience in dealing with formal logic and proofs. These two things alone made the sections on series in calc 2 much easier to handle, since most of the problems require matching the properties of a given series to the conditions of one (or several) of like 15 theorems. The set theory encountered in a discrete course is also very useful not just for calculus but nearly all of mathematics.

[Anonymous No.9375411]

>>9369339
Most recommend making sure your algebra skills are good. I would add trigonometry, recap differentiation and integration and review series and sequences.

>>9371976
Depends on what you mean by geometry. Euclidean geometry? Never hurts to recall how to construct a proof, and knowing geometry on a plane helps with the intuition for other forms of geometry. Will it be essential? Probably not.

>>9373663
>>9373671
C is basically R^2 with an additional structure, in this case it's safe to split integration into two components. int [u+iv] = int [u] + i int[v].

>>9374637
Try \- instead of -

>>9374793
Google the order of operations and try for yourself.

>>9375360
No

[Anonymous No.9375463]

How does one block correspond to one state if it actually has 8 points in k-space, for the free electron gas model? I thoght a single point should correspond to a single state.

Pic related.

[Anonymous No.9375475]

>>9375061
Say you have a continuous function f.
Consider the function [math] g(x)=\int_a^x f(x) dx [/math].
g(x) represents the area under the graph of f given that you have traveled from a to x.

The derivative of a function is the (unique) best linear approximation of the function:
[math] k(x+h) \approx k(x)+k'(x)h [/math] when h is close to 0.

Now, consider g.
You are at the point x.
You know how much the area from a to x is, it's g(x).
And you want to estimate the area from a to x+h, which is g(x+h).
If you know the height at x, then you might wanna say that g(x+h) is going to be approximately

(area from a to x) + (height at x) * h
which is g(x) + (height at x) * h

(since height doesn't change much if you don't travel too far away, that's true due to continuity)

But, what's the height at x? It's f(x).

[Anonymous No.9375504]

>>9375061
>Does it justwerk?
yes.

[Anonymous No.9375508]

>>9375504

kek

[Anonymous No.9375546]

Best tablet for notes under $500? Im thinking surface pro atm but want to know if there is better

[Anonymous No.9375702]

Good books on electricity and magnetism?

[Anonymous No.9375713]

what are some useful applications of knowing the volumetric flow rate

[Anonymous No.9375741]

>>9375702
At what level? How much math do you know?

[Anonymous No.9375751]

>>9375713
bump

[Anonymous No.9375762]

>>9373189

[Anonymous No.9375765]

>>9375741
I've finished a class on mechanics, calc 2 and differentials so that much

[Anonymous No.9375795]

>>9375765
If you know vector calculus, I recommend Introduction to Electrodynamics by David Griffiths. Feynman's Lectures of Physics Vol 2 can be challenging, but worth a read to gain physical insight. I also recommend Yale lectures on the subject: https://www.youtube.com/watch?v=NK-BxowMIfg&list=PLB1A0BF14EB31C3BE

I'm not sure what other books in English are available.

[Anonymous No.9375944]

lads

firstly, i need to understand RF theory. what books and resources do you recommend?

secondly, i'm a mechanical engineer. i would like to generally understand electrical engineering, so please recommend resources for this as well.

Lastly, here is a stupid question(s): I don't think understand wavelength or electromagnetic radiation (instead of magnetic /electric fields). plz explain

[Anonymous No.9376080]

Someone said "[character name] did nothing wrong" about a game I haven't played yet, should I assume I got implied spoiled and that this character will obviously do something wrong in an important way? Or just not worry about it it's probably nothing

[Anonymous No.9376170]

gcd(4024, 52)=4024a+52b

how do i find a and b

[Anonymous No.9376173]

>>9376170
https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm

[Anonymous No.9376517]

what's the motivation behind defining [math]a^x[/math] as [math]\exp(x\log a)[/math]? and is it not possible to define [math]a^x[/math] without using something as "advanced" as calculus?

[Anonymous No.9376521]

Is the Universe being procedurally generated?

[Anonymous No.9376523]

>>9376521
dude

[Anonymous No.9376536]

>>9376170
wlog let b>a and q=b/a
[a']=[-q 1][a]
[b']=[1 0 ][b]
Continue until a'=0. Then b'=gcd(a, b), and the bottom row of all the matrices multiplied in order is x and y such that a*x+b*y=gcd(a,b)

[Anonymous No.9376541]

So, if a black hole is infinitely dense, but the event horizon appears to outside observers as an empty shell (because the information exists only on the horizon at the Planck scale).

But conventional thought implies a singularity.

Is there truly empty space past the horizon, or is the interior topologically equivalent to a point?

So the information on the horizon itself is the singularity

[Anonymous No.9376564]

>>9376517
the [math]n[/math]-th rooth, exponentation and logarithm are defined using the least upper bound property of real numbers. e.g. you define [math]\sqrt[n]{a}[/math] to be [math]\sup \{ x \in \mathbb{R} | x^n < a \}[/math]. if you monkey around with it, you can show that it's (at least when [math]n[/math] is odd) the only real number satisfying the equation [math](\sqrt[n]{a})^n = a[/math] and it satisfies all the familiar properties. then you can define exponentation first for a rational argument (i.e. [math]a^{\frac{p}{q}}[/math]), because you know what both [math]a^p[/math] and [math]a^{\frac{1}{q}} = \sqrt[q]{a}[/math] are. then for a real exponent [math]a^x[/math] you take the supremum over all rationals lesser than [math]x[/math] or whatever.

[Anonymous No.9376566]

>>9376517
power series of e^x and complex x

[Anonymous No.9376567]

>>9375944
http://4chan-science.wikia.com/wiki/Physics_Textbook_Recommendations#Electrodynamics
http://4chan-science.wikia.com/wiki/Electrical_and_Electronics_Engineering

> I don't think understand wavelength

Wavelength is period in space.
Wavenumber is frequency in space

read: http://www.people.fas.harvard.edu/~hgeorgi/new.htm

[Anonymous No.9376595]

>>9374299
En passant?

[Anonymous No.9376639]

>>9376567
thanks anon

[Anonymous No.9376698]

>>9376517
You can define [math] a^x [/math] as the limit of [math] a^{x_n} [/math] where [math] x_n [/math] is a sequence which has limit [math] x [/math] .
But that's impractical, and in the end it is equal to [math] e^{\log(a) x} [/math] .
[math] e^x [/math] is used pretty much just because it's its own derivative which makes calculations simpler.

[Anonymous No.9376703]

>>9376698
>where xn is a sequence
meant rational sequence

[Anonymous No.9376730]

>>9368782
Quick algebra question

i found Ker f = Vect(-2,-1,1,0)

i'm supposed to have dim( Ker f) = 2

am i correct ?

[Anonymous No.9376734]

>>9376730
>Vect(-2,-1,1,0)
Wtf is that notation. It's denoted span( (-2,-1,1,0) ) or < (-2,-1,1,0) > .
Anyway,

>i'm supposed to have dim( Ker f) = 2
>am i correct ?
Obviously not. You'd need Kerf=span(v1,v2) where v1 and v2 are linearly independent.

[Anonymous No.9376764]

>>9376517
...you realize there's no calculus whatsoever in that definition? Basic algebraic manipulation shows that this definition agrees with the usual one for rational numbers.

[Anonymous No.9376794]

Okay I might be a brainlet but I've never understood the proof that the set of rational numbers is countable. How exactly does going in triangles prove that there's a bijection on naturals?

[Anonymous No.9376830]

>>9376734
that's the french notation, sorry

That's what i thought, but i dont know where i got it wrong
My matrix for f is :
1 -1 1 1
1 0 2 -1
1 1 3 1

To find the kernel I added a row of 0 at the right side, and when i solve i get :
1 0 2 0
0 1 1 0
0 0 0 1

<=>
x = -2z
y = -z
z = z
t = 0

I don't know where is my mistake
Sorry for the broken english

[Anonymous No.9376837]

If everything is a field, then why can't matter (bigger fields) occupy the same space?

[Anonymous No.9376851]

>>9376794
>How exactly does going in triangles prove that there's a bijection on naturals?
because you enumerate all the rationals by counting along each "top left to bottom right" diagonal

[Anonymous No.9376857]

>>9376794
"going in triangles" is an explicitly constructed bijection from N to Q

[Anonymous No.9376862]

>>9376830
you got the assignment or the solution wrong. this matrix has 1-dimensional kernel.

[Anonymous No.9376865]

>>9376837
The fields repel each other. Like the nuclear force and shit

[Anonymous No.9376873]

>>9376862
Ah shit you're right
Got one number wrong, AGAIN
Thanks

[Anonymous No.9376879]

>>9376865
what makes them repel eachothers? aren't fields made of space?

[Anonymous No.9376882]

>>9376879
dunno man it's like charges and stuff

[Anonymous No.9376891]

>>9376882
charges come from fields which are made of space. i dont understand physics.

[Anonymous No.9376899]

>>9376862
>>9376873

Okay I fixed it, now I have this for the final matrix
1 0 2 -1 =0
0 1 1 -2 =0
0 0 0 0 =0

So I write Ker f = < (-2z + t, -z + t, z, t) >

How can I write it better ?

[Anonymous No.9376911]

>>9376899
no wait im wrong
the kernel is the linear span created by the row of the matrix, right ?

[Anonymous No.9376958]

>>9376911
Scratch that, i was wrong again.

[Anonymous No.9377018]

>>9376730
maybe i fucked up somewhere, but i think you're right. i also got [math]\ker f =\langle(-2,-1,1,0)\rangle[/math]

[Anonymous No.9377042]

>>9377018
how do you write like that ?

I had a mistake in the original matrix, the last line is supposed to be 1 1 3 -3

i'm still stuck at the transformation matrix
i have a 4x4 multiplied by a 4x3 multiplied by a 4x4, which is incorrect ?

[Anonymous No.9377056]

>>9376899
if you meant [math] \ker f = \{ (-2z + t, -z + t, z, t):t,z\in\mathbb{R}\}[/math], then [math]\{z(-2,-1,1,0)+t(1,1,0,1):t,z\in\mathbb{R}\}=\langle(-2,-1,1,0),(1,1,0,1)\rangle[/math] might be how you want to write it. not sure if that answers your problem though.

>>9377042
>how do you write like that ?
Latex? use [ math ] 1+1=2 ... [ /math ] without the spaces in the tags. there's probably a guide on the wiki somewhere.

what is the original question?
i'm guessing you have some linear map [math]f[/math] with the associated matrix [math]A=\begin{pmatrix}1 & -1 & 1 & 1\\1&0&2&-1\\1&1&3&\color{red}{-3}\end{pmatrix}[/math] and youre asked to find [math]\dim\ker f[/math], right?

[Anonymous No.9377067]

if i have an application f that goes R4 -> R3
its matrix is a 3x4, correct ?
with each row j being equal to f(ej),with ej the image of the standard vector ?

[Anonymous No.9377074]

How would you rank the positive environmental effects of the following?

not eating bovine meat
not eating porcine meat
not eating all mammals
not eating poultry
not eating fish

[Anonymous No.9377080]

>>9377056
i'll try to type it, i don't know Latex
You have {math](e1, e2, e3, e4)[/math] standard basis of R4

[math]
f(x,y,z,t) = x-y+z+t, x+2z-t, z = x+y+3z-3t
[/math]

1) What's the matrix of the application f ?
2) Prove that [math] (f(e1) , f(e2)) is a basis
3) Prove that [math]dim(Ker f ) = 2[/math] and define a basis [math](u1, u2)[/math] for [math]Ker f[/math]
4) Check that [math](e1,e2,u1,u2)[/math] is a basis in R4. What's the transformation matrix of in in the basis [math](e1,e2,u1,u2)[/math] ?

[Anonymous No.9377089]

>>9377080
shit i completly botched that

[math] f(x,y,z,t)=x−y+z+t,x+2z−t,x+y+3z−3t [/math]

2) Prove that [math](f(e1),f(e2)) [/math] is a basis of [math] Im f[/math] and complete it to create a basis for R3

3)Prove that [math]dim(Kerf)=2[/math] and define a basis [math] (u1,u2)(u1,u2) for Kerf [/math]

4) Check that [math](e1,e2,u1,u2)[/math] is a basis in R4. What's the transformation matrix of in in the basis [math](e1,e2,u1,u2) [/math]?

[Anonymous No.9377097]

>>9377089
so far i got for [math] f =
\begin{pmatrix}
1 & -1 & 1 & 1 \\
1 & 0 & 2 & -1 \\
1 & 1 & 3 & -3
\end{pmatrix}
[/math]

[math] B =
\begin{pmatrix}
1 & -1 & 1 \\
1 & 0 & -1 \\
1 & 1 & -1
\end{pmatrix}
[/math]

{math] Ker f = < ( -2 \\ -1 \\ 1 \\ 0), (1 \\ 2 \\ 0 \\ 1) >

[Anonymous No.9377107]

>>9377074
+++++
+++
+++++
+
+

[Anonymous No.9377112]

>>9377097
>{math] Ker f = < ( -2 \\ -1 \\ 1 \\ 0), (1 \\ 2 \\ 0 \\ 1) > [/math]

so is this normal that f is 3*4 ?

[math] (e_1, e_2, u_1, u_2) =
\begin{pmatrix}
1 & 0 & -2 & 1 \\
0 & 1 & -1 & 2 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1
\end{pmatrix}
[/math]

because i cant mutiply my transformation matrix with my application matrix :

[math]
M(f)_B = M(id)_eb * M(f)_e * M(id)_be
[/math]

[Anonymous No.9377126]

>>9377067
>its matrix is a 3x4, correct ?
yes
Let B and C be the standard bases of R^4 and R^3, respectively. Then the matrix with respect to the standard bases of [math]R^3[/math] and [math]R^4[/math] is [math]\begin{pmatrix}[f(\mathbf{e}_1)]_{C},...,f(\mathbf{e}_4)]_{C}\end{pmatrix}=\begin{pmatrix}\begin{pmatrix}1\\1\\1\end{pmatrix},...,\begin{pmatrix}1\\-1\\-3\end{pmatrix}\end{pmatrix}[/math]. so your answer for 1 is correct.

>>9377097
what is B?

[Anonymous No.9377146]

>>9376830
http://www.wolframalpha.com/input/?i=Null+space+of+%7B%7B1,-1,+1,+1%7D,%7B1+,0+,2+,-1%7D,%7B1+,1+,3+,1%7D%7D
So, your answer was correct.

>>9376911
Nope. But they are related.

[math] Ax= \begin{pmatrix} (\text{first row of } A) \cdot x \\ \vdots \\ (m \text{-th row of } A) \cdot x \end{pmatrix} [/math]
Therefore, Ax=0 if and only if x is perpendicular to each row of of A.
Which means that x is in the kernel if and only if x is perpendicular to the row space of A.
Which means that [math] \ker (A) = (\text{row space of } A)^\bot [/math]

For any subspace [math] U [/math] of [math] \mathbb{R}^n [/math] this holds [math] \mathbb{R}^n = U \oplus U^\bot [/math]
Therefore [math] \mathbb{R}^n = (\text{row space of } A) \oplus (\text{row space of } A)^\bot = (\text{row space of } A) \oplus \ker (A) [/math]
So, [math] \dim \ker (A) = n - \dim (\text{row space of } A) [/math] , which is the number of columns of A minus the number of non-zero rows after you performed row reduction.

By the way, [math] \dim (\text{row space of } A) = \dim (\text{column space of } A) [/math] .
That's true because:
[math] \dim (\text{column space of } A) = \dim ( im A ) = n - \dim (\ker A) = n - (n - \dim (\text{row space of } A) =\ dim (\text{row space of } A) [/math] .

[Anonymous No.9377173]

>>9377126
B is the basis of [math]f[/math] in R3
[math] B = ( 1\\ 1 \\ 1),(-1 \\ 0 \\ 1), (1 \\ -1 \\ -1) >
[/math]
>>9377146

But [math] Ker f = < ( -2 \\ -1 \\ 1 \\ 0), (1 \\ 2 \\ 0 \\ 1) > [/math], right ?

what you mean by perpendicular is collinearity right ? I'm lost in the translation

[Anonymous No.9377177]

>>9377173
ok LateX is all fucked up
i can't believe i'm asking people for help on a peruvian butter forum for help when my midterm is tomorrow
i have nothing to help me but you guys, thanks

[Anonymous No.9377186]

>>9377089
>2) Prove that (f(e1),f(e2)) is a basis of Imf
[math] Imf= \langle f(e_1), f(e_2) , f(e_3) , f(e_4) = \rangle [/math]
[math] f(e_i) [/math] is the i=th column of the matrix.
Prove that the 3rd column is as a linear combination of the 1st and the 2nd columns
You can do this by adding multiples of the 1st and 2nd columns to the 3rd so that the 3rd becomes 0.
Do the the same for the 4th column.
Prove that the 1st and the 2nd columns are linearly independent.

>and complete it to create a basis for R3
Pick (0,0,1)

>3)Prove that dim(Kerf)=2
dimKerf + dimImf = dimR^4

> and define a basis (u1,u2) for Kerf
Just solve the system and find a basis.

>4) Check that (e1,e2,u1,u2) is a basis in R4.
It suffices to show that they are linearly independent.
Put them in a matrix show that the matrix is invertible.
Row or column reduce. Or just compute the derminant.

>What's the transformation matrix of in in the basis (e1,e2,u1,u2)?
Well, just compute that xD

[Anonymous No.9377191]

>>9374297
glad I'm not the only one caught off guard by this

[Anonymous No.9377195]

>>9377186
For the first one, you can just compute the kernel first, find that it's dimension is 2, which means that dimIm=2 and since f(e1),f(e2) are linearly independent, they have to be a basis.

[Anonymous No.9377202]

Has dark matter or dark energy been disproved?

[Anonymous No.9377210]

>>9377186
>>9377195

the first three question are good, but it's for the transformation matrix, i find someting impossible because i have multiply a 4*4 by a 4*3 by a 4*4

but you can't multiply a 4*4 by a 3*4

so i dont know

[Anonymous No.9377308]

>>9377210
You want to compute the matrix of f under the basis (e1,e2,u1,u2)?
That's not possible.
You need two bases. One for R^4 and one for R^3.
You can represent a linear map f with a matrix using only one basis if and only if [math] f:V \to V [/math] (domain and codomain are the same).

Are you sure that this is what part 4 is asking?
Maybe it asks the matrix of f with respect to (e1,e2,u1,u2) and (e1,e2,e3) ?

[Anonymous No.9377313]

>>9368782
How do I know if I like Mathematics or if actually I just like doing calculations?

[Anonymous No.9377330]

>>9377308
>Maybe it asks the matrix of f with respect to (e1,e2,u1,u2) and (e1,e2,e3) ?
If that's the case:

f(e1)= 1 e1 + 1 e2 + 1 e3 (note that the first e1 is not the same as the second one; I just used the same notation for simplicity)
so, first column is [1 1 1]^t

f(e2)= -1 e1 + 0 e2 + 1 e3
so, second column is [-1 0 1]^t

f(u1)= 0 = 0 e1 + 0 e2 + 0 e3
so, third column is [0 0 0]^t

f(u2)= 0 = 0 e1 + 0 e2 + 0 e3
so, fourth column is [0 0 0]^t

The matrix is [math] \begin{pmatrix}
1 & -1 & 0 & 0 \\
1 & 0 & 0 & 0 \\
1 & 1 & 0 & 0
\end{pmatrix} [/math]

[Anonymous No.9377331]

Language learning question. /sci/ used to be the place to ask, but I'll take it to /his/ if I need to. I'm going to start learning Mandarin. I want to simulate a college class type of learning because that helps me. My field and department are rich in native speakers that will help me practice my conversation. I'm looking for suggestions on texts for beginner studies.

Textbook: Integrated Chinese 4E
Workbook: Integrated Chinese 4E Workbook
Audio Component: ?
Vocabulary: HSK Flashcards + English-Chinese Dictionary
Grammar: Chinese Grammar Wiki

I have a fairly length commute so a good audiobook would be a plus. I don't intend to hand write any Chinese characters; resources that skip over stroke order will work fine.

[Anonymous No.9377445]

>>9377308
The full question is :"
What is the matrix of [math]f[/math] in the basis [math] A = (e_1, e_2, u_1, u_2) [/math] and [math]B[/math]

[math]B[/math] is the basis of the question 2 : [math] B = (f(e_1), f(e_2), v) [/math]

So i have to go from basis A to basis B ? I thought that was 2 different questions

[Anonymous No.9377474]

>>9368782
Definitionally:
[eqn]\text{true } (a) \text{ } (b) = (\lambda t . \lambda f . t)(a)(b)[/eqn]
By successive beta reduction over free variables:
[eqn](\lambda t . \lambda f . t)(a)(b) = (\lambda f . a)(b) = a[/eqn]
I'm not doing your second homework problem, but git gud and prectice.

[Anonymous No.9377544]

>>9377445
Yes, it asks you for the matrix of [math] f:\mathbb{R}^4 \to \mathbb{R}^3 [/math] under the bases [math] A [/math] (for [math] \mathbb{R}^4 [/math] ) and [math] B [/math] (for [math] \mathbb{R}^3 [/math] ).
You can do this by computing [math] Q^{-1}FP [/math] where [math] F [/math] is the matrix of [math] f [/math] and the usual bases, [math] P [/math] is the matrix with columns [math] e_1,e_2,u_1,u_2 [/math] , and [math] Q [/math] is the matrix with columns [math] f(e_1),f(e_2),v [/math] .
But that's too time consuming and a bit dumb.

Read the definition of "the matrix of a transformation [math] f:V \to W [/math] given a basis of [math] V [/math] and a basis of [math] W [/math] in your textbook.
It's easier to compute the new matrix of [math] f [/math] using just that definition:

[math]
f(e_1) = 1 f(e_1) + 0 f(e_2) + 0 v \\
f(e_2) = 0 f(e_1) + 1 f(e_2) + 0 v \\
f(u_1) = 0 f(e_1) + 0 f(e_2) + 0 v \\
f(u_2) = 0 f(e_1) + 0 f(e_2) + 0 v \\
[/math]

Therefore the matrix is [math] \begin{pmatrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 0 & 0
\end{pmatrix} [/math]

[Anonymous No.9377609]

Is it worth getting rec letters and applying to a math REU as a freshman? I've only taken classes like: java programming, discrete math, honors calc. (honors calc is like an intro to analysis class taught out of spivak)

[Anonymous No.9377641]

WHY THE FUCK IS THE PRICE PLACED AT THE VERTICAL AXIS WHEN IT'S ALMOST ALWAYS THE FUCKING VARIABLE OF THE FUCKING FUNCTION FFS WTF IS WRONG WITH ECONOMICS RETARDS AAAAAAAAAAHHHHHHHHHHH

[Anonymous No.9377652]

>>9377544
The first method with Q and P is what we actually learned.
I redid the exercise from scratch, but Im not sure on how to find the base [math]B[/math]

I know that [math]( f(e_1), f(e_2) ) [/math] is a base, but how do I find [math] v [/math] ?

I feel like the more I start over the less I get, this is frustrating but thanks for the help

[Anonymous No.9377654]

>>9377544
We don't have a textbook, I tried to find some at the library but the exercises are way easier than they gave us. Also the test is gonna be exercises from the sheet, I need to know how to do them

[Anonymous No.9377664]

So if lim as n->infinity of members of a row represents what number they're approaching, then why is the limit of some random number c lim c equal to c?

[Anonymous No.9377684]

>>9377664
>So if lim as n->infinity of members of a row represents what number they're approaching
Are you talking about sequences?

>why is the limit of some random number c lim c equal to c?
Follows trivially from the epsilon-delta definition of limits

[Anonymous No.9377690]

>>9377652
>The first method with Q and P is what we actually learned.
There is no way you learned how to represent a matrix of a tranformation under a new basis without even defining what "matrix of a transformation" actually is.
And by noticing that the answer doesn't actually depend on what u1, u2 and v actually are, it should make you suspicious.

To compute the matrix of f given a bases v1,...,vn and w1,...,wm you do this.
1) Compute f(vi)
3) Write f(vi) as a linear combination of w1 .. wm. f(vi) = c1 w1 +.... + cm wm
3) [c1 ... cm] is the i-th the column
That's it.

>I redid the exercise from scratch, but Im not sure on how to find the base B
>I know that f(e1),f(e2) are *linearly independent*, but how do I find v ?
I told you, (0,0,1) does the job.
I personally found it by seeing the first two columns of the matrix A here >>9377056 and considered adjoining a column so that the 3x3 matrix created has a non-zero determinant.
You can also just write down the span of f(e1) and f(e2) and pick an element that's not in it.

[Anonymous No.9377701]

How can blue eyes originate from only one common ancestor (in a time dominated by brown eyed people) if it's so much more recessive than brown eyes

[Anonymous No.9377713]

>>9377701
inbreeding

[Anonymous No.9377717]

>>9377690
Yeah sorry about the (0,0,1), i just reread the entire thread.

We learned it with this drawing, Idk if it's readable.

Thanks for the help, I learned a lot, but I'm still way off, this midterm is fucked anyway.

[Anonymous No.9377770]

>>9377717
I don't understand exactly the notation, but I think I know what it says.

Let f be a linear map from R^n to R^m.
Let A and B be bases of R^n and R^m respectively.
Let A' and B' be two other bases of R^n and R^m respectively.
Let M(f,A,B) be the matrix of f with respect to A and B.

In general, this holds (read it from right to left):
M(f,A',B') = M(id,B,B') M(f,A,B) M(id,A',A) [1]
(A' to A , then A to B , then B to B')

This also holds:
M(id,A,B) = M(id,B,A) ^(-1) [2]

So you can write [1] as
M(f,A',B') = M(id,B',B) ^(-1) M(f,A,B) M(id,A',A)

Now, let E and E' be the usual bases of R^n and R^m respectively.
M(f,A,B) = M(id,E',B) M(f,E,E') M(id,A,E) = M(id,B,E') ^(-1) M(f,E,E') M(id,A,E)
You know the matrix in the middle: M(f,E,E')
What is M(id,A,E) ?
Well if you do this: >>9377690 , you will easily see that it is just the matrix with its columns being the vectors from A.
Same goes for M(id,B,E).

By the way, both [1] and [2] follow from this:
M(f,B,C) M(g,A,B)= M(f o g,A,C)

[Anonymous No.9377790]

I'm really confused about longitudinal waves.

Here's what I understand:

There's a displacement wave and a pressure wave and they are 90 degrees out of phase. When a particle's displacement is at max or min from equilibrium, it's at a zone of normal pressure. When it's at equilibrium it's either in a compression or in a rarefaction.

Ok. But now what if you just have a particle sitting there in your medium in normal pressure before the wave comes along. Now a density wave comes along and disturbs the particle. You would say it oscillates back and forth. But the equilibrium it oscillates around isn't the normal pressure zone it started in. Particles oscillate around compression/rarefaction zones. Is it pushed over or something?

I am getting myself so freaking confused trying to think about this.

[Anonymous No.9378090]

Are there any books or articles on the math behind static electricity (friction induced electricity like the old balloon on hair etc)? Does it all just tie into coulomb shit?

[Anonymous No.9378101]

>>9377609
Maybe if you are a minority. I mean you can apply anyways but it will be a very low chance of acceptance

[Anonymous No.9378128]

>>9377609
it's never a bad idea to try applying.

[Anonymous No.9378131]

>>9378090
You mean the math of vector fields or a book on static electricity?

For the latter
https://archive.org/details/textbookonstatic00maso
https://www.amazon.com/Electrostatics-Exploring-Controlling-Static-Electricity/dp/1885540043/r

[Anonymous No.9378136]

>>9377331
/int/ is the place for foreign languages
http://4chanint.wikia.com/wiki/The_Official_/int/_How_to_Learn_A_Foreign_Language_Guide_Wiki..

[Anonymous No.9378164]

>>9368782
Brainlet question: why is it c^8 in the solution and not c^16? Sorry for shit tier photo

[Anonymous No.9378167]

>>9378164
looks like a typo

[Anonymous No.9378240]

>>9378167
Alright thought so, there's tons of typos in the textbook, but I figured I'd check to be sure. Thanks anon.

[Anonymous No.9378361]

Can you do anything with a bachelor of arts if you don't get into medicine with it? Only asking because it would save me a year of study and a whole lot of bullshit.

[Anonymous No.9378405]

>>9369381
this is incorrect

[Anonymous No.9378547]

Do cellphones cause cancer? If I turn off mobile data and keep airplane mode on can I still get cancer? Does WIFI cause cancer?

[Anonymous No.9378595]

>>9378547
>If I turn off mobile data and keep airplane mode on can I still get cancer?
The risk is significantly reduced. And make sure to turn off "bluetooth" too.
>Does WIFI cause cancer?
The jury is still out on that one.

[Anonymous No.9378995]

If [math]E/F[/math] is a finite field extension, then [math]E/F[/math] is algebraic.

How do I show this?? [math]\mathbb Q (e)[/math] is not algebraic over [math]\mathbb Q[/math]??

[Anonymous No.9379012]

>>9377713
It seems like it would be eradicated almost immediately

[Anonymous No.9379072]

>>9376764
Try defining exp and log without calculus.

[Anonymous No.9379086]

>>9377313
take a proof-based course

[Anonymous No.9379101]

>>9377664
Because the number is only close to itself. The limit can either be approached or attained.

[Anonymous No.9379106]

>>9378995
Define finite field extension. I'm guessing it means E and F are both finite, in which case it's trivial.

[Anonymous No.9379110]

>>9379106
given this answer, i know you dont have a clue what im on about

[Anonymous No.9379115]

I can't into math, so one question

if I have a 0.7% chance of winning and I roll 80 times, how do I calculate my percentage of winning?

[Anonymous No.9379119]

>>9379110
Sorry, had to brush up on my Galois theory. Here is a very simple proof: http://planetmath.org/afiniteextensionoffieldsisanalgebraicextension

[Anonymous No.9379129]

>>9368782
im a big retard who needs to learn diophantine equations, modular inverses and shit for cryptography.
can someone help me find some NOT shit notes or books on these subject
>whats wrong with the ones i posted
a lot of shit
for example just before he declared that d=ka+bt
and then using d=x'a+y'b
and timesing k and x' together at somepoint we find c and some other shit?
the full thing here if you think im just being a fag:
https://www.scribd.com/document/367529822/shitty-notes

none of this is explained. these shitty notes are all my hippy teacher gives as resources and when asked what book to use, he just says 'any crypto book'.

[Anonymous No.9379225]

What's the answer?

[Anonymous No.9379262]

>>9379115
It's [math]1 - (Chance of not winning^{number of rolls})[/math]

so [math]1-(0.993^{80})[/math]

[Anonymous No.9379272]

>>9373296
Wait wait wait wait, is burgerland calculus this easy?
We had to do
>>>triple integrals
by hand! (and a lot of other stuff more difficult than what they do)

[Anonymous No.9379276]

>>9379225
Why do you want to know?

Either use inclusion/exclusion to compute the number of 3-way competent students, or just solve the simultaneous linear equations.

[Anonymous No.9379280]

How do I work out the limit for [math]log(n^2) / n[/math] ?
I have no idea how to "change" the n within the log.

[Anonymous No.9379288]

>>9379115
(7/10)^80
Imagine you have a code with 4 digits, from 0 to 9, there are 10*10*10*10 different ways of doing it, or 10^4

[Anonymous No.9379364]

>>9379280
Here is a hint:
log(ab) = log(a) + log(b).

[Anonymous No.9379467]

Is there a scientific reason why i should do my work/chores during the morning/day and use my evening nights to relax or should i just work whenever i choose?

[Anonymous No.9379482]

>>9379467
regular habits make for easier healthy lifestyles

[Anonymous No.9379497]

>>9369711
>>9370083
>>9370933
>>9371003
>>9374562
Most appreciated guys.

[Anonymous No.9379611]

[Anonymous No.9379633]

>>9379611
Why would it be true? In general the exponent rules are usually given as (x^a)(x^b)=x^(a+b) and (x^a)(y^a)=(xy)^a (along with some conditions)

[Anonymous No.9379688]

>>9379633
Well, I started with a problem asking to evaluate whether the statement [math]2^{4x}/1^{3x} = 2^{4x - 3x}[/math] was true or false, so [math]2^{4x} * 1^{-3x} = 2^{4x-3x}[/math] should be an equivalent statement. In the back of the book it said it was false.

[Anonymous No.9379715]

How do I find the combinator F so
[math]F\mathbf{IKK} = F\mathbf{K}[/math]
where
[math]\mathbf{I} \equiv \lambda x.x[/math]
[math]\mathbf{K} \equiv \lambda xy.x[/math]

[Anonymous No.9379741]

>>9379482
Good enough, thanks

[Anonymous No.9379787]

>>9379611
Interesting penmanship...

[Anonymous No.9379830]

>>9379787
fuck off nigger

[Anonymous No.9380019]

Can someone explain limits? Like, let's say we've got a function. And that function attaches a y value to an x value. So, as we get infinitesimally close to a certain x value, we're also getting infinitesimally close to its a certain y value, but never actually reach it. That all makes sense. But, what is a "limit"? What does it mean? What are we limiting exactly?

[Anonymous No.9380054]

>>9380019
Like, why are we looking for a limit of a function as it approaches 1? Would the limit of the same function be different if we were approaching a different number, say 8? Would it even make sense to approach different numbers in the same function, or does that depend on the function itself (say it's got 5 breaks where its not continuous, so we can approach 5 different numbers to see what the limit of a function would be in each of those values)?

[Anonymous No.9380071]

>>9380019
Someone please correct me if im mistaken, but to my understanding limits map a function to what it should evaluate to, even if it (the function) is actually undefined at the particular value.
If you've had some set theory and formal logic, you really should study the actual mathematical definition of the limit (commonly called the delta-epsilon definition) . By study I mean think about what it means, then sit down and apply it to an actual example (like the one in your image), then reflect on how it works for any general example. Make sure you're comfortable with nested quantifiers first.

[Anonymous No.9380154]

Saw this in a textbook regarding eigenvectors, with no explanation ("trivial")

x!=0
(A - Iλ)x = 0
that means
det(A - Iλ) = 0

Why not (A - Iλ) = 0?

[Anonymous No.9380229]

>>9380019
I'm the first guy who answered, but I would like to attempt to address your other questions. Hopefully someone will speak up if im mistaken or articulate something better if I fail to
>as we get infinitesimally close to a certain x value, we're also getting infinitesimally close to its a certain y value, but never actually reach it.
Yes but I would like to add, often we actually can reach it, i.e. the function is actually defined at the value. Now I ask you, provided the limit exists and the function is defined for a particular value, is it necessarily true that the two are equal?
>What are we limiting exactly?
The name limit was chosen because this concept captures the limiting behavior of the function as it approaches a particular value. Not sure how else to describe it.
>Like, why are we looking for a limit of a function as it approaches 1?
In the context of this problem, the answer is because that is the most interesting point of the graph, but we could technically evaluate the limit at any x value (it just wouldn't be as interesting)
>Would the limit of the same function be different if we were approaching a different number, say 8?
In this case the limit is the same for each point. as your graph suggests, It will be 1. But in general you should not expect this. The limit must be evaluated at each point to see what it actually is ,though often you will have a good idea of what it will be.
>Would it even make sense to approach different numbers in the same function
Of course, but as mentioned previously they may be trivial or uninteresting. The point is that we can try to take a limit at any point we'd like, for any function

[Anonymous No.9380253]

If I have a multivariate continuous probability distribution, and want to know the projection of one of the variables at a fixed value of the other variables, how would I go about that?

[Anonymous No.9380319]

>>9380229
Thanks for the answer. Not sure about the first question. I'm still wrapping my head around it.

[Anonymous No.9380425]

>>9380319
Which question exactly?

[Anonymous No.9380495]

>>9380154
>Why not (A - Iλ) = 0?
(A - Iλ) = 0 is too strong to follow since it would mean (A-Iλ)x=0x=0 for all x. Consider
[math] (\begin{bmatrix} 2 & 0 \\ 0 & 1\end{bmatrix} -2Id)\begin{bmatrix} 1 \\ 0 \end{bmatrix}=0[/math] where we don't have A-2Id=0

[Anonymous No.9381236]

>>9375463
Each electron is only 1/8th included!! I hope you see this.