Previous: 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.
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Is there a method for this or am I just supposed to 'see' it?
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
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?
Can someone pls recommend an advanced book on R?
sifting algorithm
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?
>Reduce the term: and tru tru.
How? You haven't given any reduction rules.
are the field "axioms" axioms or definitions?
i understand them being axioms for R, but in most cases you have to prove them right?
>are the field "axioms" axioms or definitions?
The axioms are axioms. The field is defined by those axioms.
You should start by noticing it's of the form [2^(n+1)-1]/2^n
>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 .
but they don't assert anything do they? what makes them axioms instead of properties of operations?
don't question it, bad goy. -500 shekels have been withdrawn as punishment
>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
>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?
>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.
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
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.
And that's an "if AND ONLY if"
is nofap a meme?
What fun stuff can I do with 3% hydrogen peroxide mixture?
Not only that, it's literally cancerous. And yes, I mean literally.
how come? isn't it true that it increases testosterone levels?
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.
I'm on week 3 and kissed a girl for the first time on it so I'd say no
...
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.
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
Can someone's blood type ever be changed? Either the letter or the rhesus factor?
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?
I changed mine so apparently it's possible. It was after I received severe brain damage though.
Any idea of how I should start tackling this problem? Just need suggestions to get me in right direction
it looks like a trig substitution question
>I changed mine so apparently it's possible.
Letter or Rh or both?
RH can change apparently for women during pregnancy, but only from - to + and only if the father has + (and the baby too)
>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.
>does that mean the column vectors are dependent?
Yes
Yes, he's saying it's an 3x3 system with one row zero
When is the electric potential maximum with respect to a magnetic field?
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?
>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"
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.
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.
Think about what row reduction is doing and what independent means.
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.
If y=sin(t).
can someone explain what's going on
This, except you might not reach 0 and be left with r < y things. Then r is the remainder. Integer multiplication has no inverse.
That is, it has an inverse operation "/" such that (xy)/y = x but no unary inverse operation.
1. dividing a line into equal parts.
2. rows and columns with a little bit left over.
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.
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:
fneuron-mc.myselph.de
and implement them into my own physics engine.
I already created a basic demo: jsfiddle.net
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
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.
Should I study geometry? Is it important for future courses?
I remember some basic shit like area and volume, but thats all
Α1+Α2
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
=> Aq = sqrt(A1^2 + A1*A2 + A2^2)
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!
There are no closest points other than the point itself.
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?
>too stupid for this right now
>right now
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)?
fuck forgot pic
just manually calculate the distance between all of them with point p?
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.
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
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...
This user 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
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?
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
What subject?
Also, from where? Highschool? University?
How to tell whether it's a shart or not without wiping?
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.
Has there ever been any obese contributors to science or mathematics?
University. Anything math, physics, chemistry, biology, or EE related
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 Veeky Forums, so can't really say.
I just realized I contradicted myself, but the point still stand.
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.
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.
How do I prepare myself for calc II? Just watch the patrickJMT and 3blue1brown playlists? I remember an user 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.
>How do I prepare myself for calc II?
Just start reading whatever textbook you'll be using
>I remember an user 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
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.
What is [math]\int_{}{}idx[/math]?
ix+c
I guess what i meant to say was how do you extend integration into the imaginary field?
same as in R^2??? my math is terrible but don't tell anyone
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?
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.
>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
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
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
sure kid
>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
You don't sound very confident with that answer
How do I meet professors? I'm not a brainlet so I never have to go into office hours
