/sci/ - Science & Math

Is there a way to represent the following function:

>f(x) equals the number of 1s in the word x.
as a function like "f(x) = y"?

So if I were programming, I would do:
>Create a counter variable to count the occurrences of 1
>Create a loop to step through each character in x
>+1 the counter variable for each time x[index] = 1
>Return the value of the counter variable

Is there a way to represent functions like this like f(x) = y? I'm interested in learning to write functions this way, what are some resources I should look into?

>>9245697
[math] f(x)= \sum_{1\in x} [/math]

>>9245715
Alright, sigma notation. And what field of mathematics deals with this sort of thing? Like what books should I read

Threadly reminder to work with physicists.

>>9245627
Recently I've been doing a bunch of problems of the form "Here is a sequence of natural numbers, find a formula for this sequence using the floor function" and I started to wonder, has there ever been a deep study on what general class of sequences can be written using elementary operations (addition, multiplication, division and natural roots of integers) and floor functions?

An interesting example a sequence that can be written with floor functions is [math] 1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,... [/math] (the sequence that repeats the nth number n times) as [math] \lfloor \sqrt{2n} + \frac{1}{2} \rfloor [/math] so obviously the class of sequences that have this property is diverse and interesting, but what are the limits? Are there any papers on this?

>>9245720
Algebraic Topolgy

>studying
>not just watching Rick and Morty
I'm too smart for this brainlet board

redpill me on the Curry-Howard correspondence

there's so much i want to do why am i limited to 24 hours in a day

Guys anyone has a good text on inequalities?
I'm struggling with any inequalities that are not linear.

Also yeah I'm a fucking retard, I know.

>>9246013
Guys anyone has a good text on inequalities?

>>9246013
>Guys anyone has a good text on inequalities?
I'm not a "guy".

>>9246016
will you go out on a date with me?

>>9246019
>will you go out on a date with me?
Maybe. Are you handsome?

>>9246021
I'm a solid 7/10.
I think.
I'm bad at math though.

Still Kalman filter stuff. More for GPS systems and such.

Something else: Is anybody here knowledgable in C# and up for a short programming challange?
I need a very simple realization of a classical one-tape Turing machine. Will have two classes and a bunch of for loops.
If someone's up for that, I'd +tip ya 30$ or so, it'll only be 300 lines of code max (write me an email www.axiomsofchoice.org).

>>9246030
sorry, I only help qts

>>9246038
I know a few, I can hook you up

I also just started a series on (the very most) basic math of finance with a dancer, this is also something I study right now, I suppose. Wrote a trading bot, but he wasn't very effective.

Today I did a proof on comparison of the Riemann and Lebesgue integral...basically any Riemann int'able function is also lebesgue int'able
Then I went to class and graded a bunch of papers for the trigonometry class I teach. Riveting shit.

You can continue by completing the hierarchy, here some more

>Riemann integral
>Lebesgue integral
>Burkill integral
>Bochner integral
>Daniell integral
>Darboux integral
>Henstock–Kurzweil integral
>Haar integral
>Hellinger integral
>Khinchin integral
>Kolmogorov integral
>Lebesgue–Stieltjes integral
>Pettis integral
>Pfeffer integral
>Riemann–Stieltjes integral
>Regulated integral
>Itô integral
>Stratonovich integral
>Skorokhod integral

And here some trig function stuff to check

[math] \forall \, f.[/math]
[math] \int_{-a}^a f(x^2) \dfrac{1}{1 + e^{ x^2\sin(x) } } \,dx = \int_0^a f(x^2) \,dx [/math]

:^)

>>9246060
You can continue by completing the hierarchy, here some more

>Riemann integral
>Lebesgue integral
>Burkill integral
>Bochner integral
>Daniell integral
>Darboux integral
>Henstock–Kurzweil integral
>Haar integral
>Hellinger integral
>Khinchin integral
>Kolmogorov integral
>Lebesgue–Stieltjes integral
>Pettis integral
>Pfeffer integral
>Riemann–Stieltjes integral
>Regulated integral
>Itô integral
>Stratonovich integral
>Skorokhod integral

And here some trig function stuff to check

For all positive values [math]a[/math] and all functions [math]f[/math], you have the simplification

[math] \int_{-a}^a f(x^2) \dfrac{1}{1 + e^{ x^2\sin(x) } } \,dx = \int_0^a f(x^2) \,dx [/math]

:^)

>>9246023
>I'm bad at math though.
BEGONE THOT

>>9246102
I'm working on it though.
And studying engineering.

Would anyone be willing to help? I don't know how to answer this.

Let f : W → X, g: X → Y , and h: Y → Z be func-
tions. Must h ◦ (g ◦ f ) = (h ◦ g) ◦ f

>>9246110
(h ◦ (g ◦ f ))(w)=h((g ◦ f)(w))=h(g(f(w)))=(h ◦ g)(f(w))=((h ◦ g) ◦ f)(w) for every w in W.

>>9246107
>engineering
my boner is gone

>>9245797
why?

>>9246107
>engineering
Lmao might as well just get neutered.

>>9246138
Come on, I'm thinking on switching to CS. I like math, just bad at it.

>>9246091
>no Tai's integral

>>9246013

this: >>9246016
Also:
. Equations and Inequalities by Kucera et al.
. Problems and Theorems in Analysis by Polya and Szego

>>9246178

Everyone here either was or still is bad at math. Just practice more. Every day all day.

>>9245720
What book deals with sigma notation? Huh? Just check the wikipedia article

>>9246016
Here's /sci/'s famous tranny fucktard again. Do kill yourself you pathetic attention seeking cuntfuck.

>>9246295
>Here's /sci/'s famous tranny fucktard again.
Not everyone who isn't a "guy" is a tranny.

>Do kill yourself you pathetic attention seeking cuntfuck.
You're the only one here looking for attention.

>>9246014
I am not that guy but THIS. This is exactly what I needed! I have 3-month breaks from uni starting December and I was wondering what I should study in that time. I do not want to spoil topology or algebra for myself so I was afraid to study those topics but this is perfect!

Do you have any commentary on the difficulty of this book in terms of mathematical maturity?

>>9245984
>the BHK interpretation of intuitionistic logic
ftfy

>>9246016
>I'm not a "guy".
Leave this board then since it's strictly for humans.

>>9246360
>>the BHK interpretation of intuitionistic logic
Uh, can you please repeat that in English next time Mr. Scientist?

>>9246373
Suit yourself.

>>9245627
Analysis / Group theory exam in 2 weeks lads
what should I expect

>>9245627
python


literary analysis


ligand shyt

>>9246434
>what should I expect
Probably some analysis / group theory

>>9245984
intuitionistic conjunction is product type is product in a category

taking product with A in a category has an adjoint (-)^A which acts like "currying" of the ambient category is cartesian closed (the existence of all such adjoints is the statement of being cartesian closed). The adjunction induces a version of modus ponens, which shows that this type can be seen as intuitionistic implication. Since this is essentially currying, applying (-)^A to any object B returns B^A, which can be thought of the "internal hom". Things of type B^A can be thought of as being of "function type".

We then finally say something like
intuitionistic conjunction <=> product type <=> products in a category
intuitionistic implication <=> function type <=> exponentiation

they are related by:

modus ponens <=> function application <=> evaluation counit

>>9246023
i'm cute and good at math but i do a lot of drugs and am currently emotionally unavailable

test, think im banned?
Anyway, I admire Jim Simons too OP.

>>9246453
Are you the same
>girl
I thought I was talkjng to?
let's be internet bf and gf

>>9245627
Studying algebra for the first time. Just got done with quotient groups.

I am new on the subjects and I was looking to purchase some books.

Anybody here had any experience with these? If so, do you recommend them? (I am an absolute beginner).

Thanks

>>9246763
That topology book is good.

What's a good book for calculus? Stewart's level is alright for a dummy like me but it has way too much fluff... I know Rudin and other people get recommended here but are they actually any good or are they just memes?

>>9245984
Basically, if you have a function of type X then you can interpret X as a logical statement and your function as a proof of X. Then the typechecker that compiles your program is essentially verifying that your proof is correct (that it actually produces type X).

So, in a programming language with a sophisticated enough type system you can encode logical statements as types, functions/programs as proofs, and the typechecker can verify correctness. Curry Howard was the first correspondence discovered but now the idea has been generalized to all sorts of logics and stuff. It has also created a special class of programming languages called "theorem provers" that are especially geared towards encoding mathematical statements inside the type system.

In general you have a correspondence that looks like:
Type Theory <-> Logic <-> Category Theory <-> Type Theory
also, type theory can be used to describe or implement the type systems for programming languages. Abusing this allows one to give a language all sorts of interesting semantics based on the associated logic (eg. temporal logic may be useful for concurrent programming languages or something).

>>9245627

Sorry that I could not reply to the anon who sent the probabilities questions last thread. Thank you though.

The first questions seems easy. There are n! ways that the letters can be labelled, and (n-1)! ways that there can be one or more correct ones. Therefore, the probability that there is atleast one is 1/n, which approaches 0 as n grows.

However, I have no idea how to do the second one. Am I supposed to start with proof thorugh induction, or can I have a hint?

PS are smilies tolerated here?

>>9246926
>PS are smilies tolerated here?
No, we will personally hunt you down, and hunt down everyone you hold dear and torture them before your eyes. Why even ask? Just keep spamming smilies so those superautistic faggots will get a brainstroke and die. We will fight cancer with cancer.

>>9246887
Spivak

>>9246932
What are you talking about, anon?

>>9246322
Stop making the thread about yourself you disgusting thirsty tranny/or ugly whale.

>>9247192
Why are you even responding to his garbage?

>>9246178
>implying cs isn't even worse

lads how the fuck do I prove limits at infinity of sequences? I can do epsilon delta proofs for functions. pls help

>>9247259
im going to the gym lads, if I dont get help by the time I go back then OP gets it

>>9246941
Answer: find some reflective surface and take a look.

>>9247208
It's not "his" garbage, it's her garbage.

>>9247259
>lads how the fuck do I prove limits at infinity of sequences?
By using the definition of a limit.

>>9247326
anon, if he was born with a dick he will always be a he.
I am sorry.

>>9247346
>anon, if he was born with a dick he will always be a he.
I'm not a "he".

>>9247350
Firstly there are some unwritten rules on this website (but please post them in an unrelated thread, to not pollute the purity math).

Secondly having a neo-vagina does not make you a "she".

>>9247353
>Firstly there are some unwritten rules on this website (but please post them in an unrelated thread, to not pollute the purity math).
Irrelevant, anyway I've been here long enough to know any rules.

>Secondly having a neo-vagina does not make you a "she".
Who said anything about a "neo-vagina"?

>>9247360
>Irrelevant, anyway I've been here long enough to know any rules.
Then follow them and post them already.

>Who said anything about a "neo-vagina"?
I.

>>9247362
>Then follow them and post them already.
Posting unwritten rules would make them written rules.

>I.
And so what is its relevance?

>>9247366
>Posting unwritten rules would make them written rules.
I was not talking about the rules, I was talking about you finally following the rules and post "them" (not the rules).

>And so what is its relevance?
You should know.

Anyone here from mathematical physics? Can you give me some insight into the field? I interested in what you guys do/research, and what is the main difference between a mathematical physicicist and a typical physicist.

What's the best textbook for Classical Mechanics given that I have a solid understanding of pretty much all undergrad math subjects?

>>9247607
>What's the best textbook for Classical Mechanics given that I have a solid understanding of pretty much all undergrad math subjects?

>>9247612
Thanks! I'll check it out?

>>9247618
I don't know why I put that question mark there.

>>9247523
Fields in mathematical physics include geometric quantization, toplogical quantum field theory, quantum algebra, tt* geometry, integrability, etc. Basically it's the study of mathematical underpinnings of physical theories and the new fields of mathematics that are borne from them. It does not care about the real world, but rather where it can abstractly lead starting from it. That's why you get theories (like string theory) from mathematical physics that use sophisticated mathematical machinery while having very little physical relevance.
Theoretical physics studies actual real systems with mathematical models. They're less concerned about formalism and more about investigate the right models and cold hard calculations.

What category theory have you done on windows today /mg/?

>>9248256
I was tinkering around the category of all axioms when I found a huge contradiction and realized that category theory is a lie. A dirty trick played to us by very powerful people or beings that really do not want our math to get more advanced. They want us to stop discovering things. Maybe we are getting too close to something important. So close that they needed to personally interfere and make sure that for the next years all we would do is draw arrows on windows like autists while accomplishing nothing of value.

>>9248277
What was the contradiction? I thought the category of all axioms was well defined

>>9248304
>What was the contradiction?
You know what it is. He, I bet you are one of them. Go shove those arrows up your ass retard. You will never stop mathematics. Everyone knows set theory is the highest level of abstraction. Anything beyond is pointless drivel meant to distract us from the real shit. What are you huh? Are you aliens? The descendants of some ancient civilization? WHO IS BEHIND CATEGORY THEORY?

>>9245627
can anyone help me with a pumping lemma problem? I'm trying to prove that a language is irregular through contradiction.

I know the outline but am getting stuck on the first step. The language is:

L = { w ∈ {a, b, c}* | number of 'a' chars in w = number of 'b' chars in w + number of 'c' chars in w}

1) Assume L is regular
2) Let P be pumping length for L
3) w =

This is the part I get stuck at, choosing a string w. I'm trying to think of ways to write the language in terms of P.

Maybe something like w = a^(num b chars + num c chars) b^(num b chars) c^(num c chars)

>>9248612
I think you can represent the language by
a^(j+k) b^(j) c^(k) , but Im having trouble writing that using the pumping length, maybe

a^(n+j) b^(n) c^(j)
where n >= p and j >= p

?

>>9247326
Sorry, but a dog you wanted to eat suddenly attacking you and mutilating your penis doesn't make you into a "she".

>>9248256
Those are the brainlet definitions of a monad and adjunctions.

>>9246939
Thanks. What about Rudin, or Apostol?

>>9249066
Rudin is a meme.

>>9248004
Is it possible for a mathematical physicist to discover a theory for quantum gravity? Thanks for the info

>>9247320
I don't understand...

>>9246434
proofs boii

>>9246851
>>9246763
the topology book is very short, although it's quite good. Maybe you should look into a cheap (like international?) edition of Munkres if you want to go further

>>9246926
Some other anon got the right answer, idk if you saw. As for the second one, a hint is:

the problem can be reformulated as: for every integer [math]M[/math], we can find positive integers [math]n,k[/math] such that [math]10^k\cdot M\leq 2^n < 10^k(M+1)[/math]

Then you can take logarithms of both sides, create appropriate real line intervals, and wind them up in a circle of circumference 1.

Please help...

So is the dog-eater the tranny poster as well? His posts just got deleted. Not like I'm surprised.

>>9249336
What have you tried?

>>9249350
>His posts just got deleted.
It's "her" posts.

>>9249370
No, I think I mean "his" posts. Being a roleplaying subhuman doesn't make you a "she".

>>9249372
>No, I think I mean "his" posts.
I'm a "her", so it should be "her" posts.

>Being a roleplaying subhuman doesn't make you a "she".
No one is "roleplaying".

>>9249375
Mutilating your penis does not make you female.

>>9249378
>Mutilating your penis does not make you female.
Agreed, but this is irrelevant to me being a "her".

>>9249379
Non-humans aren't welcome in these threads. You can leave.

>>9249364
fuck off back to stack exchange

9249370
lurk before posting or fuck off >>>/r/eddit/

Something else: Is anybody here knowledgeable in C# and up for a short programming challenge?
I need a very simple realization of a classical one-tape Turing machine. Will have two classes and a bunch of for loops.
If someone's up for that, I'd +tip ya 30$ or so, it'll only be 300 lines of code max.

>>9249400
I wouldn't be surprised if the retarded physishit is roleplaying again. Fuck off.

>>9249400
stop spamming

>>9245627
1. A mechanic is fixing a car and he assumes that at least one of the main parts in the car is
faulty. The main parts that are being checked by him are the Engine, Gearbox and
Steering. All these parts contain a feedback system that is able to provide data on condition (whether it is good or faulty) of each part. Now, the problem is that the
mechanic cannot determine whether a part is indeed faulty, or whether the actual
problem lies in the feedback system in any of the parts. When the mechanic conducted
the checks on the parts, he obtained following data from each part’s feedback system:
- Engine provides feedback that Gearbox is faulty while Steering is good.
- Gearbox provides feedback that Engine is good if and only if Gearbox is good.
- Steering provides feedback that at least one of the other two parts is faulty.
Your task is to assist the mechanic in determining the condition of the car parts by
answering the following.
a) Let E = "Engine is good", G = “Gearbox is good”, and S = “Steering is good”. Convert
the three data from the feedback system above into propositional logic notations
using E, G, S and logical connectives.
b) Using the template of the truth table below, fill in the truth values accordingly.

e g s E feedback data G feedback data S feedback data
T T T
T T F
T F T
T F F
F T T
F T F
F F T
F F F

c) Suppose the mechanic assumes that the feedback system of all the parts are
working fine, determine part(s) is/are good? Briefly explain your answer.
d) Suppose the mechanic assumes that the three parts are in good condition, which
feedback system(s) is/are wrong? Briefly explain your answer.
e) Suppose the mechanic assumes that a part’s feedback system is correct if and on
if that part is in good condition, what is the condition of each processor? Briefly
explain your answer.

>>9249474
https://programming.dojo.net.nz/study/truth-table-generator/index

>>9249404
wat?

>>9249419
no, u

>>9249480
>- Engine provides feedback that Gearbox is faulty while Steering is good.
>- Gearbox provides feedback that Engine is good if and only if Gearbox is good.
>- Steering provides feedback that at least one of the other two parts is faulty.
I don't understand this part. What does it mean?

given k points in the plane, I need to find a separation of the plane into k congruent (isometric) regions such that each of them contains precisely one point. any tips? pic unrelated

>>9249614
I'm inclined to believe that there is no way to do this, or at least no obvious way to do this.
If you add the restriction that the union of the regions does not have to equal the plane, then this is as trivial as taking some small open discs around the points.
On the other hand, if your definition of region does not mean simply-connected, I think I can imagine a way to do it that involves quotient groups of the lattice.

I don't believe Simons left academia, he still works at Stony Brook (I think)

Or maybe he left a while and came back. I didn't know he worked in cryptography though. I wish I knew a little about cryptography.

>>9249650
>I wish I knew a little about cryptography
This is easily fixed: pick some textbook and start reading.

>>9249638
Maybe I should elaborate on the last line.
Consider the case when k = 3. If all of the k lie on the same line, then you can create three strips of the same width containing the three points. From there, you continuing creating strips in the plane and assign every other one to the right k and you have your isometry.
E.g.
...ABCABC...
(where a letter indicates a strip belonging to the specific region, each region containing exactly one of the k points).

If all k do not lie on the same line, find two points on the same line and you can repeat this process; repeat the process again by reducing the strips to rectangles such that the third point no longer shares a region with one of the others, and construct a grid by extending the lines and partioning in the obvious way, assigning the right rectangles to the right region.
E.g
...
...ABCABC...
...BCABCA...
...CABCAB...
...
(where a letter indicates a rectangle belonging to the specific region, each region containing exactly one of the k points).

I think from here you might be able to proceed by induction.

Is this correct guys?

[eqn]A\cap(B\cup C)=(A\cap B)\cup(A\cap C)[/eqn]LHS
[eqn](A\cap B)\cup(A\cap C)[/eqn]
[eqn]=(A-B)-C [Alternate Representation] [/eqn]
[eqn]=(A-\bar{B})\cap\bar{C} [AlternateRepresentation][/eqn]
[eqn]=A\cap\bar{B}\cap\bar{C}[Associative Law][/eqn]
[eqn]=A\cap(\overline{B\cup C})[De Morgan's Law][/eqn]
[eqn]=A\cap(B\cup C)[Alternate Representation][/eqn]
RHS
[eqn]A\cap(B\cup C)[? Law?][/eqn]
[eqn]=A+(B\cup C)[? Law?][/eqn]
[eqn]=(A\cap B)\cup(A\cap C)[? Law?][/eqn]

>>9249655
B-but that means effort and time anon! >w<

Can someone check my steps in pic related? I'm not so sure about the RHS.

Why is combinatorics so much fun?

>>9245627
>have people been using /mg/ as a /sqt/ for math? sorry if not...

Can someone give me some intuition about/example of computation + application of resolutions and derived functors? I'm just starting to wrap my mind around basics of homology, like how to build a long exact sequence; I know a few basic applications like Mayer-Vietoris.

>can assume basic knowledge of: affine and projective varieties/ring and scheme theory/modules and coherent sheaves

>>9246148
To solve problems which consist of both mathematics and physics.

>>9250135
>physics
And why would I care about such garbage?

>>9250142
I'm not asking you to care, i'm giving you an example of why it is plausible to work with other fields. The co-operation of both fields together can be used to solve both applied problems and pure problems.

>>9245627
Is there a math god here willing to help a brother in need? I can't solve this with the correlation coefficient equation.

People got disease D and there is a test T for it.
D+ means having AIDS.
D- means being healthy.

P(D+) = 0,01
P(D-) = 0,99

Now about the test: T+ means HIV+
Sensitivity P(T+ | D+) = 0,98
Specificity P(T- | D-) = 0,98
therefore:
P(T- | D+) = 0,02
P(T+ | D-) = 0,02


I need to find the positive predictive value for when two tests are done when

a) the tests are correlated
b) rho=0,7


I figured that for rho=0 the PPV for two tests is 0,4475. For a single test it's 0,4475. But I can't figure out a and b.

>>9250267
>I'm not asking you to care
Why are you advertising it here then? Make a dedicated thread, nobody here gives a fuck about your garbage.

>>9250068
The universal coefficient theorems, the Künneth theorems. Those are important examples of how to use Tor and Ext.

>>9250290
I did not advertise it, I am defending the post of another, dick try not to make assumptions so soon.

What is the best advance linear algebra book?

>>9250333
Kunze & Hoffman

>>9250312
Take me to your leader.

>>9250346
>insert snarky irrelevant reply here


Me

Studying Linear Transformations.
I'm trying to understand the use of Kernals and Images

>>9245720
I'm sad that nobody answered this guy's question. You want a book on discrete math if you're a computer science guy. For example, "Concrete Math" by Knuth.
>>9250333
I concur with >>9250336
>>9250735
Many of the objects we study can naturally be thought of as linear transformations. For example, the derivative is a linear operator on the space smooth functions. Integration is a smooth operator on the space of linear functions. Two very basic questions we can ask about linear transformations are: (1) what sort of objects do I get if I plug something into this linear transformation (i.e., what is the image), and (2) what things are sent to zero (i.e., what is the kernel).
In finite dimensions, things are nice because you can use a basis to describe what a linear transformation does. If T: V -> W is linear, and v_1, ..., v_n is a basis for V, then if you write any vector in terms of that basis, you can easily compute what T does to that vector. In other words,
[math] T(c_1v_1+\dotsc+c_nv_n) = c_1T(v_1) + \dotsc c_nT(v_n)[/math]
In this sense, you can figure out how a linear transformation behaves just by knowing what T(v_1), ..., T(V_n) are. Some of the T(v_i) might be zero, while the others won't be. It turns out the vectors which are mapped to zero for a basis of the kernel (which is a subspace of V), while the vectors which aren't are a basis of the image (which is a subspace of W), so we get the rank nullity theorem!
[math]
\dim \text{im}(T) + \dim \text{ker}(T) = \dim(V)
[/math]
This is an incredibly powerful theorem, because it's often easy to understand a space as the image or kernel of some linear transformation. Hopefully this helps motivate things a little :)

What is the point of using Cramer's rule? It seems so inefficient compared to simple Gaussian elimination.

Why are math professors such cool guys?

>>9251089
9000x9000

I'm going full autistic. Someone please help me.

Solving

[math]U_t = U_{xx}-U[/math]
homogeneous BC's
[math]U(x,0) = \sin(\pi x)+\dfrac{1}{3}\sin(2x)[/math]

So,

[math]\sin(\pi x)+\dfrac{1}{3}\sin(2x) = \sum(A_n\sin(n\pi x))[/math]

How do I find [math]A_n[/math] and n? Doesn't n need to be an integer?

>>9251164

Nevermind I was being autistic.

Can someone help me with part b? I literally have no idea how to even get started.

>>9251279
Prove that the map x->(2x+1)/(x+1) fixes phi and is increasing on (0,+inf), then use induction

>>9249614
Let x be the smallest distance between any two points of the set. Then, draw circles of radius x-1/x with center on every single point. Done.

>>9251279
This is the core part you need.
[math] r_2 = 2 > \phi [/math]. Now suppose [math] r_{2k} > \phi [/math], then [math] r_{2k + 2} = \frac{2r_{2k} + 1}{r_{2k} + 1} = 2 - \frac{1}{r_{2k} + 1} > 2 - \frac{1}{\phi + 1} = \phi [/math]

>>9251089
It's not used in practice. Only in proofs.

>>9251445
I need a partition of the plane. Well, probably not an actual set-theoretic partition, but something like interiors of the regions are disjoint and union of their closures cover the plane.

>>9251089
>>9251462
it shows that the inverse matrix operation is a smooth map (even analytic/algebraic).

I want to understand the generalization of the Fundamental Theorem of Calculus: [math] \int_{\delta G}F = \int_{G}dF [/math] .
I have a very good grasp on basic linear algebra, but haven't studied differential forms.
Does anyone know a good PDF to read?

>>9251487
I got interested from this. Seems really cool.

>>9251487
what is your background ? do you know multivariable calculus ? do you know what a manifold is ?

>>9251498
I do.

>>9251505
then start reading Differential Forms in Algebraic Topology by Bott and Tu

>>9251507
>Algebraic Topology

>>9251490
Who the fuck uses [math]\delta[/math] to denote boundary?

Thoughts on The Theoretical Minimum?

http://theoreticalminimum.com/

>>9251505
Start on the multilinear algebra chapter of Analysis on Manifolds by Munkres and finish the book. Bott and Tu is for people already familiar with algebraic topology.

How do I solve [math](y')^2 + y^2 = k^2[/math]? Any hints? I forgot all of my differential equation stuff and I don't know a good textbook......

I'm reading the proof of the 3-covering lemma (https://en.wikipedia.org/wiki/Vitali_covering_lemma#Finite_version)), but there is one thing that I'm having trouble convincing myself of. In the latter part of the proof, the inclusions [math]B_i \subset B_{j_k} \subset X[/math] implies that, if we write [math]B_i = B(r_i; b_i)[/math] and [math]B_{j_k} = B(r_{j_k}, b_{j_k})[/math], if [math]x \in B_i[/math] then we should have [math]d(x,b_{j_k}) < 3r_{j_k}[/math]. So far, I've only managed to do the following:

Let [math]x \in B_i, y \in B_i \cap B_{j_k}, z \in B_{j_k} \setminus B_i[/math]. Then,

[eqn]d(x,b_{j_k}) \le d(x,y) + d(y,z) + d(z,b_{j_k}) \\ \le d(x, b_i) + d(b_i, y) + d(y,b_{j_k}) + d(b_{j_k}, z) + d(z, b_{j_k}) \\ < 2r_i + 3r_{j_k}.[/eqn]

Now, how do I go about dealing with the [math]2r_i[/math] term? Is there something fundamentally wrong I'm doing?

>>9251655
send y^2 to the right, take ± the square root and integrate.

>>9251663
>the inclusions [math]B_i \subset B_{j_k} \subset X[/math]
I mean "the inclusions [math]B_i \subset 3B_{j_k} \subset X[/math]", soz about the typo.

>>9251663
Note that
>the radius of Bjk is at least as large as that of Bi

So:
d(x,bjk) <=
d(x,y)+d(y,z)+d(z,bjk) <
ri + rjk+rjk <
3rjk

>>9251689
Oh. Okay. That makes sense. I was having difficulty understanding what it meant, but now that you point out how it means "[math]r_i \le r_{j_k}[/math]", I now get it. Thanks!

>>9251678
Thanks! That worked!

I have a quick question about pointwise convergence. Specifically, let [math]x \in \mathbb{R}^n, r > 0[/math]. Now, I want to prove that if [math]x_n \to x_0[/math] and [math]r_n \to r_0[/math], then [math]\chi_{B(r_n; x_n)}[/math] converges pointwise on [math]C = \mathbb{R}^n \setminus S(r; x)[/math], where [math]S(r; x)[/math] is the sphere in [math]\mathbb{R}^n[/math] with radius [math]r[/math] and centre [math]x[/math]. I've already shown that, given [math]y \in C[/math] such that [math]|y-x_0|>r[/math], then the sequence [math]\chi_{B(r_n;x_n)}[/math] converges, and if [math]|y-x_0|<r[/math] then the sequence also converges; hence, if [math]y \in C[/math], the sequence will converge pointwise to [math]\chi_{B(r_0; x_0)}[/math]. But what I'm not understanding is why it doesn't converge pointwise when [math]y \in S(r_0; x_0)[/math], because to me it seems like

[eqn]\lim_{n \to \infty} \chi_{B(r_n;x_n)}(y) = \chi_{B(r_0; x_0)}(y) = 0.[/eqn]

Am I just dumb?

>>9245797
Lmao best book cover ever.

What are the possible remainders of an integer square mod 5?

What books do I have to read to have more than a cursory understanding of fiber/vector bundles? Assume knowledge in Algebra and topology

>>9251975
[math]0,\pm 1[/math]
You need only check all values up to 5

>mathssssssssssss

>>9251975
multiply out (5k+n)^2
then take modulo 5 (we can always find an k so 0<n<5)

>>9251855
>let [math]x \in \mathbb{R}^n[/math]
>[math]\mathbb{R}^n[/math]
>Am I just dumb?
Yes.

>>9251553
all of homology

>>9252041
*cohomology

I hate math so goddamn much. But I still need to be able to afford a life of shitposting, eating, porn, and having a computer without relying on parents.

>>9247259
Comparison test

>>9251981
>>9251989
Thanks, I think it was 0, 1, and 4

>>9252242
[math]a^4\equiv 1\pmod5[/math]
by Fermat's little theorem

>>9252427
My mistake I was asking about integer squares so n^2 mod 5 for all n in Z

>>9245627
Is the following ever true?

[math]\operatorname{Spec} \left( {A\left[ {{x_1},{x_2},...} \right]} \right) \cong \mathop {\underrightarrow {\lim }}\limits_{n \in \mathbb{N}} \mathbb{A}_A^n[/math]

>>9252463
>Is the following ever true?
>[math]n \in \mathbb{N}[/math]
It is equivalent to [math]n \in \varnothing[/math].

>>9252469
fuck off

>>9252472
Seriously.

>>9252469
>t is equivalent to n∈O.
proof?

>>9252476
Proof:
Trivial. The membership predicate respects equality.
[math]\blacksquare[/math]

>>9252486
proof of the equality?

>>9252490
He's some dude who doesn't like infinite sets and is trying to politicise his opinion. Ignore it.

>>9252494
>He's some dude who doesn't like infinite sets and is trying to politicise his opinion. Ignore it.
i'm just curious how one would attempt to establish such a proof

>>9252497
You reject that [math]\mathbb{N}[/math] even exists and you are done.

>>9252499
>You reject that N even exists and you are done.
but how can N be equal to the empty set if one exists and the other doesn't? or are you also rejecting the empty set?

>>9252502
My point here is that it's super duper silly to reject infinite sets, because taming infinity in mathematics is so fun to do. It's also silly to reject AoC because you get fun shit when you accept AoC.

>>9252504
>My point here is that it's super duper silly to reject infinite sets, because taming infinity in mathematics is so fun to do. It's also silly to reject AoC because you get fun shit when you accept AoC.
what does that have to do with your proof?

>>9252490
Trivial. The empty set is unique.
>>9252504
>taming infinity
I don't understand what you're saying. It doesn't sound rigorous, whatever it is.
>>9252507
That's not me.

>>9252511
but how can N be equal to the empty set if one exists and the other doesn't? or are you also rejecting the empty set?

>>9252504
>It's also silly to reject AoC because you get fun shit when you accept AoC
Indeed, contradictions are pretty fun.

>>9252512
I never claimed the existence or non-existence of any set.

>>9252516
then what were you saying here >>9252499
>You reject that N even exists

>>9252519
Can you not read? I literally said that wasn't me in >>9252511
Or are you simply new to this website?

>>9252523
>I literally said that wasn't me in >>9252511
but you don't even mention >>9252499 in >>9252511

in any case then what's the proof of the equality you mention in >>9252486 ?

>>9252526
>>>/r/taiwan/

>>9252529
>>>>/r/taiwan/
ok?

N is the letter after L

>>9252511
>Trivial. The empty set is unique.
how does this prove that N = empty set?

What's a good rigorous book for statistics?

>>9252544
no it is not, you forgot about M

>>9252573
>statistics
>rigorous
No such thing.

>>9252573
>What's a good rigorous book for statistics?
knight

>>9250927
>It turns out the vectors which are mapped to zero for(m) a basis of the kernel
Not true.
>while the vectors which aren't are a basis of the image (which is a subspace of W)
Also not true (even if I am generous with interpreting what you mean).
Please review the basic concepts of linear algebra before posting again.

can you semi-visualize R^4 by turning 3 of the dimensions into a 3d shape and then using color for the 4th dimension?

>>9252759
yes

>>9252759
>can you semi-visualize R^4
No. It doesn't exist, so the correct word would be "imagine".

>>9252759
yes, of course

>>9252706
Pls halp

>>9249336
Show that an is increasing and bn is decreasing. conclude that both are convergent. then take the limit of both sides of the 3rd and 4th lines.

>>9251855
If B is the open ball, then you're correct. If by B you mean the closed ball, then it does not converge pointwise on the sphere

working through sheldon's LADR
just need a quick clarification here

so even if a vector space is contained in the span of some list of vectors [math]B[/math], the list [math]B[/math] does not necessarily span the vector space?
so [math]e_1, e_2, e_3[/math] does not span [math]R^2[/math]?

also how do you do the real number symbol?

>>9252900
forgot pic

>>9252900
I don't understand your question. e1,e2,e3 aren't elements of R^2.

>also how do you do the real number symbol?
\mathbb{R}

>>9252910
>[math]\mathbb{R}[/math]

so it won't make sense to talk about a list of vectors spanning [math]W[/math] a vector space if not all vectors in the list are in [math]W[/math]

like if [math]U[/math] is a subspace of [math]V[/math], not equal, it doesn't make sense to talk about a basis of [math]V[/math] spanning [math]U[/math]

>>9252915
It's not correct to say that the basis of V spans U, since span(basis) =/= U.

>>9252925
>>9252910
okay thats fine, thanks dudes

>>9252513
>The axiom of choice does not contradict the other axioms of set theory (e.g. the system ZF)

>>9252956
>the system ZF
Who mentioned ZF?

Undergraduate 'new math' retard here. How do I go from skimpy understandings of calc, LA, combinatorics to solving math Olympiad problems?

>>9252991
>AoC gives contradictions and that's all I know of it :^)
honestly fuck off. modern math uses AoC (over ZF) everywhere, and if you did any, you would know

>>9253055
IMO problems are very specific, and require very specialized training (different than the one to learn math per se). if you want to train for IMO, contact your local IMO groups

>>9253063
Oh ok maybe it's more lame than I thought, I just wanna be a late bloomer Terrance Tao copy pasta t b h

>>9253088
then you want to git gud at math? start with Tao's Analysis I and Hoffman&Kunze's Linear Algebra. (it's not quite like the linear algebra you know)

>>9253098
I'm working on those exact titles now (kinda weird desu) but feel my roots should be deeper and stronger. I'm skimming through terry's book on solving problems, and these would fuck me up

>>9245946
To be fair it takes an altitudinal IQ to comprehend, nein, fathom Rick and Morty. The humour is extrêmement subtile, and without a doctorate degree covering Bell inequalities, micro-lattice structures, and Schrödingerian quasi-contradictory quandaries et cetera (basically common knowledge among the top 10.3% among the world's best theoretical physicists) most of the jokes will evanesce or float away like Kantian noumena vis-a-vis Kantian phenomena, in other semantic units AKA words to plebes, as they say in some ethno-linguistic communities, but I digress: ありがとうございました. Furtherthus, to neologize a neologism henceforth, Rick’s existential-ideological naysaying, which ITSELF located within/via Althusserian/Foucauldian poststructuralism along the subversive-critical lines of various neo-Marxist-Leninist-Maoist analyses - his tacit (cf. Polanyi) schemata appropriates affective resonances from Narodnaya Volya literature, AKA 네 엄마는 너무 뚱뚱해. The fans understand this 陰毛, as colloquially known (excepting for Gettier cases), to quote the Chinese media scholar Jean-Claude Baudrillard: "Un jugement négatif vous donne plus de satisfaction que d'éloges, à condition que cela ressemble à de la jalousie" ; they have the Intelligenz/くそ to truly (BUT WHAT IS TRUTH, cf. Sura 2:140, John 18:38) appreciate the Aristotelian-Thomistic-Hegelian synthetic a priori interpenetrative dialogic concealed within and without these tokens of jokes, to realise that they’re not just totalitarian HAHAHAs :D in a post-postmodern world of hegemonic HUHUHUs :( - light-hearted Chopin to your heavy-handed Brahms, if I may, no pun intended - they betoken something deep about Heidegerrian Dasein (cf. Mahabharata 5.39.58) through which we can, in the words of the poet William Wordsworth, 一个巫师从来没有迟到,他总是一个有力量的人 (Yīgè wūshī cónglái méiyǒu chídào, tā zǒng shì yīgè yǒu lìliàng de rén for those who aren’t fluent in Korean).

>>9253108
>has /sci/ gone too far?

>>9253059
>:^)
>"modern math"
>AoC instead of AC
>people using ZF somehow makes it the only foundation
Retarded engineer scum isn't welcome in these threads.
>AoC gives contradictions
It indeed does if you can prove its negation.

>>9253103
try "how to prove it" or "book of proof", is that what you mean?

>>9253127
prove its negation in ZFC then. oh you can't? too bad, math uses ZFC

>>9253135
>math uses ZFC
Retarded engineer detected.

>>9253138
oh guess not every ideal is in a maximal ideal, guess there are empty products of nonempty sets, guess the product of compact spaces isn't compact, guess sequences are useless in analysis, guess local convergence in an open base does not guarantee global convergence...

kill yourself faggot freshman

>>9253135
Halfway through how to prove atm. I think I'll just skim through Terry's aforementioned book, How to Solve It, Numbers and Geometry by Stillwell and some Olympiad primer. I'm full NEET so I have the time right now.

>>9253152
sounds reasonable. spend as long as you need, but don't feel you need to go into the books "fully prepared" or something. reading new books is always challenging, and it will take effort, but those two (tao, h&k) are very beginner friendly and gently guide you into the difficulty curve

>>9253146
b-but muh banach tarski 1=2

>>9253168
if banach tarski seems contradictory to you, consider that you can split N into two sets (odds and evens) both which are bijective to N.

>>9253158
Thanks, maybe I'll try just toughing it out a bit more instead of pussy in out and running back to more elementary things

>>9253146
>guess there are empty products of nonempty sets
>think unprovable implies false
Literal retard detected. I have no doubts you are an engineer at this point.

>>9252956
>quoting pop-sci tier garbage
Engineer trash.
>>9253146
>negation of the universal quantifier implies existence of a negated formula without LEM
Engineer trash.
>>9253174
>"""if banach tarski seems contradictory to you"""
>consider that you can split N into two sets (odds and evens) both which are bijective to N
>this is somehow "odd" to him
I hate trash like you.

>>9253146
>faggot
Why the homophobia?

>>9253280
>>>/r/dogs/

>>9253283
What about dogs?

>>9252804
You're correct, I mean [math]B(r;x) = \{y \in \mathbb{R}^n \colon |y - x| < r\}[/math]. But I'm just ... why does it not converge pointwise there? To me, it seems to follow the definition of pointwise convergence.

>>9253135
You probably aren't familiar with the things adults keep whispering about, but there are other axiomatizations, and, more importantly, a theorem by Diaconescu shows that the axiom of choice implies the law of excluded middle. Refute LEM and see what happens. He may be a bit vegan-like with his exposition, but that doesn't mean he's wrong. Oh, now that I mentioned veganism in a math general, did you know that the vegetarian diet was called the Pythagorean diet back in the days?

>>9253283
It's a meme you dip

so are most of you in the academia or do this for a hobby? which path is better to do math?

>>9245627
Hey guys - I'm not very good at math and I'd like to get better. I'm an undergraduate math and philosophy major and I recently got picked up to do graduate-level research with a professor because I guess he saw promise in me. I'm working alongside graduate students and I often have to have them bring me up to speed on things (the research is in complex analysis/number theory/cryptography and I'm currently in a linear algebra class).

I realize many of you are way better at math than me and I'd like to some day be good at math - is there anything that you might recommend so I can go from a shitty undergrad math major to someone who might be somewhat competent? Thanks

>>9253805
Welcome to maths, learn to love definitions and axioms and you'll be golden.

>>9253805
>pick up a student who hasnt completed LA to do grad research
what dumb ass college is this?

>>9253809
Is it normal to get tired of "lesser" math? After doing research having to just do simple calculation in my algebra class seems like the biggest waste of time ever and I find it so boring. I also tutor kids in calculus and I can't stand it at this point.

I guess after being exposed to everything that I don't know (which it seems is a vast majority of math) I get really tired of just solving simple problems and shit like that, because I know that the part of math that I'm interested in isn't just doing calculations.

>>9253817
brainlet

>>9253816
I go to UCLA; I think it's more like I'm along for the ride but I want to actually have some valuable contributions to the project and am prepared to dedicate a lot of time to bring myself up to speed.

>>9253817
Yes, that's pretty normal. I'm a master's student and whenever a first year asks me "can you prove that [math]\lim_{x \to 0}e^x = 1[/math] by using the definition of the limit", I just don't know what to do. I know too much, so I can't do it. And whenever I have to do a calculation in my head that is more complex than adding or subtracting numbers, I usually rely on calculators.

>>9253821
you are a delusional idiot and conceded faggot that thinks ur brainley brain will contribute anythin yet, try later stupid.
>>9253822
if u cant prove it you dont really understand it and what u stated is kiddie real analysis
also
>masters
stick to applied or engineering pretentious cunt

>>9253820
That might be the case, but I've thought about it and it actually doesn't have to do with the level of the problems, but more with the monotony. I find problems interesting even if they require "simple" math but are interesting in their content.

>>9253822
I think my issue is that now that I know the vastness of math and how little of it I've been exposed to, it seems like I would rather spend my time learning learning all of that. At the same time though I realize the importance of those founding principles and I'd prefer to retain as many of them as possible.

>>9253825
Hey man I have no pretensions about my intelligence - if I'm a delusional idiot then I'm a delusional idiot and all I can do is try to go about life in the best way I can. That doesn't change the fact that I'm interested in what I'm studying and would like to know more/get better, especially if I'm stupid and it's going to require a lot more work than if I was smarter, which is definitely a possibility.

>>9253138
what is your fucking problem dude.
Someone says "AC is contradictory" and the only reasonable question to ask is "in what axiom systems" as it's clearly not in common ones like ZF, topos theory, NBG set theory, etc. Just because someone cites the most common ones does not mean they don't know about others, you're just sperging out.

>hey anon, this doesn't make sense under common assumptions
>fuck you you fucking retard engineer other math exists than the things you mentioned in 2 sentences I am math faggot lord and my diamond cut mind can tell exactly what you know and your abilities from a single fucking 4chan post

All of your teachers think you're insufferable btw

>>9253825
>>9253831

this guy has no control over himself and has nothing to show for himself so he spergs out on strangers on the internet who are earlier in their studies than him. I wouldn't worry about it. The best people like him hope for is to hide in academia bc they're insufferable to talk to and usually terrible teachers too.

>>9253822
that means you didn't learn shit mate, review ASAP

>>9253204
>he showed a lot of examples of every day uses of the axiom of choice showing how much it's used by mathematicians... but wait! his phrasing was ambiguous and I can make it seem like he's saying something wrong :^)
>>9253217
>I'll also throw in some idiocy about not having LEM because I like memes and I don't realize math uses LEM as well

you'll never make it as a mathematician, don't even try.

What's the spivak's calculus of probability?

>>9253897
as in a nice memey probability book

I was doing some Bessel function homework today and came across a concept that I don't entirely understand and my textbook doesn't explain very well.

The solution to a first order Bessel function can be expressed as a linear combination of two Bessel functions of a given value for v.
e.g. y(x) = cJv(x) + dJ-v(x)

The solution to a second order Bessel function can be expressed as a linear combination of a Bessel function and Neumann's function OR the negative Bessel function of a given v. What conditions determines if a second or Bessel can be a linear combination of two Bessel functions instead of a Bessel and Neumann's ?

Is the empty set reflexive?

This book says yes but I also hear no?

>>9254188
>Is the empty set reflexive?
The empty set is a reflexive relation over the empty set, but not over any non-empty set.

https://math.stackexchange.com/questions/1081333/prove-that-the-empty-relation-is-transitive-symmetric-but-not-reflexive

>>9253848
you mean like 99% if /math/ posters and students?

why are you math students so fucking obnoxious? If i ask an easy question, you fucking sperg out. All math majors are fukcing pretentious insufferable cunts who think they will get 300k out of college lmao
fuck you all. I fucking hate math because of you insufferable cunts

>>9254262
>why are you math students so fucking obnoxious? If i ask an easy question, you fucking sperg out. All math majors are fukcing pretentious insufferable cunts who think they will get 300k out of college lmao
>fuck you all. I fucking hate math because of you insufferable cunts
cringe

>>9254262
this is some next level bootyblast

>>9246050
How does one charm a maiden with stochastic finance? Will they appreciate the fact I can solve PDEs via sample paths? Will anyone?

>>9254188
It is vacuously true since reflexivity is universally quantified(and there is nothing in the empty set).

>>9254551
>It is vacuously true since reflexivity is universally quantified(and there is nothing in the empty set).
Only if the relation is over the empty set.

>>9253921
Boundary conditions.

>>9254717
There weren't any BCs in the problem set I was working. In case my previous post didnt make any sense here (pic related) is the question I was working. I just don't understand when you could use J-v instead of Yv. The book doesn't mention anything about it as far as I can tell.

>>9253891
Engineer garbage is not welcome here. Please learn some basic logic before posting here.

>>9253837
>the only reasonable question to ask is "in what axiom systems"
Indeed, so assuming the post had anything to do with ZF is not reasonable. I'm glad you agree.
>does not mean they don't know about others
I didn't say anything about his knowledge, engineer scum could know (or rather could have heard facts about) other systems, but that wouldn't make him less of an engineer.
It's his assumption about ZF (which let's you know that he thinks the independence of AC is not something everyone who is worth anything learns about as soon as possible) and his lack of understanding of basic logic that instantly let me know he is engineer scum.
Also, only engineers think that the most commonly used foundations are the only ones worth considering or even knowing about. Identifying "mathematics" with their axiomatic system of choice is a common trait among their pitiful kind.

>memes
>:^)
>>>/v/
>his phrasing was ambiguous
Ambiguous as in outright and retardedly wrong?
We don't like "ambiguous phrasing" in math, just so an engineer such as yourself knows. Why are you even posting in a math thread? I'm sure there is an engineering one nearby.

>>9255054
Are you okay?

>>9255054
you already replied to that post though. are you drunk?

>>9255039
it's amazing that you think not everyone knows AC is independent from ZF. are you going to tell us power set is independent from the other axioms as well, and call everyone who didn't mention that an engineer?

math uses ZFC, as much as you want to cry about it. if you ever get to higher courses you'll see, though by how you sperg out about things your don't seem to have the attention span to make it

>>9255063
In what sense?
>>9255069
Genuinely kill your retarded engineer self. You are clearly brain damaged.

>>9255077
>In what sense?
In whatever sense came to mind when you read it.

>>9255077
Why are engineers one of the smartest people?
Why the only other people who come close are the ones with a Physics degree?

Why are mathfags the most useless, lowest form of skill-less losers?
Why can't they accept the fact that their degree in itself is useless and math is something you use in conjunction with something else?
Why can't they understand that you can literally teach yourself math at home by opening a book? You can teach yourself a lot of other subjects that way as well, like physics, circuit theory, etc.

Just take a look at Heaviside, rigorous mathfags rejected his shit, yet in the end he was right. Just as engineers are always right.

>>9255076
>it's amazing that you think not everyone knows AC is independent from ZF
Yeah, it's pretty sad actually, but most engineers such as yourself don't seem to, otherwise they wouldn't make such retarded posts.
>from the other axioms
From the other axioms? Axioms of what? Of engineering?
>math uses ZFC
You claimed that math is somehow the same thing as ZFC. Fucking kill yourself, subhuman engineer.

>>9255092
>From the other axioms? Axioms of what?
I dunno anon, did you already forget what we were talking about?

>>9255093
I see, you're the "axioms of all math" guy. Fucking kill yourself.

>>9255096
Yeah, it's pretty sad actually, but most engineers such as yourself don't seem to, otherwise they wouldn't make such retarded posts. Engineer garbage is not welcome here. Please learn some basic logic before posting here. Genuinely kill your retarded engineer self. You are clearly brain damaged.

>>9255099
Hey, are the axioms of math ? Or are they not?

>>9255108
Still no arguments to be found except diverting from the original question or repeating the question in a meme manner.

In other words, thanks for proving my point. :^)

Where are the axioms of math? Why can't I calculate them approximately? Is math not as rigorous as engineering?

>>9255096
>I see, you're the "axioms of all math" guy
You seem confused.

>>9255111
>:^)
>memes
>"""proving"""
I'm not responding to your shitposts any further.

>>9255127
>your shitposts
Oh the irony

>>9252746
hes right tho

>>9255154
He/she is not right. There's way more vectors in the kernel and image than you actually need to form a basis.

>>9255132
>>9255168
>He/she
>>>/r/taiwan/

>>9255154
>>9255168
Also he/she is not right in saying that the vectors which don't map to zero under T: V -> W form a basis of the image (a subspace of W), since those vectors live in V, not W.

>>9255178
>he/she
Fuck off to >>>/r/eddit/

>>9249384
>fuck off back to stack exchange
No need to be rude.

>>9245627
Does any textbook have a harder reputation than Hartshorne?

>>9255172
What about Taiwan?

>>9251978
>What books do I have to read to have more than a cursory understanding of fiber/vector bundles?

>>9256212
what prerequisites?

CE student here.

I'm too fucking retarded for Analysis of Algorithms.
Just got off my first exam, it covered asymptotic notation and function growth, through solving recurrence relations.
Recurrence relations was specially hard for me. I just can't grasp the idea behind Iteration Method and Master Theorem.

I expect to score around a 4/10.

What previous topics will help me to be more prepared when I inevitably take this course again next semester? Any good text to read to help me better understand Algortihms by Cormen?

>>9246267
>guy can't solve basic inequalities
>gets recommended a book for graduate level students

Is this outdated?

If so, what's a modern alternative?

>>9251978
For vector bundles, it depends on what you want to know about them.

You could study them from the perspective of algebraic topology, differential geometry, or algebraic geometry.

>>9256894
https://courses.csail.mit.edu/6.042/spring17/mcs.pdf

https://mitpress.mit.edu/books/introduction-algorithms

>>9257008
>https://mitpress.mit.edu/books/introduction-algorithms
>algorithms: brainlet edition

>>9256232
learn induction/recursion
prerequisite cormen
https://courses.csail.mit.edu/6.042/spring17/mcs.pdf

Never read an algebra book.

Pic related any good?

>>9257121
>Pic related any good?
No.

>>9257122

Why not?

And what do you recommend?

>>9257124
>Why not?
Read it and see.

>And what do you recommend?
Of all the introductory 'algebra' books, Hungerford, but really they're all a waste of time. Pick the algebraic structure you want to read about and find a book devoted to them instead, i.e. Mark Armstrong's 'Groups and Symmetry'.

>>9257122
what about topics in algebra by I.N. Herstein?

>>9257121
it's supposed to be decent, I guess.
dummit&foote is very commonly recommended, artin has a heavy linear algebra flavor, rotman is just cool

>>9257121
It's an algebra book for people who aren't totally comfortable with proofs. It's slow and spends lots of time on history and exposition. If that sounds good to you, read it. If not, there are other good recommendations in this thread.

>>9256936
algebraic topology

Who pays for your food and accommodation, /mg/?

>>9257429
I do.

>>9257458
How do you manage to study then?

>>9257475
Badly

>>9247523
Basically what a mathematician does in any other field, is simplifying equations, either into simple calculus functions or sometimes even into linear functions (not really linear more like a polynomial interpolation but only dealing some number of points). They also take on problems, math related of course, and see if they can take a mathematical approach to it and prove if its right or wrong. Ex: a physicist needs to know whether his long ass expression works for all cases, that's were mathematicians would come in, check it, and give a result. That's the jist of it anyway.

>>9250735
https://drive.google.com/file/d/0B_aVQROkVqlsWG5SenBHcjY3ZDg/view
This is the book I used in Linear, should contain most the information about kernals and images. I'm not a graduate student, but I am doing research based on linear algebra (Polynomial Interpolation), I could help you if you want, what are you mostly interested in?

>>9257429
If we consider from the first year then something like 40% my family(first year and few emergencies)
the rest was sporadic work and scholarships, I illude myself that I can make a living out of it

>>9257121
See if it teaches Rings before Groups.
If yes, then it is trash.

>>9257645
This, also check if it teaches about vector spaces before modules.

>>9257657
>>9257645
pretty much a shit book if it teaches any sort of algebra before universal algebra and category theory

>>9257121
any book you understand is good, this one is friendly and from the toc seems to cover what you would expect to do in a first algebra course

>>9257133
>Read it and see.
nice argument anon
>Of all the introductory 'algebra' books, Hungerford, but really they're all a waste of time. Pick the algebraic structure you want to read about and find a book devoted to them instead, i.e. Mark Armstrong's 'Groups and Symmetry'.
you mean that shitty reference book? Armstrong is a nice reading but if I recall right it was highly expository
>waste of time
if you say so

>>9257134
>what about topics in algebra by I.N. Herstein?
a bit outdated but was my first book, and as a high school student I understood most of the material

>>9257171
this is best answer

>>9257645
>>>9257121
>See if it teaches Rings before Groups.
>If yes, then it is trash.
this is ridiculous

>>9257959
>>>9257657
>>>9257645
>pretty much a shit book if it teaches any sort of algebra before universal algebra and category theory
this is b8

>>9257959
Unironically this.

>>9258010
>this is ridiculous
Not at all. Teaching about rings before groups is acceptable only for engineers and similar scum.

>>9258116
thinking the order has any relevance is plain brainlet
theories are different, if there are overlaps then it does not matter
the important thing is to build knowledge from all of them, period.

>>9258185
It's a way to instantly tell if the book is badly planned engineer trash, nothing more. So it's fine for people with low intelligence, but higher beings should simply ignore these books.

>>9258198
if you are a higher being you should completely avoid books and post on 4cha.. oh!
you rulez xD

>>9258215
That's not necessary for higher beings. They can do as they please, for such is their nature.

>>9258010
>you mean that shitty reference book?
No, Hungerford is not a "reference" book.

>>9256232
Do the stanford algorithms analysis mooc on coursera

>>9258491
Yeah but I'm poor.