/mg/ - Math General - Young’s lattice edition.

[Anonymous No.14640814]

Formerly >>14616492.

Talk math.

[Anonymous No.14640820]

>>14640814
Is this where the ruskies got the ideas for tetris?

[Anonymous No.14640828]

>>14640814
Alfred Young

[Anonymous No.14640835]

So I'm making a digital circuit to do reciprocation of a floating point number and I've encountered an interesting problem.

A little background: A single precision floating point number is represented by a binary form [S][EEEE,EEEE][MMM,MMMM,MMMM,MMMM,MMMM,MMMM]
Where s=[S], e=[EEEE,EEEE] and m=[M,....].
Given the integer representation of these, a normal floating point number is given by:

[math]f=\left(-1\right)^{s}2^{e-127}\left(1+\frac{m}{2^{23}}\right)[/math]

0 is represented using the sub-normal form which is activated when e=0, where the 1 in the mantissa addition is dropped, i.e.:

[math]f=\left(-1\right)^{s} 2^{-149} m[/math]

The problem:
Let's say you're not graced with the ability to perform division, subtraction etc. in floating points, but instead only:

addition/subtraction [cheap, can probably do 4 in a cycle]
fixed shifts [free]
dynamic shift [medium expense: likely a full cycle]
multiplication [medium expense: likely a full cycle]
look up tables [high expense: certainly full cycle]

How would you implement the reciprocation operation, i.e. 1/x in the minimum number of cycles while attaining full precision and using the minimal lookup memory?

[Anonymous No.14640869]

>>14640814
So I'm making a digital circuit to do reciprocation of a floating point number and I've encountered an interesting problem.

A little background: A single precision floating point number is represented by a binary form [S][EEEE,EEEE][MMM,MMMM,MMMM,MMMM,MMMM,MMMM]
Where s=[S], e=[EEEE,EEEE] and m=[M,....].
Given the integer representation of these, a normal floating point number is given by the diagram to the side.

The problem:
Let's say you're not graced with the ability to perform division, subtraction etc. in floating points, but instead only:

addition/subtraction [cheap, can probably do 4 in a cycle]
fixed shifts [free]
dynamic shift [medium expense: likely a full cycle]
multiplication [medium expense: likely a full cycle]
look up tables [high expense: certainly full cycle]

How would you implement the reciprocation operation, i.e. 1/x in the minimum number of cycles while attaining full precision and using the minimal lookup memory?

[Anonymous No.14640891]

>>14640869
https://en.wikipedia.org/wiki/Fast_inverse_square_root
same concept if you have the architecture planned out ahead of time

[Anonymous No.14641125]

>>14640814
So I am taking a course into modern elliptic pde theory and it all seems over the place.
We spent a great deal of time studying approximation of functions in [math]W^{1,p}(U)[/math] by smooth functions and then never really used that elsewhere.
We also spent a lot of time studying embeddings and then that was also not used further on.
The following semester I am taking a course that will go deep into nonlinear elliptic theory, maybe it will be used there?

[Anonymous No.14641147]

>>14640814
>>14640828
>worked his whole life solving complicated mathematical problems and developing insightful mathematical theories
>the reward: get this trivial Candy Crush looking shit named after you

[Anonymous No.14641182]

what ethnical framework does /mg/ use for their maths?

[Anonymous No.14641222]

>>14640814
How do I develop intuotion for number theory? I've gotten decent at topology, algebra and geometry but number theory has always been my weakness.

[Anonymous No.14641360]

>>14641222
frequent /x/

[Anonymous No.14641361]

>>14641222
oh wait that's spectral theory oopsie
huh i guess timelines do change?

[Anonymous No.14641520]

>>14641182
I only study the work of Ashkenazi Jews.

[Anonymous No.14641529]

imagine reliving 9th grade math class again
how feel you

[Anonymous No.14641542]

>>14641529
Integration techniques were comfy af, great part of being 15.

[Anonymous No.14641621]

Number theory is so fucking interesting. I'm new to this and I'm really enjoying the experience. Following these articles since they're retard friendly http://math.oxford.emory.edu/site/math125/

[Anonymous No.14641893]

Trying to teach myself stuff. Is Lectures in Abstract Algebra 1 a good starting point or are there better options for the modern autodidactic tranny?

[Anonymous No.14641915]

What's the standard English name for this operation: [math] \bigcup [/math] so as to distinguish it from a binary union

[Anonymous No.14641921]

>>14640814
nice "irreducible" lattice. too bad the entire left or right half reduces to the other half

[Anonymous No.14641958]

>>14641621
Prove the weakest form of the Goldbach conjecture: Every number larger than 11 is the sum of two composite numbers

[Anonymous No.14641966]

>>14641529
>how feel you
bist du deutsch?

[Anonymous No.14641980]

What are the best schools in California for algebraic geometry? What are some prominent researchers in the area I should look into?

[Anonymous No.14641992]

>>14641915
That’s called cup and it’s the same operation over a variable amount of sets.

[Anonymous No.14642029]

>>14641915
[math] A \cup B [/math]
is read as “A union B”
[eqn]\bigcup_{i\in I} A_i [/eqn]
is read as “union over I of A sub i” or if it’s obvious what you mean you might just say “the union over all the A’s”
>>14641992
I’ve never heard anyone say cup for this in real life, it’s just what the latex is called for some reason

[Anonymous No.14642030]

>getting brainmogged by power series
bros... it wasn't supposed to be this way.
I'm going into my second year of uni this coming fall and am taking summer classes as well. Is it normal in university to get A's and B's but feel like you know nothing at all?

[Anonymous No.14642045]

>>14641915
Arbitrary indexed union

[Anonymous No.14642051]

>>14641147
Which complicated problems and insightful theories?

[Anonymous No.14642070]

>>14641125
Most math doesn't have a use

[Anonymous No.14642079]

>>14641980
People are moving towards geometric algebra instead of algebraic geometry. You might want to rethink that

[Anonymous No.14642082]

>>14642070
Most math doesn't have a use *yet*

[Anonymous No.14642089]

>>14642030
The only things that will be remember or matter are the fun topics. Useless shit aka boring and idgaf you can just immediately dump. For your topics;

>integrals of power series, trigonometric functions
I sleep

>radius of convergence, interverals, taylor and maclaurin series
This is where the fun is, its unforgettable.

[Anonymous No.14642096]

>>14642079
I don't think Clifford algebras are as popular as algebraic geometry.

[Anonymous No.14642148]

>>14642079
Geometric algebra and algebraic geometry are not in conflict. They describe completely different aspects of geometry.

[Anonymous No.14642188]

>>14642148
They aren’t necessarily in conflict, but GA is much more fruitful in its results

[Anonymous No.14642631]

Can I ask for math help here?

[Anonymous No.14642655]

>>14642631
No. Ask for help in /sqt/

[Anonymous No.14642737]

>>14642655
it's not a stupid question though
I'm looking for proofs

[Anonymous No.14642835]

Any textbook recs on beginner-ish algebraic number theory?

[Anonymous No.14642898]

>>14641980
Well, the obvious choices are UCB, UCLA, and Stanford, but in all likelihood you're not going there unless you're fields medal material or you have race and gender cards to play.

Outside of this, UCSD is quite strong and a quick google search shows that UC Riverside at least has a good seminar in AG. In general you probably just want to shoot for the highest-rated school you can get in to.

>>14642835
The end of Ireland and Rosen could work. Marcus and Serre are good, too.

[Anonymous No.14642983]

>>14641915
A direct limit of the index set in the category Set viewed as a partial ordering

[Anonymous No.14642997]

>>14642898
>Ireland and Rosen
This is perfect. I remember wanting to go through this during my postgrad but never had the time to do it, and completely forgot it existed. Thanks

[Anonymous No.14643254]

>>14642737
Then ask on quora or whatever.

[Anonymous No.14643261]

>>14642188
>GA is much more fruitful in its results
kek

[Anonymous No.14643490]

>>14643254
Not him but what's this thread for then?

[Anonymous No.14643497]

>>14643261
All video game programmers are learning GA to take their game engines to the next level. How many of them are learning AG? Zero.

[Anonymous No.14643538]

Lectures in Abstract Algebra fucking sucks, there must be an alternative

[Anonymous No.14643541]

>>14642737
Just ask it instead of asking permission to ask it

>>14643490
For dying

[Anonymous No.14643747]

I've finished the first two chapters of exercises in this book. I think I'm finally getting over my lifelong fear of math, doing the work has so far been very satisfying and even fun. I recommend it to anyone else just starting out.

[Anonymous No.14643797]

How do you interact with midwits who are totally ignorant of math?

>hey anon, you're a math brain, what's 2637489 times 467378?
>sorry, I don't do math with numbers
>only with letters? solving for x? damn, I never understood this in school
How am I even supposed to reply to such brainletism?

[Anonymous No.14643823]

>>14643538
Aluffi is the GOAT beginner algebra textbook

[Anonymous No.14643830]

>>14643747
Teachers being shit and the "memorization" approach to mathematics is the biggest blight to the subject.

[Anonymous No.14643923]

Eventually AI is going to be advanced enough to make very realistic simulation games. I think it'd be very comfy to play full dive VR as a mathematician in Ancient times, just reinventing math for the plebs.

[Anonymous No.14644088]

>>14643490
Maths-related shitposting.

[Anonymous No.14644140]

>>14643797
>How am I even supposed to reply to such brainletism?
you don't, some of friends saw one my books with the most basic logic (literally just quantifiers) written down and they were acting like I was the next Newton, afterwards when I read out the statement to them in plain english, they were all "wow that's it?"

Norms really like to jack off symbols they don't know the meaning of for some weird reason, you have to just ignore it

[Anonymous No.14644245]

So formally speaking, a 2D vector V would be defined something like this:
[eqn] V=(v_1, v_2):=\{\{v_1\}, \{v_1, v_2\} [/eqn] as any n-tuple would, but if you think of functions as vectors: [eqn] F:\{0, 1,2, ..., 10\}\to \mathbb{R}, x \to x^2 [/eqn] would be represented as a 11-dimensional vector [eqn] (0,1,4,..., 100) [/eqn], which could be represented very long nested set, but the issue is when the domain is an interval, you'd end up with an uncountably-dimensional vector and hence the necessity of an uncountably nested set.

this seems kind of weird to me, is it logically valid?

[Anonymous No.14644253]

>>14644245
The definition of vector space does not include that you must be able to write them as tuples.

[Anonymous No.14644485]

>>14640814
this image can fuck off desu

[Anonymous No.14644530]

>>14640814
Why no t-piece?

[Anonymous No.14644709]

>>14642051
I now hate the term 'Young' in math because of a course I took in representation theory. Most utterly inexplicable shit I have ever heard bar none. The few bits I understood were very cool, but not even Turing reductions had the same level of "what crack were they smoking" when it came to coming up with some of the algorithms involved here. Get me to fucking shudder if I hear "Robinson-Schensted" or "Jeu de Taquin" ("teasing game", fr*nch) or the fucking Viennot shadow diagram again.
Anyways, the applications I saw were mostly related to character theory and representations of Sn. You can get almost all the info you need with this stuff about all the possible representations of various permutation subgroups. This moved into info about the graded algebra of symmetric functions (finding bases for the various parts and such) and ended on some research-adjacent questions of calculating irreducible characters
For more practical purposes, I think it's used in crystallography? For still pure math but less so, the growth of the partition function is an interesting problem that still has some meat on the bone iirc

[Anonymous No.14644746]

>>14644245
You can write finite-dimensional vectors as tuples because there's a basis (and usually an obvious choice for a specific canonical basis); then the coordinates are how many of that basis vector you need (which is well-defined because bases are linearly independent). In infinite dimensions, dimension is well-defined, but the existence of a basis in all cases is equivalent to the axiom of choice (proving it in one direction is easy-ish with Zorn's Lemma iirc).
For instance, C is a vector space over R with basis {1,i}, since it's a field extension. Now, what about R over Q? Both are fields, and the latter is an extension of the former, but the degree is uncountable and actually specifying a basis would probably win you an award or something (something something well-ordering?).
Sidenote: not *all* infinite-dimensional spaces have impossible-to-find bases: polynomial rings, for instance, are vector spaces (algebras, in fact), and eg C[x] has the basis of monomials {1,x,x^2,...}. You can even pick an orthonormal basis with eg Chebyshev polynomials.

[Anonymous No.14644769]

>>14644746
The concept of Hamel basis is kinda sus and useless in infinite dimensions. As you said, often it cannot even be stated explicitly. Schauder basis is the much more natural concept of basis.

[Anonymous No.14644942]

>>14642188
ㄱㄱㄱㄱㄱㄱ

[Anonymous No.14644950]

>>14643497
lol

[Anonymous No.14645593]

>>14643747
What was your favorite exercise?

[Anonymous No.14646815]

>>14644530
my thought exactly

[Anonymous No.14649299]

mathematics is for men
trannies are women
trannies aren't mathematicians
trannies do category theory
category theory isn't mathematics

[Anonymous No.14649460]

any Germans here? i'm thinking about where i should do my masters, so far i've come up with Bonn and Munich and neither is particularly attractive, because one is too far away for my tastes (my family lives between Munich and the Austrian border), while the other is too expensive to live at. are there any good algebraically-oriented unis in Bavaria?

[Anonymous No.14649608]

>>14640814
passed my algebraic topology exam lads :D

[Anonymous No.14649746]

Every base is an extension of base-2

[Anonymous No.14650975]

99% of the time I spend studying math is spent trying to understand *what is being said*. Not understanding it once I know what it's even supposed to be saying.

[Anonymous No.14650995]

>>14649746
Did you just forget base-1 exists?

[Anonymous No.14651000]

How do I cope with the fact that I'm slowly forgetting proofs of nice theorems and that I can't just come up with their proofs on my own?

[Anonymous No.14651007]

>>14649299
Decently okay bait

[Anonymous No.14651017]

>>14650995
I did not

[Anonymous No.14651023]

>>14641915
>What's the standard English name for this operation: ⋃
and/or

[Anonymous No.14651027]

>>14650975
Is there any way to fix this problem?

[Anonymous No.14651046]

>rings are not circular structures
I just.

[Anonymous No.14651160]

>>14651000
Which theorems?

[Anonymous No.14651178]

>>14649299
shouldn't it be
>women aren't mathematicians
to complete the logical inference?

[Anonymous No.14651562]

Logic: The Laws of Truth just arrived. What am I in for? I don't know a thing about mathematics (outside of high school courses) but for some reason I want to relearn it from the beginning so I'm following pic rel.

[Anonymous No.14651706]

>pre-exam study guide is 30 problems of taylor and maclaurin series.
>derive the series from large trig functions, graph them, find intervals and radius

Man these take a really long time. Not as long as solving large trig sub and fractional decomposition integrals for the last section, but still a pretty long time.
Is calc II just a bunch of really long problems? Does it get more adhd friendly as time goes on? I have calculus 3, physics I, and linear algebra next semester.

[Anonymous No.14652410]

>>14651562
The book you got seems alright if you're interested in foundations and set theory but your pic is a huge meme

[Anonymous No.14652416]

when and how did category theory begin to be associated with troons?

[Anonymous No.14652560]

>>14652410
Post a better sequence please

[Anonymous No.14652624]

Brainlet tankwatcher from /sfg/. Let's say you have
>30 ton electric vehicle, 15 ton battery pack (260 watthour/kg so 3900 kwh total)
>8 wheels, individually powered induction motors
>mars surface gravity 3.7ms/^2, so 30T ~ 11.25T vehicle weight, if that matters
I just want to know, what would be the theoretical range of such an abomination on the mars surface, assuming it was flat ground and DC motor efficiency with the gravity and weight of said vehicle. Tried finding a way to do the rough calculation myself but couldn't figure it out.

[Anonymous No.14652817]

https://math.stackexchange.com/questions/2799939/proving-a-%E2%86%92-a-%E2%86%92-a-in-a-hilbert-system
Is it possible to give a shorter proof than the one offered as the answer?

[Anonymous No.14652860]

>>14652560
It depends heavily on what you want to do, but I think that as a foundation you should read Basic Mathematics by Lang followed by a calculus text, Spivak is wonderful, anything beyond that is almost entirely up to your interest

[Anonymous No.14653013]

>>14646815
>>14644530
Are you guys serious right now?

[Anonymous No.14653063]

>>14652416
Probably because transgenderism and category theory attract the type of person who is interested in things that others don't do or understand. The same type of people to have 4chan hobbies rather than reddit hobbies: people who lift, who use artix, who flirt with being a tradcath, who quit all social media yet spend 12 hours a day online, etc.

[Anonymous No.14653212]

>>14640814
I LOVE COMBINATORICS AND THEORETICAL COMPUTER SCIENCE

[Anonymous No.14653377]

What are some good books to get into geometric algebra.
Bonus points if it's focused on the applications of geometric algebra for physics.
Extra bonus points if the book is straightforward and easy to read (as easy as possible with a topic like this).

[Anonymous No.14653918]

>matlab can't do elliptic curves over finite fields out of the box
yurusenai

[Anonymous No.14653955]

>>14653063
I don't understand about half of what you wrote and I think I'm better off not knowing.

[Anonymous No.14653983]

>>14653377
How about the original books by Hestenes? He's a physicist and developed GA specifically for applications in physics.

[Anonymous No.14654006]

What do we know about screw theory and the embedding of 3D space into 2D space

[Anonymous No.14654011]

>>14653377
Alan Macdonald's books can teach you the basics
>>14653983
Hestenes is impenetrable

[Anonymous No.14654342]

>>14651562
this nigga got memed on hard

[Anonymous No.14654376]

>>14653918
There's a lot of features Matlab doesn't come with by default and you have to pay for the add-on's. Alternatively try Octave.

[Anonymous No.14654557]

I'm reading this proof of the division lemma http://math.oxford.emory.edu/site/math125/proofDivAlgorithm/
>However, since 0≤r1,r2<a and r2>r1, it must be the case that 0≤r2−r1<a. The only multiple of a in this range is zero, so r2−r1=0, or equivalently, r1=r2.
Why is the only multiple of a in that range zero?

[Anonymous No.14654562]

Is there any book about geometric number theory for kids?

[Anonymous No.14654578]

>>14654557
The multiples of $a$ are then numbers $na$ with $n \in \mathbb{Z}$.
>If $n \geq 1$ then $na \geq a > r_2 - r_1$ so it's not in the range.
>If $n = 0$ then $na = 0$ which is in the range.
>If $n < 0$ then $na < 0$ so it's not in the range.

[Anonymous No.14654587]

>>14654557
I think I got it. If a is a positive number multiplied by some number and the result of that is less than a, either that result is a negative number, or the result is 0. We have that the result is greater or equal to zero so it can't be a negative number. Therefore it is 0.

[Anonymous No.14654605]

why do the jannie hate enoch and his hitomi analysis, lain point theory, and monad theory?
I mean he's literally right
his work should be held as some of the most important work ever done on the level of Cantor considering how wrong Cantor was so often

[Anonymous No.14654798]

>>14654557
Is there some trick in figuring out how to proof stuff like this using sets? I understand the proof, but I would never think of constructing a set
S={b−ka, where k is an integer and b−ka≥0} on my own. Is there a trick to "seeing" why this will work?

[Anonymous No.14654994]

>>14654798
The idea in a lot of proofs is to consider a set of objects, then consider a maximal or minimal element of the set. Typically you can exploit some sort of theorem or axiom to guarantee the existence of the element. In this case you had the well-ordering principle, but sometimes you need Zorn's lemma or Noetherianness or something like that.

I can't exactly tell you how you could have come up with that proof, and it certainly would be hard to consider it if it's your first time seeing it, but a typical problem you encounter when you prove a statement is that you need to construct a certain object (in this case the remainder), but you have no idea how to do it, so you invoke a theorem that abstractly constructs a remainder-like object (a "minimal element"), and then you prove that it is the remainder.

[Anonymous No.14655071]

>>14654605

[Anonymous No.14655419]

>>14654994
Thanks anon.

[Anonymous No.14655474]

>>14654562
your dead mom

[Anonymous No.14655482]

Why are so many mathematicians schizo?

[Anonymous No.14655503]

>>14655482
>limited insight
Couldn't be me

[Anonymous No.14655908]

What topics should a beginner who wants to relearn math from the start concern himself with?

[Anonymous No.14655915]

>>14655908
pre-calc, then calc, then advanced calc, calc on manifolds, algebra, etc.
It all culminates with algebraic geometry

[Anonymous No.14655920]

>>14655908
>What topics should a beginner who wants to relearn math from the start concern himself with?

[Anonymous No.14655926]

Is this a good book for cohomology

[Anonymous No.14655937]

>>14655926
is cohomology really the hardest, most schizo field of math?

[Anonymous No.14656026]

So what is the difference between a maximal and greatest element? According to Lang:
>greatest element of [math]S[/math]
an element [math]b\in S[/math], such that [math]b\geq x[/math] for all [math]x\in S[/math]
>maximal element of [math]S[/math]
an element [math]m\in S[/math], such that if [math]x\in S[/math] and [math]x\geq m[/math], then [math]x=m[/math]

I don't get it.

[Anonymous No.14656038]

>>14656026
there is only one greatest element
while you can have many maximal elements

[Anonymous No.14656064]

>>14656038
Thanks, I'm still a bit confused by how it follows from the definitions Lang gave.
Does the first one effectively say [math](\forall x\in S)(\exists b\in S)(b\geq x)[/math] and the second one [math](\exists x \in S)(\exists m\in S)[ (x\geq m)\Rightarrow (x=m) ][/math]? In other words, the quantifier implies this property?

[Anonymous No.14656084]

>>14655937
No, lol. Cohomology is basically anywhere where algebra even touches.

Idk what the most schizo field is, but the most schizo notation i've seen is from quiver representations, pic related.

[Anonymous No.14656112]

Not homework + I've already tried posting on /wsr/ but it won't let me upload the image for some reason
In pic related, I know that x = n^(n-1). How do I get to that conclusion?

[Anonymous No.14656129]

>>14656064
the quantifiers often get in the way and just confuse people
an element b is the greatest element of S if every other element x of S is smaller than b
an element m is a maximal element of S if no other element of S is greater than m

in the context of real numbers those two definitions coincide, so if there is a maximal element of a set of real numbers, then that element is also the greatest element, so maximal elements (if they exist) are unique
in the context of arbitrary partially ordered set you can have many maximal elements

consider two bounded regions of the plane, like in the pic, and consider all the subsets of each of the regions
order the union of all the subsets of each of the two bounded regions by inclusion, so a subset A of is smaller than B if A is contained in B, this gives you a partially ordered set
it's easy to see that this partially ordered set has two maximal elements, namely the two regions themselves, as there is no larger set containing any of them

[Anonymous No.14656149]

>>14656112
>Not homework
Suuure.

Anyway:
[math] (nx)^x = (nn^{n-1})^{n^{n-1}} = (n^n)^{n^{n-1}} = n^{n\cdot n^{n-1} } = n^{n^n} [/math]

[Anonymous No.14656161]

>>14656149
>Homework: schoolwork that a student is required to do at home.
>school
I'm self-learning, so it technically isn't

[Anonymous No.14656163]

>>14654376
octave doesn't have it builtin either
sage is the only viable option, maybe maple too but i'm not sure

[Anonymous No.14656193]

>>14656161
I kid. Anyway, this is all just exponential rules, so i'd read up on that.

[Anonymous No.14656199]

>>14656193
Well, thanks

[Anonymous No.14656233]

Are there any podcasts that cover biographies of famous mathematicians? I always find that stuff very interesting, there are quite a bunch of very special personalities in the field.

[Anonymous No.14656258]

>>14656129
Thank you very much, I think I understand it now. I should probably read a few more introductory books before continuing with Lang

[Anonymous No.14656396]

>>14656112
You shouldn’t have mentioned homework if you wanted help

[Anonymous No.14656448]

>>14655482
Isn't this just the typical nerd archetype? You should instead say:
>Why are so many mathematicians lonely virgins?

[Anonymous No.14656566]

>>14655926
>.pdf
wtf since when

[Anonymous No.14656584]

>>14656026
The concept coincides in totally ordered sets for obvious reasons, so you can't think of numbers. Consider the 3 element set, partially ordered by taking subsets, consisting of black circle, purple circle, and the pink intersection. Each circle is maximal, but neither is the greatest

[Anonymous No.14656678]

"Which of these relations A -> R, A= [-1; 2] , represents a function?"
Answer key says a & d.
Now, it's quite obvious to me that b) is not a function since it doesn't pass the vertical line test, but
why is d) considered a function if the graph extends a bit further from the domain? And
why is c) not a function?

[Anonymous No.14656724]

>>14656678
A= [-1; 2] means that the function exists (is a real number, A is mapped to R) at every point from -1 to 2.

[Anonymous No.14656744]

Someone explain to me how, if dedekind cuts are defined with respect to the countable rationals, the dedekind cuts are uncountable

[Anonymous No.14656751]

>>14656724
That part is clear to me, my question is in regards to the author's classification, see:
>why is d) considered a function if the graph extends a bit further from the domain? And
>why is c) not a function?

[Anonymous No.14656771]

>>14656751
for c) I'd say it is a distribution instead a function. There's a point at x axis that doesn't map to any value on the y axis, then no inverse because no injectivity applies in this case. Maybe I'm wrong tho, I'm rusty on this subject.

[Anonymous No.14656807]

>>14656771
What point are you referring to?
Also, do you know what the small white ball in the line means?
>no injectivity applies in this case
I haven't even gotten to this part yet lol, just started functions.

[Anonymous No.14656808]

how come Keith hasn't posted anything new in years? does he not teach at all lately? i have learned more from his blurbs collectively than i have from any single textbook

[Anonymous No.14656815]

>>14656807
>What point are you referring to?
>Also, do you know what the small white ball in the line means?
precisely that little white ball indicates a 'not defined value', (case c) and in d) the little white ball have a little grey ball above which indicates the defined value corresponding to it's value on x axis.
>I haven't even gotten to this part yet lol, just started functions.
Now I understand. Then now you have a good motive to study, anon. Inyectivity study is the very basic in functions. Almost any first year math book talks about these stuff.

[Anonymous No.14656838]

>>14656678
c) is not a function because there's a hole in it
d) is a function because there is no hole. It is defined everywhere between [-1,2].

Don't concern yourself with d) outside [-1, 2] because that has nothing to do with the question

[Anonymous No.14656850]

I need a book on partial diffirential equations. I'm completely new to this subject, it would be nice if it would build some intuition. Please help.

[Anonymous No.14656869]

>>14656850
Haven't studied this yet but as far as I have looked into resources, these two are good

Partial Differential Equations Sources and Solutions by Arthur David Snider

Partial differential equations by Nakhlé H. Asmar

[Anonymous No.14656908]

>>14655915
You mean geometric algebra

[Anonymous No.14656920]

>>14644950
Post argument

[Anonymous No.14656992]

>>14655937
>most schizo field of math
I'm gonna have to go with advanced point-set topology.
>>14656869
>Haven't studied this yet but as far as I have looked into resources
The /mg/ special.

[Anonymous No.14657002]

>>14656992
>The /mg/ special.
lol, sorry for that. Althought, it's true I haven't studied it in depth I have some basic knowledge on it so I can spot good books without having to study all the stuff first. At a beginner level at least. Idk anon. You help us with diff eqs shit.

[Anonymous No.14657004]

how do you know if you're good at math? as in, better at math than other things. I'm better at math than everyone i've met, but that's probably because my general IQ is so high. I think my verbal ability is way better than my math ability.

[Anonymous No.14657006]

>>14640814
This thread is too monolithic... it needs some more diversity and multiculturalism...

We will get migrants to come here soon...

[Anonymous No.14657012]

>>14657006
I am an immigrant

[Anonymous No.14657024]

>>14657012
Good, feel free to talk about politics, anime, videogames, working out, or whatever culture you have from your home board.. if any bigot tries to shame you and accuse you of being off-topic, accuse him of xenophobia...

This is a global imageboard, we cannot tolerate artificial separations created decades ago by racists, we must integrate.

[Anonymous No.14657040]

>>14657024
>feel free to
no no, I think I should feel oppressed, or is that only for the mid-upper class white girls anons only?

[Anonymous No.14657058]

>>14656992
whores

[Anonymous No.14657092]

>>14657024
Yes, and feel free to talk about how much you hate liberals and white girls. If anyone complains about it being unrelated to math in a math thread, accuse them of being a white woman. After all 4channel (and the facebook group) is for Extremists Only, and anything non-political must be destroyed.

[Anonymous No.14657108]

>>14654011
>Alan Macdonald
Do those books help you understand what GA is used for?

[Anonymous No.14657110]

>>14654011
Hestenes seems readable enough, but it’s not clear to me what GA adds

[Anonymous No.14657118]

>>14657108
>what GA is used for?
>>14657110
>what GA adds

Copium for physicists

[Anonymous No.14657220]

>>14656869
I got Asmar's book as well. What a massive son of a bitch it is...(the size)

[Anonymous No.14657225]

>>14655926
>author just randomly puts pictures with him and other mathematicians, like Deligne, Weil, etc. in the book
kino book

[Anonymous No.14657252]

>>14657220
>What a massive son of a bitch it is...(the size)
lol, yes it is

[Anonymous No.14658093]

Is there anything comfier than elementary number theory.

[math]\mathbf{Theorem} [/math]
[math]\mathbf{If}[/math] [math] 30|(a+b+c),[/math] [math]\mathbf{then } [/math] [math] 30|(a^5+b^5+c^5)[/math]
[math]\mathbf{Proof:}[/math]
Of course, any toddler knows
[math] 30|(n^5 - n) [/math], thus
[eqn]30|(a^5 - a)+(b^5 - b) + (c^5 - c)[/eqn]
thereforely, from thy hypothesis,
[eqn]30|a^5+b^5+c^5[/eqn].

[Anonymous No.14658159]

>>14656678
what does f(1) equal?
For a function to be defined, this question must have an answer. And that answer must be in R.

[Anonymous No.14658162]

>>14658159
must have a unique* answer

[Anonymous No.14658207]

>>14656850
I enjoyed this one. Well written and comprehensive.

[Anonymous No.14658265]

>>14656026
Here’s some random partial ordering off of Google images. It’s got four maximal elements (labeled 5,6,7,8) but no maximum (aka greatest) element. It’s a worthwhile definition to have around.

[Anonymous No.14658297]

>>14657004
if you are enrolled in a reputable university mathematics program and you are better than all your peers then you are probably quite good.

[Anonymous No.14658308]

Can I blogpost here? After finishing my maths degree I left to become a code monkey and I hate it so much

[Anonymous No.14658372]

>>14658093
Why are mathfags like this. I remember one test I had in uni where a Lemma on the 3rd page was worth 1 point (out of 100) and was used to prove a theorem on the first page worth 35 points. If you didn't know that Lemma (never talked about in class/book) you wouldn't be able to prove the theorem without rediscovering it.

[Anonymous No.14658580]

>>14658093
> Of course, any toddler knows
> [math]30|(n^5 - n)[/math], thus
this triggers me far more than like. this anon knows the pain of a number theory course.

[Anonymous No.14658590]

>>14658580
>>14658372
To be fair, that property is fairly standard and easy to prove, so should be springing to mind if you see 30

[Anonymous No.14658603]

>>14658590
I've taken both elementary and analytic number theory and I can honestly say I've never seen it before. Which is exactly >>14658372 point. As long as you encounter and learn a bucket load of "tricks" it's a bitch of a subject.

[Anonymous No.14658609]

>>14658590
I've taken both elementary and analytic number theory and I can honestly say I've never seen it before. Which is exactly >>14658372 point. As long as you encounter and learn a bucket load of "tricks" it's fine, without it's a bitch of a subject.

[Anonymous No.14658625]

>>14658609
If you've done elementary number theory I have no doubt you've seen the identity [math]8|n^2-1[/math] if n odd, or factorizations for [math]x^i\pm y^i[/math] as standard procedure, both of which are alluded to in the statement of the theorem.

[Anonymous No.14658654]

>>14658625
Neither are alluded to in that theorem, also the theorem clearly comes from someone playing around with [math] 30|(n^5-n) [/math] until they found a cool string of symbols, and then finding a hypothesis that makes it true. It's not math, it's mental masturbation.

[Anonymous No.14658745]

>>14658625
>factorizations for [math]x^i\pm y^i[/math] as standard procedure
kek. none of my textbooks ever taught those and I remember my lecturer just assuming we all knew them already. that was a fun semester.

[Anonymous No.14658797]

>>14656163
I've used sage but it was pretty shit. For it example it supports isogenies but not computing isogeny compositions. Not sure if it's good or not but it could be worth looking into Macaulay2.

[Anonymous No.14658804]

Why does the angular momentum schizo hate Noether? >>14658786

[Anonymous No.14658815]

>>14658804
why can't we physicists have a comfy general like /mg/ that isn't shat up by schizos? Why does math have so few schizos compared to physics?

[Anonymous No.14659075]

>>14658804
this guy has to be the most retarded schizo to ever visit this site

[Anonymous No.14659229]

>>14658308
Why do you hate it?

[Anonymous No.14659312]

Why is there a meme of associating math with autism when so much of it involves reading between the lines and definitions you just have to "get"?

[Anonymous No.14659378]

>>14659075
sneed

[Anonymous No.14659383]

What is the function so that all the natural numbers of the graph have a vertical line?

[Anonymous No.14659387]

>>14659383
Not a function, and there are more than 1

[Anonymous No.14659690]

>>14659383
Dirac comb

[Anonymous No.14659720]

>>14656815
>>14656838
Thank you guys, this has def cleared up my questions.

>>14658159
Are you referring to the definition of a function, that it for each element in A there's only one correspondent in B? That much I know, I just couldn't really read the graph, it was a bit confusing.

[Anonymous No.14659751]

>>14659378
>5 panels portray difficulty in unlearning the established fundamentals
>6th portrays difficulty in learning the established fundamentals
>le reddit midwit irony

[Anonymous No.14659757]

>>14659751
>Missing the point this hard because of the joke last panel
Peak autism, go read Proofs and Refutations by Lakatos

[Anonymous No.14659760]

>>14659757
Like I said, the first 5 panels look like they're building towards an actual point, but then the 6th collapses it into some midwittery about how it took all le smart men a gazillion years to process a thing while le poor brainlet students are expected to pick it up quickly. You're the autist here, clearly, and a low-functioning one at that.

[Anonymous No.14659765]

>>14659760
>autist misses the point about institutionalised ego so he can complain about reddit

[Anonymous No.14659767]

>>14659760
Nope, you are missing the point. That comic is literally how math works, teaching students the "nonsensical conjectures" as trivially true axioms is how we teach mathematics.

[Anonymous No.14659772]

>>14659765
>>14659767
>t. 105 iq

[Anonymous No.14659781]

>>14659772
There's that ego again

[Anonymous No.14659782]

>>14659772
Peak autism, go read Proofs and Refutations by Lakatos

[Anonymous No.14659783]

>>14659781
Indeed. Someone needs to cut you back down to size.

[Anonymous No.14659785]

>>14659782
The sheer degree of your misunderstanding... I know Proofs and Refutations is mindblowing for a 105 IQ, and the connection to this comic makes you feel like somekind of a deep-thinking intellectual, but your vacuous shart is literally obviated in my first post.

[Anonymous No.14659788]

>>14659785
Peak autism, go read Proofs and Refutations by Lakatos

[Anonymous No.14659796]

>>14659788
Literally read it as a 12 years old. Off yourself, low-tier midwit. You will never be a mathematician.

[Anonymous No.14659802]

>>14659796
Read it again, it went over your head when you were 12.

[Anonymous No.14659804]

>>14659802
>confirming that this midwit-tier book and its midwit-friendly conclusions sound deep and complex to you
105 IQ things.

[Anonymous No.14659813]

>>14659804
Reddit autism moment

[Anonymous No.14659831]

>>14659813
Explain, in your own words, what you think le epic reddit comic is saying. I know midwits struggle with forming thoughts of their own, and feel more comfortable referencing le midwit intellectual books, but try. :^)

[Anonymous No.14659833]

>>14659751
Who said there were established fundamentals that said the proof was wrong? How could there even be established fundamentals that are wrong?

[Anonymous No.14659842]

>>14659833
>Who said there were established fundamentals that said the proof was wrong?
That's right, who said that? This is some funny stuff.

[Anonymous No.14659965]

You are all pseuds. Shut up

[Anonymous No.14660008]

How do I put this function in the fucking geogebra it doesn't let me put it?

[Anonymous No.14660042]

>do math at work so I can learn more math in a day
>no longer feel like doing math at home now that it's a "work thing"

[Anonymous No.14660160]

Is he right? Is pure math actually really just simple but autists disagree on said simple things?

[Anonymous No.14660196]

>>14660160
Proofs are just strings of tautologies so yes. If you want something complex try telepathy or something

[Anonymous No.14660228]

>>14660160
>"Literal" PhD Canidate thinking you know shit about mathematics
>thinking you know shit about undefined adjectives about mathematics
>woman
Explains it.

[Anonymous No.14660509]

>grand old time doing sequences and series
>"Finally we get to the whole point of this, converting indefinite integrals into a series equivalent we can integrate"

[Anonymous No.14660770]

>>14660160
PhD candidates don't know shit yet. They merely finished a curriculum of the absolute basics and constantly need someone smarter than them to hold their hand. High level research math is way beyond what a mere PhD candidate can understand.

[Anonymous No.14660777]

I am reading about context free grammars

[Anonymous No.14660859]

>>14640814
what branch of mathematics is parameter estimation of chaotic dynamical systems?

[Anonymous No.14660871]

>>14660859
Probably a bit of Stochastic Calculus, control theory, and dynamic models. Also just normal statistics since parameter estimation is like the bread and butter of statistics (a statistic is typically just a parameter estimate)

[Anonymous No.14660912]

>>14640814
I need you help anons, what are the best math books? [ for uni/college math and up]

[Anonymous No.14661082]

>>14660912
There is a textbook list in the /sci/ wiki. Usually in this general only troll answers are given, like the one already posted in this thresd

[Anonymous No.14661235]

>>14660912
First, you want to brush up on arithmetic at the college level, so get A course in arithmetic by Serre. Should only take a couple of days or a day at the least.
Next some would say calculus, but I think you can put that on hold for linear algebra, Roman Advanced Linear Algebra (it's college level) is a good choice, but you only need the first chapter and then the later half of the book, this will take you at least a month.
Next, you can study from Thomas's Calculus, which should take you a few years or a year if you go hard. This will give you enough context to decided what you should study next. Good luck Anon.

[Anonymous No.14661248]

>>14660196
>Proofs are just string of tautologies
Peak autism, read Lakatos' proofs and refutations

[Anonymous No.14661529]

>>14660912
Algebraic Geometry by Hartshorne. Any other book will just make you dumber.

[Anonymous No.14661821]

>>14658654
>30 = 2*3*5
>2: n(n^k-1)
>3: n(n^2k-1)
>5: n(n^4k-1)
but yea i agree number theory has some garbage because it's ill-suited to having its results enumerated by a computer

[Anonymous No.14662403]

"zero elements" were never defined. I can guess what it means but I shouldn't have to guess with a math book is what I thought before

[Anonymous No.14662615]

https://en.m.wikipedia.org/wiki/Loop_space
>In topology, a branch of mathematics, the loop space ΩX of a pointed topological space X is the space of (based) loops in X
What makes a loop based?

[Anonymous No.14662660]

>>14662615
You can tell by the way that it is

[Anonymous No.14662839]

>>14662615
>"math" joke
>the joke is (barely) based on math itself, but instead a coincidence of how something is named

[Anonymous No.14662917]

I have no idea how I'm supposed to prove that if a is positive and b is negative then ab is negative.

POS 1 only talks about what happens when a and b are both positive

POS 2 only says if a is a real number then a is positive or 0 or -a is positive

to be honest the "very simple" proof in the upper half of the page also loses me at the sentence "but this product is equal to 1"

I don't wanna just check the solutions at the end of the book, but I'm running out of things to think. Can I get a hint?

Feels like I'm missing the way I can leap from POS 1 and POS 2 to saying something about operations that involve both a positive and a negative number.

[Anonymous No.14662938]

>>14656869
Compact quantum groups

[Anonymous No.14663049]

How do i find someone willing to take my dumb ass for a PhD?

[Anonymous No.14663125]

>>14662403
>>14662917
Are these all for real numbers? Real numbers are convergent Cauchy sequences, so you could show it’s true for every element of each sequence for maximum rigor.

[Anonymous No.14663321]

>>14663125
yes, it's all for real numbers in Serge Lang's basic mathematics. could I handle cauchy sequences when I can't even figure out the way the book expects me to do it?

[Anonymous No.14663327]

What do you mean for someone to "have a problem with" something in math?

[Anonymous No.14663394]

I am trying to prove the fundamental theorem of arithmetic. The general statement is that every integer greater than 1 can be represented as a product of prime numbers. Let us assume otherwise, that there exists an integer a>1 such that not all of its factors are reducible to products of prime numbers. Then there exists a factor x of a, such that xk = a, and x=mn where 1<m<x and 1<n<x. m and n in turn can not be prime numbers. Since m is a factor of x, then their greatest common divisor is m. Using bezout's identity we have that: qx + wm = m. So qmn + wm = m. Multiplying both sides by n gives us qmnn + wmn = mn, i.e qmnn + wmn = x.
So x= mn(qn +n), so x=x(qn +n). This means that qn+n=1. In other words, n(q+1)=1. Since n was assumed to be greater than 1, it cannot be a factor of 1.

[Anonymous No.14663395]

>>14663394
Is this right, or did I fuck up?

[Anonymous No.14663603]

What's the relationship between [math] \infty \in \mathbb{\overline{R}} \space \& \space \aleph_0 [/math], are they equal? What about [math] \aleph_1[/math]?

[Anonymous No.14663624]

>>14663394
God I am retarded

[Anonymous No.14663677]

>>14662917
>to be honest the "very simple" proof in the upper half of the page also loses me at the sentence "but this product is equal to 1"
(-1) * (-1)
= (-1) * (-1) + 0
= (-1) * (-1) + (-1) + 1
= (-1) * (-1) + 1 * (-1) + 1
= ((-1) + 1) * (-1) + 1
= 0 * (-1) + 1
= 0 + 1
= 1


>First equality is because 0 is the neutral element of addition
>Second equality is because -1 is the additive inverse of 1
>Third equality is because 1 is the neutral element of multiplication
>Fourth equality is because of the law of distributivity
>Fifth equality is because -1 is the additive inverse of 1
>For the sixth equality you use that 0 * x = 0 in every ring see the proof below
>Seventh equality is because 0 is the neutral element of addition
0 * x = 0 * x + 0 * x - 0 * x = (0 + 0) * x - 0 * x = 0 * x - 0 * x = 0

Always do everything in very small steps.

[Anonymous No.14663688]

>>14662917
>I have no idea how I'm supposed to prove that if a is positive and b is negative then ab is negative.
If you want a hint: Your difficulty is in dealing with negative numbers, try instead dealing with them indirectly by simply using their additive inverses, as those are always positive.

Also just a reminder not to read the book too quickly, math is incredibly subtle and your brain needs all the time it can get to absorb the material, don't make the same mistake I did.


I don't recall BM having a solutions manual at the back but if there is one, then feel free to ignore the solution I'm about to type in case you want to check:

.

.

.


[eqn] a>0, b<0 \\b<0 \implies -b>0 (POS2) \\ a*(-b)=-ab>0 (POS1) \\ -ab>0 \implies ab<0 (POS2)[/eqn]

[Anonymous No.14663893]

what I do feel while reading K-ly book on Topology:

https://www.youtube.com/watch?v=BHfE682mm3c

[Anonymous No.14663912]

>>14661529

slap this bad boi

[Anonymous No.14663917]

>>14663912
I worked mainly with Qing Liu's book and the Hartshorne. Only opened EGA3 since everyone was screeching about how hard and obsolete EGA/SGA was. I opened EGA1 this week to review some stuff and while it's really presented coldly as tools for AG, it's very readable and coherent.

[Anonymous No.14663938]

>>14662917
Begin by showing -1*a=-a (use 1+-1=0 and distributivity), and you're done:

a pos, b neg => -b pos => -1*b pos => -1*a*b=-ab pos => ab neg

[Anonymous No.14663982]

>>14663917

Good. It was ahead of its time.

[Anonymous No.14664064]

>>14663893
..why?

[Anonymous No.14664074]

Where can I learn about Chow groups and cycles in K-theory?

[Anonymous No.14664092]

>>14663677
>>14663688
>>14663938
Thanks for all the replies guys. Gonna let it all settle and swirl in my head and only then move on. Read all your posts in a way that I wouldn't spoil myself but still get some hints and I think I'll get it tomorrow.

It's really fun that something "so simple" could occupy me for hours. This feels a lot more challenging and motivating than the grind of linear equations in the previous chapter.

Reminds me of that one Wittgenstein sentence Steve Reich used in Proverb: "How small a thought it takes to fill a whole life!"

[Anonymous No.14664161]

>>14664064

Feels a bit like a good code.

[Anonymous No.14664317]

Lately I got interested in p-adics. It's a really nice topic from a geometric/analytic perspective. However, I have absolutely no background in number theory and I'm completely unaware of the original context in which p-adics were discovered. Could a knowledgeable anon enlighten me?

[Anonymous No.14664395]

What do you guys think of Velleman's How to Prove it and Courant's What is Mathematics?
I'm an undergrad math major and want to read these books

[Anonymous No.14664437]

>>14663917
No one says EGA/SGA is hard, just that it is massive and very abstract and untranslated french. And you are right, at some point I was struggling with an exercise in some book and the only resource I found that answered whatever question I had was in something like SGA IV, and I understood the proof perfectly from there despite not reading any other of his stuff and not speaking french

[Anonymous No.14664445]

>>14663321
They are the same thing as real numbers though. You can do it.
https://jdhsmith.math.iastate.edu/class/0420M201.pdf

[Anonymous No.14664460]

>>14663603
Infinity in the extended reals is [math] \mathfrak{c} [/math], because there is a bijection between the set and [-1, 1]: https://www.maths.tcd.ie/~dwilkins/Courses/221/Extended.pdf
If we were using [math] \aleph_1 [/math] we could pull out a set of measure zero and run past infinity (might require axiom of choice).

[Anonymous No.14664463]

>>14664460
>[math] \aleph_1 [/math]
[math] \aleph_0 [/math].

[Anonymous No.14665504]

day i don't know what
fixed points of discrete logartithms are driving me to madness
pages of number theory identities have been written with seemingly no algorithm yet
the number of points is insufficient to classify the structure (mod 7, 11, 13 all have six) but i know there's something more there

[Anonymous No.14665537]

a is either a>0, a=0, a<0.
when a=0 a^2=0*0=0
0 is not positive

is this task wrong or am I wrong?

[Anonymous No.14665554]

>>14665537
it should say non-negative, yes

[Anonymous No.14665580]

The distance between the the bottom of a wall and a foot of a ladder is 20m Calculate the height of the wall if the angle of depression from the top of the wall is 16° and the angle of elevation from the bottom of the ladder to the top of the wall is 12°.

[Anonymous No.14665731]

>>14665580
The question is not fully clear to me. Do you mean pic related or something else?

[Anonymous No.14665743]

>>14665580
>>>/sci/sqt

[Anonymous No.14665753]

I always think about buying some math books, but since I'm using all these English and American books the shipping costs (living in EU) make it so that even used books are more expensive than what I'd consider a fair price.

while it's nicer to flip around in a physical book, especially with math where you might look at earlier theorems and proofs, I think maybe I should just give up. or maybe printing out the pirated pdfs for myself could work?

I could buy ~43-45 kilograms of bread for the price of one math book, what's the ratio like at you guys?

[Anonymous No.14665847]

The Greatest Maths Mistakes?

[Anonymous No.14665861]

>>14665847
Infinite Sets

I have never seen infinite objects of anything in real life.

[Anonymous No.14665869]

>>14664460
Hmmm, so is [math] 1/\aleph_0 = 0? [/math]

[Anonymous No.14665872]

>>14665861
The universe is infinite

[Anonymous No.14665878]

The Peano axioms can all be derived as theorems from just one axiom: A is equal to B if and only if a bijection exists between A and B.
Neat and all but what are the applications?

[Anonymous No.14665887]

>>14665878
>A is equal to B if and only if a bijection exists between A and B.
So {1} = {2} since f(1) = 2 is a bijection between {1} and {2}?

[Anonymous No.14665933]

>>14658093
BASED.
I UNIRONICALLY ALWAYS THROW PHRASES LIKE "OBVIOUSLY" OR "IT'S EASY TO SEE" IN NON-TRIVIAL THINGS IN MY PROOFS.

[Anonymous No.14665945]

>>14665933
>NON-TRIVIAL THINGS
It's not something you'd know from memory but it's still trivial.
Even if you're stupid you can just exhaust for all possibilities of [math]n \mod 30[/math]

[Anonymous No.14665948]

>>14665945
sure, I just meant "things you need to actually think about to understand and are quite difficult to come up with for the proof if you haven't seen them before" but I didn't know any other word to describe that better.

[Anonymous No.14665968]

>>14665887
Yes, {1} = {2} = {Andrew}. They are all the set containing zero sets and one urelement. How tf you derive the peano axioms from just that is beyond me.

[Anonymous No.14665979]

>>14658093
>>14658580
>>14658590
>>14658609
>>14658625
>>14658654
>>14661821
I can see why it's dividable by 2 and by 5 but I don't see why it's dividable by 3.

[Anonymous No.14665985]

>>14665979
n^5 -n = n(n^4 - 1 ) = n(n^2 - 1)(n^2 + 1)= n(n-1)(n+1)(n^2+1) and one of n, n-1, n+1 is divisible by 3.

[Anonymous No.14665988]

>>14665985
Thanks bro. That was easier than expected. I should have seen it.

[Anonymous No.14665990]

>>14665979
Fermat's little theorem says that
n^3 = n (mod 3)
Multiply it by n^2:
n^5 = n^3 = n (mod 3)
Subtract n:
n^5 - n = 0 (mod 3)


Alternatively just consider the 3 cases
n = 0 (mod 3)
n = 1 (mod 3)
n = 2 (mod 3)

[Anonymous No.14666227]

>>14664317

[Anonymous No.14666305]

good morning /mg/

[Anonymous No.14666368]

>>14666305
Good morning and good night posting should get you autobanned.

[Anonymous No.14666410]

>>14640814
what's a good book on hamiltonian and euler graphs in polytopes?

[Anonymous No.14666581]

>>14665580
>>14665731
the question is completely confusing until you realize the ladder doesn't go all the way up the wall and that it's two triangles sharing a side

[Anonymous No.14666625]

I love that a parabola is called 放物線 in Japanese.

[Anonymous No.14666658]

hi math ! i found a bug in math. check the image attached.

PS : IT WELLCOME

[Anonymous No.14666798]

>>14666625
https://en.wiktionary.org/wiki/%E6%94%BE%E7%89%A9%E7%B7%9A

[Anonymous No.14666942]

>>14666798
>Etymology
Borrowed from New Latin parabola, from Ancient Greek παραβολή (parabolḗ), from παραβάλλω (parabállō, “I set side by side”), from παρά (pará, “beside”) + βάλλω (bállō, “I throw”). Doublet of parable, parole, and palaver.

Didn't realize the English/latin/etc. word comes from throwing shit as well. I like it. Throwing shit is good.

[Anonymous No.14666961]

>>14666658
You don't need introduce complex numbers for that.

[eqn] \frac{1}{0} = \frac{(-2) \cdot 1}{(-2) \cdot 0} = \frac{-2}{0} \\
\frac{1}{0 \! \! \! \backslash} = \frac{-2}{0 \! \! \! \backslash} \\
1 = -2[/eqn]

[Anonymous No.14666967]

>stuck on something
>think about it for a while
>go through material again
>carefully go over the problem again
>actually solve it
no better feeling than this

[Anonymous No.14667178]

>notation table doesn't have text attached to it explaining what anything means and author just expects you to figure it out by context
WHAT THE FUUUUUUUUUUUUUUUUUUUUUUUUUCK
HOW DID SPRINGER LET YOU PUBLISH THIS

[Anonymous No.14667380]

>>14666967
I agree. Better is when you solve a row of
problems with the whole material in mind within
minutes of each other. Satisfying.

[Anonymous No.14667544]

What are some good books I can go through as a refresher? Like I dont need a whole book on linear algebra but id like to go back and make sure i dont lose it. Same with complex analysis, galois, etc. just undergrad stuff.

[Anonymous No.14667575]

infinity * infinity is infinity right? It’s not indeterminate, right?

[Anonymous No.14667843]

Told my sophomore cousin that the exams in a pure math undergrad are extremely easy and that it's the other parts of the degree that are hard. He said I had it the wrong way around.
Today he called me a retard after he asked a bunch of fellow students and two profs, all of whom apparently backed him up.
?? explanation please

[Anonymous No.14667907]

>>14667843
Different universities teach in different ways...

[Anonymous No.14667910]

>>14667843
Your cousin is a midwit.

[Anonymous No.14668549]

Tell me why should I learn distributions, they seem really boring, is there any other reference besides Evans?

[Anonymous No.14668697]

>>14665861
All sets are infinitely deep.

>>14665872
>The universe is infinite
That's not proven. The observable universe is finite.

[Anonymous No.14668723]

>>14668697
True for uncountable sets.

[Anonymous No.14669065]

What are the most general answers to these questions in category theory?

1. Under what conditions does a category always have direct/projective limits?
2. Under what conditions does a functor preserve direct/projective limits?

Sorry, if the questions are dumb. I'm dealing with algebraic topology and I'm actually too lazy to read a whole book on category theory to get a rigorous foundation, as I consider most of CT too dry.

[Anonymous No.14669071]

>>14668549
I'll assume you're talking about distributions in the context of PDE. Distributions enlarge the space of possible solutions to a PDE and are somehow the natural setting for PDEs. Often it is easier to derive a solution in a space of distributions and then, if the PDE is sufficiently well-behaved, show that the distributional solution does in fact correspond to a classical differentiable function.

[Anonymous No.14669112]

Is there a probability modeling system for predicting the likelihood of multiple events occurring together that defines a coordinate space where each axis represents a range of equally likely possible values for an individual event and each point in the space represents a valid state the system can be in such that the number of valid states for particular parallels, eg x=1 and x=2, represents relative likelihood since each x value has an equal likelihood of occurring?

So like only states ([1 2 3], 1, [2 3]) existing would mean all valid states are equally likely since all parallel x planes have the same number of states and the same goes for y and z, but (1,1,[2 3]) and (2,1,3) would mean (2,1,3) is twice as likely as the other two states since x=1 is equally likely as x=2 but the twice as many states for x=2 must share that probability?

I've basically half-assed this but I'm pretty sure it works and it seems like something that would already exist and if someone's developed it beyond what I've got working, I'd like to see it.

[Anonymous No.14669114]

Is there a probability modeling system for predicting the likelihood of multiple events occurring together that defines a coordinate space where each axis represents a range of equally likely possible values for an individual event and each point in the space represents a valid state the system can be in such that the number of valid states for particular parallels, eg x=1 and x=2, represents relative likelihood since each x value has an equal likelihood of occurring?

So like only states ([1 2 3], 1, [2 3]) existing would mean all valid states are equally likely since all parallel x planes have the same number of states and the same goes for y and z, but (1,1,[2 3]) and (2,1,3) would mean (2,1,3) is twice as likely as the other two states since x=1 is equally likely as x=2 but the twice as many states for x=1 must share that probability?

I've basically half-assed this but I'm pretty sure it works and it seems like something that would already exist and if someone's developed it beyond what I've got working, I'd like to see it.

[Anonymous No.14669253]

>be me
>wonder if there is always a prime (k) such that
>every substring of k's least significant digits are also prime
>confident that this sequence has infinitly many terms
>wonder if this sequence has infinitly many terms if k has n digits
>i.e. 2, 13, 113, 1223
> 2; 13, 3; 113, 13, 3; 1223, 223, 23, 3
>ok lets check oeis
>A127891 with 24 terms
>oh; pic related
What other questions can you ask about the original sequence?

[Anonymous No.14669285]

>>14656920
not him, but by "fruitful" I thought you meant providing rich in mathematical results. what video game programmers find useful is really not the same thing. But geometric algebra could be quite revolutionary in physics, particularly in electrodynamics. I haven't studied it yet, but it looks quite neat. I never really liked the Gibbs-vector approach.

[Anonymous No.14669304]

>>14668697
>That's not proven
It's very legitimately hypothesised, meaning you can't go "nothing infinite exists in the real world", which in any case has no bearing on the abstract world of mathematics

[Anonymous No.14669312]

>>14657024
can we chill out with the autism, thanks

[Anonymous No.14669319]

>>14669304
Doesn't matter, your axioms are clearly bogus and lead to so many paradoxes (Zeno, Banach-Tarski)
Math is much simpler and consistent (and beautiful) if you assume that the set of all numbers is finite (and, preferably, small enough to fit in our universe).

[Anonymous No.14669403]

>>14669253
Truncability depends on the base, so maybe see what happens in like base-37?

[Anonymous No.14669423]

>>14669319
>zeno's "paradox"
I knew finitards were undergrads, but highschoolers too?

[Anonymous No.14669458]

>>14669423
Math needn't ignore the real world, and I guess you don't consider finite-fields "real mathematics"
>ignores banach-tarskii
>laughs at zeno
At your peril.

[Anonymous No.14669524]

>Recently start getting very interested in math only after finishing engineering bachelors

I'm full of regret for not majoring in math, it's so much more fun now that I'm studying in my own time. I can't really justify spending more time on it anyway since it doesn't appear to be immediately beneficial in my career or field, most of the career development seems to be training myself to become a code monkey. The boat has sailed unfortunately. I don't think I can do a masters or it would even be wise to since I've only had engineering level math and have been working for a few years.

[Anonymous No.14669550]

>>14669304
Your brain exists in the real world and is literally what you do mathematics with. Why do you guys say stuff like this?

[Anonymous No.14669557]

>>14669550
>which in any case has no bearing on the abstract world of mathematics
to be specific

[Anonymous No.14669653]

When we enumerate decimal expansions of the reals and a diagonalization argument shows up, is there any proof that the diagonalization constructed numbers actually exist?

[Anonymous No.14669804]

>>14669653
Yes, it’s a convergent Cauchy sequence and therefore a real number. A diagonalization produces a sufficient description of a real number.

[Anonymous No.14669886]

>>14669458
Abstraction

[Anonymous No.14669891]

>>14669804
But by way of analogy to the paradoxes in naive set theory, are there convergent cauchy sequences that turn out to be inconsistent with whatever axioms you're using?

[Anonymous No.14669903]

>>14640814
Akshually...

[Anonymous No.14669954]

>>14669903
There are only five distinct partitions of 4
4 = 3 + 1 = 2 + 2 = 2 + 1 + 1 = 1 + 1 + 1 + 1

[Anonymous No.14670059]

Is quiver representations worth learning?
What are it's uses in math in Current Year?

[Anonymous No.14670133]

>>14670059
Mathematical physics and derived geometry

[Anonymous No.14670159]

>>14670133
oh rly? Could you give some pointers where i can read more?

[Anonymous No.14670212]

>>14669903
There doesn't seem to be any natural partial order here.

[Anonymous No.14670266]

I've almost finished Spivak, do I go to a multivariable book or do I start on analysis? If I go the analysis route will I miss out on important multivariable calculus topics?

[Anonymous No.14670397]

Ultra noob here. Where can one make a good start in learning fundamentals of mathematics?

[Anonymous No.14670443]

>>14670397
The fundamentals that underlie how math works are not yet completely understood and are still under active research today.

[Anonymous No.14670480]

>>14670443
Okay then, where should I start with mathematics? No complex long answer, just links to some jewish courses that I could pirate.

[Anonymous No.14670600]

>>14670480

[Anonymous No.14670680]

>>14670600

[Anonymous No.14670713]

Hey I know you guys hate faggot undergrad posts, but I just got a 100 on Series, sequences, and power series exam and I wanted to tell someone.
If Calc II is the filter course, well its really easy I have no idea how anyone fails this or gets under an A.

[Anonymous No.14671080]

>>14670713
Based. You just proved that you're not retarded.

[Anonymous No.14671595]

>>14670713
At least you're honest about being an undergrad, and on your way to not be it anymore.
The bad undergrad posts are like "hey how are the integers infinite, 3000 years into my phd btw"