/sci/ - Science & Math

fuck maths

Why do sneedposters avoid the generals? Are we just lucky?

>>14671258
Formerly fortunate.

I love maths

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°.

>>14670971
why are French so arrogant?
The man in OP is a perfect example, not rating Weyl
see: page 200 of https://link.springer.com/book/10.1007/978-0-387-79715-1

>>14670971
Any recommendation for good machine learning text or papers?

>>14671846
Not math

>>14671482
70m

>>14671695
>Goro Shimura
>French

Autism

>>14671989
Anon postingos with anime girls are gay

How exactly should I go about learning Mathematics? My current strategy is to read through a section, try and make sense of everything covered within the first sitting, and then move onto the problem set (I rarely ever do the problem set after I finish the section; I tend to put it off or not do it entirely). Problem is, after I move on, I forget what had been covered. I don't think it's an issue of understanding it-not being able it memorize what had been covered because I don't understand it. I think it's because I don't go over it for a long period of time-until it comes up in a later chapter.

So my question to you is: how should I study? Or rather, how do you study? Keep in mind that I'm a Maths pleb at the moment. I've been covering Algebra and Trigonometry. Should I just blitz through the texts, move onto Calculus, and then look back through the texts and what I've written during the relevant sections? is my issue simply the fact that I don't put what I learn to use and therefore forget it?

>tl;dr: How do I study Maths?

Is there a non-wikipedia online math dictionary that has definitions for terms used in commutative algebra?

>>14672056
OpenStax

>>14671846
Check out ak on twitter, and just lurk

Google AI has some good ones. Industry papers are good

If you're trying to learn ml, just learn from first principles

>>14672056
>Follow tree
>Find random YouTube videos (3b1b, mit open course ware)
>Learn *the essence* of the material
>Do practice test without a timer, derive all the formulas while doing it. Think.
>Don't bother with practicing computation. Derive the computational path, then get a computer to compute it for you.
>Attempt to formulate proofs through learning things

Good luck

It's boredSWE anon again

Background
>Learning math from ground up
>CS degree, industry professional

Update
>week 1 of learning math
>Started with linear algebra
>Started with Gilbert Strang's MIT open course
>Shifted over to 3b1b's essence of lin alg halfway

Everything clicked this past week. I'm fairly confident I could pass an exam now. I've got some tests set up, and I'll give them a shot in a week after reviewing the material

The laws behind linear algebra are quite astounding. I never "got" the intuition behind it in university, and to that, I blame the mediocrity of my professor at the time.

>>14639143
Thank you, very cool

>>14672056
Other anons are giving advice that I think is dumbass, considering you said you're studying algebra and trig.
Math is not a spectator sport: if you just read it, you won't retain shit; you learn by doing practice problems.The section is just there to get you up to being able to do the problem sets. So, take notes while you read (this should be your obvious first step for almost anything, btw), and do practice problems. Let's repeat that: DO THE PROBLEM SETS. If you run out, do more of them. Every few chapters, consider digging up a practice test online or something.
If you actually practice enough, then at this stage I doubt forgetting should be too much of an issue; high-school level math (which is what this is, of course) builds on itself cumulatively, because this is still the basics (and that's pretty much true up through Calc).
As a more general note: lots of people just memorize things to pass math. This is usually a bad idea; you won't retain it, and you're not actually learning anything. There's some things you gotta memorize, but you should be able to derive a lot of the formulas and such on your own from first principles.
Oh, and since you mentioned it: please don't try to sprint to calc. You need basic algebra and trig to do calc. That should be obvious. More to the point, in my experience, the biggest reason people fail Calc II (aka integrals, applications, basic sequences/series, basic diffeqs) is because they're not rock-solid on their fundamentals; likewise Calc I except people muddle through (which hurts them in the long run).

>>14672145
It's too big though. Got a simple version?

>>14672180
Solid advice. Thanks, anon.

>>14670971
Maths is garbage disconnected from reality.
Play chess instead, at least you can enjoy pwning scrubs.

>>14671482
that sounds super unsafe
>>14672021
spivak was some kind of tranny-lover, and his book covers always fall of
>>14672107
>calculus
>analysis
>fourier transform
Most of the terms on this flowchart are pretty ambiguous. Easier just to follow a university course-catalog where they describe the syllabus and list prereqs

>>14672099
>>14672107
>>14672136
kill yourself

>>14672069
https://stacks.math.columbia.edu/tag/00AO

Or just a textbook with an index on the back

>>14672099
Thanks anon. Also, what is AK twitter? I just took a ml class and want to learn more about it, but I think you are right on learning from first principles.

>>14670971
Will you be so kind to give me recommendations for books?
I am looking for exercise centered books with solutions, you know you learn by making mistakes but in maths with mistakes I don't get a solution at all so I need extensive solution pathways, in the topics Topology and Number Theory, I have heard american math education is shit but I guess this is only in primary school and not always there as well obviously, so if you are so kind you can also recommend me german books.

Pic medium related, I like Noether's Theorem

why is quantum information so much more interesting thatn quantum mechanics?

just found out that m is BEFORE n in the alphabet

awkward

>>14672781
I like it because it's mostly just linear algebra and it's very fun to work with. QI might be mathematically the cleanest and most straightforward physical theory. I don't understand why more people who do matrix / functional analysis etc. don't jump onto the QI bandwagon, your papers get cited 1000x more if you replace "positive operator" with "quantum state"

>>14672762
Which one? The normalization theorem?

>>14672056
Nah, just reading the material and skipping the exercises isn't going to be enough.
>>14672180
has the right idea.
You are forgetting the material because you are skipping the exercises. Hoping to memorize the general premise isn't the same as putting the work in. Might as well learn an instrument by flipping through sheet music.
Are you taking any notes when you read a section? Just writing it down can make a huge difference in learning the material.
Blitzing through the texts is wrong. Your algebra and trig need to be strong because calculus operations use them extensively.
If you zoom through it, you will find yourself in the terrible trap of trying to learn algebra, trig, and calculus all at the same time. That doesn't work.

>>14672821

>>14671989
Goro talks about the French mathematician Weil and also rags on Harish-Chandra too in that book

https://math.stackexchange.com/questions/736667/proving-the-division-algorithm-using-induction

How do you prove the case for m<0 here? If we assume it holds up till - m, we have that -m=qn+r. So -m-1 = qn+r-1. Either r-1>=0, in which case we are done, or r-1<0, in which case r=0 because r>=0. So -m=qn. How to proceed?

>>14670971
>>14672762
Why the fuck whole 4chan like similar memes?

The guy in the OP was the brother Simone Weil and he gets shilled on /lit/. Noerher was a based sperg femcel and she also gets shilled on /lit/.

4chan's intellectual taste is really homogenous.

>>14672762
>I like Noether's Theorem
Olver's "Applications of Lie Groups to Differential Equations"

>>14673128
>https://math.stackexchange.com/questions/736667/proving-the-division-algorithm-using-induction
Read the accepted answer more carefully. The m<0 case isn't done by induction, it's done by turning it into m = (-q-1)n + (n-r) (or -qn); eg 5 = 3*1+2, so -5 = 3*(-2)+1. You prove it for alll m>=0 and then turn all m<0 into cases of m>=0.

Redpill me on adjoint functors

>>14673363
What spergy pseud unironically talks about math on /lit/?

>>14673796
something something all i remember is that a sheaf from a presheaf is the left adjoint to the inclusion functor from the subcategory of sheaves to the category of presheaves. Might just be me but constructing the Etale space made more sense visually.

>>14673804
Some fags shill Bourbaki. Andre Weil was interested in Dharmic religions so there's that. Noether's case is pretty straightforward, based autistic femcel who never married.

>>14670971
I'm currently reading Hatchers algebraic topoloogy, he defines the barycentric subdivision opperator for linear chains S inductivly by [math] S(\sigma) = b_{\lambda}(S \partial \sigma) [/math], where [math] b_{\lambda} [/math] is the barycenter homomorphism.
But wouldn't we just get
[math] b_{\lambda}(S \partial \sigma) = b_{\lambda}^2(S \partial^2 \sigma) = 0 [/math]?

>>14673564
i don't get why this should be necessary

Red pill me on Cp theory

>>14674082
You gotta start with C_2 theory

>>14674082
>The first volume, Topological and Function Spaces © 2011, provided an introduction from scratch to Cp-theory and general topology, preparing the reader for a professional understanding of Cp-theory in the last section of its main text. The second volume, Special Features of Function Spaces © 2014, continued from the first, giving reasonably complete coverage of Cp-theory, systematically introducing each of the major topics and providing 500 carefully selected problems and exercises with complete solutions. This third volume is self-contained and works in tandem with the other two, containing five hundred carefully selected problems and solutions. It can also be considered as an introduction to advanced set theory and descriptive set theory, presenting diverse topics of the theory of function spaces with the topology of point wise convergence, or Cp-theory which exists at the intersection of topological algebra, functional analysis and general topology.

Thoughts on the Encyclopedia of Mathematical Sciences books?

>>14674082
>cp

BOB... SAGET!

>>14672762
enumerative combinatorics by stanley

>>14635314
Anyone figure out tensors yet?

>>14670971
To the zoomers taking classes in a university:
How do you write fraktur style characters, like \mathfrak{g} on your lecture notes?
I'm reading stuff on Lie groups for fun, and I'm wondering what's the convention for the fraktur style in handwriting.

Calc book: Loomis or Piskunov or Steenrod or Zorich or Adams&Essex?

>>14676444
Loomis is excellent but very advanced and has a shitton of exercises, many of which aren't trivial in the slightest. Great if you already know some calculus. I haven't read the rest you have posted but Courant would have to be my favorite elementary Calc book.

>>14676444
Zorich is amazing. It covers 99% of the stuff Rudin covers but is largely much more comprehensive with even a second volume. Rudin still has excellent problems, though.

>>14673877
Pls help.

>>14673708
But can you do the m<0 cases by induction too? Why/why not?

>book is called "Basic Algebra"
>read it
>it's not basic at all
Why is this allowed?

>>14673877
>>14676835
you should read tom Dieck instead

>>14676318
>handwritten fraktur
The standard is a highly autistic, extinct German cursive style: https://en.wikipedia.org/wiki/S%C3%BCtterlin
Here the G looks like normal minuscule printed g except the downward stroke is more to the right of the round part

why is studying math and physics torture?

are all physical phenomena/systems model-able with effectively calculable functions? I dont think they are. Some things in the universe can't be computed by any turing machine, I think. What do you think anons?

Whats the most useful, well-written book on a quite advanced topic you have worked through? By that I mean a book that takes a really difficult subject but the pedagogy is so good that you dont feel retarded.

For example. pic related has no business being as good as it is. Criminally underrated book imo.

Does anybody have recommendations for an introductory group theory book that is focused on finite groups, for someone who doesn't know anything beyond the definition of a group. Preferably with lots of problems, and *roff or *tex typesetting.

>>14677783
For the record, I tried Serre's book and got filtered.

>>14677815
Specifically, I am interested in enumeration of finite groups. I have the book of the same name by Blackburn, Neumann, Venkataraman
But it filtered me much harder than Serre's book

>>14677840
I'd find an easier textbook to learn group theory, then return to your topic-focused book if you're still specifically interested in the problem of enumeration; from a brief google, your book is graduate-level, so an undergrad group theory textbook into your book should be a good progression. For recs, I don't know enough about the field as a whole desu, but I really like Painter's A Book Of Abstract Algebra -- gentle intro, but covers a lot of ground (and the second half is ring theory culminating in basic Galois theory; some basic ring theory would be a good addition for you, especially since your enumeration textbook mentions module theory).

>>14678232
*Pinter

>>14677596
Bott Tu Differential Forms in Algebraic Topology.

>>14677547
Because of poorly written textbooks

Going through linear algebra done right. Saw that the Hadamard product is not useful "based on experience".

My intuition on why the Hadamard product definition is not useful. It's not as generalizable as other vector to vector operations because it relies on the choice of basis for the vector space.

This means if you move the origin around, the Hadamard product will change. This makes it not have some of the properties that are transitive across domains.

Is this a correct intuition? Am I getting more to the core of math? Is it more about finding generalizable truths to things that have a certain structure, and demarcating them as that generalizablility has a lot of utility?

>>14670971
Do you want to make your function g smooth?
Use the famous mollifier trick. Just write f_eps * g with writing star. You need to update the parameter eps or do grid search for the best result.

I am sick of this bullshit.

If I was trying to calculate the probability of a sequence of numbers (say 1, 2, 3) in any combination, while picking numbers at random (0-9), what would the setup/formula look like? How would I approach this? Does n! / (n-r)! cover this case? Or nCr = n! / ((n - r)! r!)?

>>14680226
It's just 1/10 for every member of the sequence.

>In mathematics, the order of a finite group is the number of its elements. If a group is not finite, one says that its order is infinite. The order of an element of a group (also called period length or period) is the order of the subgroup generated by the element. If the group operation is denoted as a multiplication, the order of an element a of a group, is thus the smallest positive integer m such that am = e, where e denotes the identity element of the group, and am denotes the product of m copies of a. If no such m exists, the order of a is infinite.
>The order of a group G is denoted by ord(G) or |G|, and the order of an element a is denoted by ord(a) or |a|
So in group theory, order means cardinality of the underlying set and period of an element in the underlying set.
Why are group theorists so retarded, just use the original names and don't name 2 very different things the same thing, this isn't difficult.

>>14680388
Really? I thought it would be something like 1/10 for 1, then 1/9 for the 2, then 1/8 for the 3. etc. Wasn't sure if that accounted for the permutations of not though.

t. brainlet

>>14680508
That would only be the case if you removed a number from your choices after each selection.

>>14680515
Ah, right. Would it not be the reverse then? A 1, 2 or 3 are valid for the first number, so 3/10, then say only a 2, or 3 are valid for the second number, so 2/10, then say only the 3 is valid for the third number, so 1/10? The initial order wouldn't matter, but the sequence (in any order) would require those 3 numbers to appear, so I thought the chance had to decrease each time.

>>14680531
If you dont care about order 10C3 if you care about order 10P3

>>14680434
>order of group
>order of (subgroup generated by) an element
>2 very different things
Wait until you find out about lattices anon

>>14680535
Thanks

>>14680604
>NOOOOOOOO THESE 2 DIFFERENT THINGS SHOULD BE CALLED THE SAME THING BECAUSE OF X
I should have inb4 because I knew some faggot was going to say something like this.

>>14680535
One last thing, how would you modify this to apply to different set lengths? i.e. probability of 123 appearing in sequence in a set that's 5 digits long, 10 digits long, etc.

>>14679667
The usual matrix product is useful in a number of common interpretations of what a matrix is, e.g.
>if they represent linear transformations, then the product is composition of functions
>if they represent number of ways to get from node i to node j in 1 step, then the product represents the number of ways to get from i to j in 2 steps
On the other hand, I don't know of anything real that the Hadamard product could represent except literally "here is a list of numbers and I want to multiply them like it's an excel spreadsheet" which is fine but doesn't really need its own separate branch of abstract mathematics does it?

>>14670971
>He can't do a 3rd order binomial expansion by heart.
Ngmi anon.

>>14670971
let's say the following is true
[math]\frac{a}{x} = \frac{b}{y}[/math]
if I turn them upside down, would it still be true?
[math]\frac{x}{a} = \frac{y}{b}[/math]

>>14681033
Yes for all complex a, b, x, y. as 0 = a , 0 = b will give vacuously true statements.

>>14681033
assuming ur shit comes from a field then yeah

>>14681091
forgot to add
[math]a, b, x, y \in \{1,2,3,\cdots\}[/math]

>>14681113
what field?

>>14677596
Calculus reordered. Worked out Taylor Series using that book with Finite Calculus. Changed my view forever

>>14681125
Same author wrote this. I'm liking it alot so far, anyone else read any of his books?

>>14681119
It is true in all fields. Do you know what a field is?

>>14681219
>science is not my field = can't into science
>math is not my field = can't into math
>chemistry is not my field = can't into chemistry
>sowing seeds in a field
so, what kind of field are we talking about here. dumbass?

>>14681243
Lol

>>14681115
Define [math]\frac{a}{x}[/math]

>>14681255
a, b, x and y are any number greater than zero that satisfy the following rule
[math]\frac{a}{x} = \frac{b}{y}[/math]

Might as well post an old Olympiad question I never found the answer to in case a genius is creeping around here.

Do there exist three right angled triangles A,B,C on the same hypotenuse, with natural side lengths, such that:

Area(A) + Area(B) = Area(C) ?

>>14681280
You didn't answer my question
Is this an acceptable definition
For
[math]
a, x \in \{1,2,3,\ldots \}, \dfrac{a}{x}
[/math] is [math] (a,x) \in \{1,2,3,\ldots \} \times \{1,2,3,\ldots\}
[/math]
Such that,
[math]
\dfrac{a}{x} * x = a.
[/math]
If that's what you mean, then your implication >>14681033 holds.

>>14672781
you're a pseud

>>14681393
a, b, x and y all have different values, obviously
[math]a \neq b, a \neq x, a \neq y, b \neq x, b \neq y, x \neq y
[/math]

>>14681459
Why? Why are you artificially limiting your theorem, it's true for all fields, and you decide to limit it to naturals and non-equal variables. Of course limiting a true theorem will still be true, If all apples are red or green then all apples are red is true.

>>14681243
Jesus do you know any abstract algebra at all, even the most basic stuff?

Field, definition:
Any commutative ring with the following properties: 0 [math]\neq[/math] 1, all nonzero elements have an inverse.

https://www.youtube.com/watch?v=iSNsgj1OCLA
(From 6:68)
Can anyone explain why the probability that there could be a loop of length 100 is 1/100?
I feel like the result is correct but he just skipped a bunch of steps so his explanation is not quite there.

>>14682174
Total number of permutations: 100!
Number of loops: 100!/100
P = number of loops / total number of permutations

>>14682199
But not every permutations in the 100! would result in a 100-length loop?
For example, if I have only 5 boxes 1 to 5, and the permutation is, 2 3 1 5 4, this creates two loops, 1 loop from box 1(2) to box 3(1), and another loop between box 4 and 5, no?

What is the justification for the notation [math]\mathbb{Z} / n \mathbb{Z}[/math]? Why not just use Z/n?

Help! I'm trying to prove that there are two *unique* complex numbers such that a * b = 1

Does this "proof" seem correct?

>>14683166
Show that 1/a has a unique solution b

>>14680608
The point is that you don't want to write "subgroup generated by" every time you talk about the order of an element. You lose a tiny bit of readability by overloading your notation, but make up for it with the extra convenience.

>>14683052
It's general notation for a quotient group.
https://en.wikipedia.org/wiki/Quotient_group

>>14683052
Because Z, /, and nZ are all meaningful concepts in the construction of this particular field. nZ are the multiples of n (an ideal), / is quotient and Z is obviously the integers. If it was just Z over n it would be confusing.

>>14683189
thanks. I'm new to doing proofs, and proving things I've taken as axiomatic has been a learning process

>inb4 you haven't proven [math] (a \cdot c) \cdot b = a \cdot (b \cdot c) [/math]

>>14683591
I guess you could prove this "geometrically" by showing that [math] y = 1\x[\math] never touches 0 at the limit, meaning there is never more than one solution x for a given y?

>>14683591
These properties you're proving are the properties that define a field. You can use that to remember them:
https://mathworld.wolfram.com/FieldAxioms.html

>>14683605
Thank you! Yes, I'm doing these exercises out of "linear algebra done right". I know that I can pretty much skip these exercises, but I'm finding it surprising how difficult some of the proofs are to do after so long after my undergrad, so I'm making it a point to work through these.

I need to go through the proofs section on
https://www.whitman.edu/mathematics/higher_math_online/

>>14683619
I recommend reading Velleman's how to prove it if you are into books.
Also for your exercise, just use the followings strategy (if you are still working on your exercise):
Assume that there are two numbers satisfying the equation: [math]\beta_1, \beta_2: \alpha\beta_1 = \alpha\beta_2 = 1[/math], just prove that [math]\beta_1 = \beta_2[/math].

Where were you when the cross product was deboonked? https://www.researchgate.net/publication/361388725_The_product_rule_cross_product_disparity

>>14670971
Does anyone see why (A.8) is true?

>>14683991
Grassmann refuted it retroactively.

>>14683991
wtf is this gibberish
why is this on researchgate? Didn't know it was vixra-tier

>>14683991
>conclusion
>"it's just stupid"
great paper, kek

>>14683991
6 MILLION JEWS FALSIFIES THE HOLOCAUST

>differntial geometry
>algebraic number theory
>seminar on algebraic curves
>functional analysis
>japanese 2
and what are you taking next semester anon?

Is this true, mathbros?
>>14684268
>>14684271

>>14684258
>>japanese 2
kys

>>14676984
These books refer to math students, not the general public dumbass

>>14680631
Here's something that I think might help
https://stackoverflow.com/questions/6790620/probability-of-3-character-string-appearing-in-a-randomly-generated-password

bros how much field/Galois theory do i need to know in order to get my feet wet with algebraic number theory? i've been reading KConrad's stuff, so far i know the basics of finite/algebraic extensions, existence/uniqueness of splitting fields and algebraic closures, a little separability and normality (primitive element theorem), equivalent conditions for when a finite extension is Galois, linear independence of characters, a little on the trace/norm, and i have yet to read about cyclotomic fields. is this enough?

>>14684258
Finished with all the required courses. I'm currently writing my thesis. Thesis writing fucking sucks except for the part of learning about new shit by studying papers, but even then there's a lot of shit you have to go through even though they are not necessary because some uptight old professor may quiz you on during the defense.

>>14684282
You can derive the existence and invariation of angular momentum from the Lagrangian's invariation under rotations and Noether's theorem, yes.
So he's at least broadly correct, but I'm not reading all of that to check for mistakes.

>>14670971
Here is some maths that you retards can’t defeat but are too chickenshit to face up to:
http://www.baur-research.com/Physics/MPS.pdf

>>14684863
>not in [math]\LaTeX[/math]
don't care

>>14684880
Fuck off formattist pice if shit.

>>14684884
If you can't format your math in [math]\LaTeX[/math], I won't speak to you nor engage with your garbage. I will now filter you.

>>14684889
Fuck off you ignorant moron. You can’t defeat my paper so you run away with your tail between your legs faggot. Fuck off.

Is this a good intro book for mathematicians who want to get into physics?

>>14684909
Nope, it is an angular momentum conservers bible. Which is one step below a flat earther

>>14684911
you're like a dog licking its arse in public: lacking self-awareness

>>14684911
angular momentum isn't even mentioned once in the book though?

>>14684919
That does not mean it is not assumed. Asshole. If the book has any maths that is advanced beyond 350 years ago, then it is infected.

>>14684924
lol so what do you recommend I read? Galileo?

>>14684929
I recommend you read this and open your mind to the revolution: http://www.baur-research.com/Physics/

>>14684909
>just links the whole heckin pdf

>>14684915
I present truth and you insult me in evasion of the truth which makes you the retard licking his ass instead of learning something uselful.

>>14684935
I want a book though.

>>14684941
Well all modern books are infected with this idiotic nonsense, so go ahead and read bullshit if that turn you on retard.

>>14684949
So I should read an old book? Which one? Tell me already.

>>14684952
No, you should read this. http://www.baur-research.com/Physics/MPS.pdf
Then acknowledge that since you can’t falsify the maths, that 12000 rpm does objectively falsify COAM because it does not happen in reality and so by the scientific method the theory must be rejected. Then recognize that this is a historical moment in human existence.

>>14684936
and I'll do it again

>>14684976
And I’ll do it again. http://www.baur-research.com/Physics/MPS.pdf

>>14684968
Can you read? I want a book.

>>14684019
Research gate is the same shit as arxiv except that you also have a profile lile a facebook account.

>>14684980
Nope. Arxiv is the repository of unpublishable academic papers. ResearchGate is a place for researchers to hang out.

>>14684978
here's the second one

>>14684987
You circular fuckjng retard.

>>14684019
here's another one https://www.researchgate.net/publication/357345132_SQUARE_SUB_ONE_PAPER_SECUREpdf

>>14684993
What? Don't like Zorich?

>>14684589
Read until you’re completely comfortable. ANT is no joke.

>>14685000
We had our Calculus I and II courses taken from Zorich back in my first year in uni. I thank however picked it for helping me instill really solid fundamentals. Really fond memories despite being tough.
Unfortunately, only 27% passed the course and the leftist student committee cried about it until they reverted to Spivak.

Consensus on Gorodentsev's books?

>>14684589
hello anon

>>14684863
ever heard of friction?

>>14684924
>Gauss is le bad
>Euler is le bad

>>14685099
Ever heard of centuries old mainstream well established demonstration using referenced equations which assume that friction is negligible and you try to shift the goalposts after the fact retard. My proof that physics is wrong is wrong because physics is wrong. Stupid defeated fuck.

>>14685072
>le doxx
yes, i'm on reddit, now what?

Is it viable to finish or even start a graduate degree without having read Munkres? My advisor says that any other intro to the topic is inferior.

>>14685117
>physics is wrong is wrong because physics is wrong
retard, speak english

>>14685123
you have to let asoiaf go
its never coming out and you know it

>>14685124
research COAM

>>14685127
i'm cautiously optimistic for Winds, but Dreams is never coming out. i just hope he writes a couple of Dunk&Egg stories, i really like those

>>14685117
What the fuck are you saying.

>>14685126
I am speaking English you retarded fuck.
The claim that is being made against my work is literally that my proof that physics is wrong is wrong because physics is wrong which is fucking insane. Am I allowed to point out that the argument is literally stupid. You dumb fuck.

>>14685124
i don't know about viability, but it's honestly an exemplary textbook, you should check it out. i've only read a couple of chapters on coverings, but they're what made the topic click for me, i expect the rest of it is just as good
>>14685132
>research COAM
>t. Baron Harkonnen

>>14685141
I am saying - fuck it. Read rebuttal 9 asshole. https://www.researchgate.net/publication/357302312_Rebuttals

>>14685154
Try to calmly put your thoughts into words before posting. Nobody understands you.

>>14685163
Is “rebuttal 9” difficult to understand you ignorant cunt.

>>14685186
Elaborate on it.

>>14684909
>just links the whole pdf
based

Not using latex to discuss advanced math is like typing words without spacing:

itfuckingsucksanditbecomeshugelydifficulttounderstandlikewhatkindofretarddoyouhavetobetothinkthisisfine

>>14684282
wtf is this thread

>>14684909
No. Just learn physics like a physicist.

I once heard an anon here say it's better to read up on predicate logic than to read a proof book to "get" proofs. I was wondering if Simpson's "Mathematical Logic" would be a good one to read. It's only 100 pages

Everyone check out
>>14685659

>>14670971
Alright...to both sides of the COAM debate, please
continue the arguments to the nearest physics
thread or a separate thread (unless there's an
important math issue to bring up). Thank you.

>>14684258
Model Theory
Category Theory
Lambda Calculus and Type Theroy
Principles of Programming Languages
Advanced Complexity Theory
Computational Game Theory
Categorical Quantum Computing

>>14685462
Just looked at the contents, looks perfect for a first intro to logic will cover precisely what all mathematicians should know (sadly the reality is that few mathematicians really know anything about the foundations of their subject!)

guys i'm too afraid to come out to my supervisor but i recently found out that i'm a constructivist

what can math majors even place on their resume? other than coding projects that is

>>14686633
I don't even have a resume and I got an industry job.

>>14686030
How long have you known that you're a
constructivist and how did it came to you?

>paper got rejected by the editors
feels bad man

>>14684909
>>14684976
Wait when did they allow you to upload PDFs on 4chan?

Dae not understand why representations are interesting? I understand the concept, but I don't get what information we are getting about a group by studying it's representations.

>>14687402
Depends on the board

The more I study math (either college or by myself) the less I enjoy it
What should I do?

>>14687474
What have you studied?
I loathed math when I was an undergrad because of too many homework and assignments, but I only started to like it when I study it at my own leisure and study subjects I find intriguing.

>>14687482
Math was not my favorite discipline during school but it was the easiest one for me.
I tried an engineering course at my college but in the first semester I realised how much I suck at physics and chemistry.
Then I switched to a math teaching course (there is no math only course around here) and I have been doing alright so far. I enjoyed disciplines like number theory and combinatorics, but stuff like linear algebra and statistics are a chore.
I still enjoy solving geometry puzzles and whatever but the more I learn about math philosophy the less I enjoy it, and I feel less confident about doing math than before I got into college, not sure if I'm fit to be a teacher.

Is there an agreed upon notation for the set created by composition of the Cayley-Dickinson construction n times? CD_1 = complex numbers, CD_2 = quaternions, CD_3 = octonions etc

So tell me /mg/, which is the demonstration you are more proud of?
For me it is picrel, is not even hard but i did it in my second semester when i had zero experience in writing formal proofs and felt great when i got a perfect score in that question.

>>14687520
Don't be a teacher unless you are going to teach in a good college.
The pay just sucks in general.

>>14687613
I remember Fred Cohen having a paper where he looked at the proportion of zero divisors in these as n goes to infinity, so you might check there.

>>14687899
[math]\mathbb{A}_n = \mathbb{R}^{2^n} [/math]

Is it possible to ‘extend’ the Lebesgue integral to work with stochastic processes similar to how the Ito integral is meant to be an extension of the Riemann-Stieltjes integral? Would such an integral even be applicable to more things than the Ito Integral?

>>14688017
What's the Ito Integral applicable to?

>wolfram student project on traversing 3D automatons and trying to figure em out
They're blatantly hypercubes

>>14688017
Damn, your question is really interesting, though I have no idea the answer. Just learned the Lebesgue integral myself.

Principia is largely obsolescent. Much of the text is dedicated to notations now surplanted by new construction techniques.
For instance there's a large amount of "code duplication" in that they have all the axioms for set operations and then identical axioms for relations. This happens a few times.
In modern mathematics, relations are just sets of ordered pairs, which eliminates this duplication.
Additionally the interest in this kind of 'axiomatic foundation' has kind of waned with the advent of proof theory and model theory which allows rigorous study of arbitrary first-order logic systems.

>>14688034
So the Ito integral is applicable to things such as Semimartingales eg Brownian Motion. the real key requirement is they have bounded quadratic variation but they are allowed to have unbounded variation which is why these traditionally can’t be used with Riemann or Lebesgue integrals. My line of thought was what if you had a “random” version of the Dirichlet function where instead of f(x) = 1 when x is rational and f(x) = 0 elsewhere, f(x) was say a Normally distributed random variable with mean 0 and variance x when x is rational and f(x) = 0 elsewhere. I suspect this is actually still Ito Integrable even though the traditional Dirichlet function is one of those examples of a Lebesgue but not Riemann integrable function.

>>14688083
Interesting

>>14688083
>can you take the sum of random numbers
yes, but what do you gain from this?

let's say I have a function called lcm() that will calculate the lowest common multiple which takes two inputs
what if I have three inputs, will this work?
[math]lcm(lcm(x,y),z)[/math]

Can I get a quick rundown on spinors? I know what tensors and tensor fields are but I skimmed through the spinor wikipedia page and couldn't grasp it. Do I need symplectic geometry? I only know Riemannian/pseudo-Riemannian stuff

>>14688593
The spin group double covers [math]SO(n)[/math] (ignoring the details for a second).
Sometimes, you can give a manifold a spin group structure (a spin structure) and use the spinor group's spinor representation to construct a vector bundle on the manifold (the spinor bundle). Sections of the spinor bundle are spinor fields.
Spinor fields have different transformation behavior compared to vector and tensor fields, which is why physicists usually need them.

which one /mg/
>if ... satisfies the equivalent conditions...
or
>if ... satisfies any of the equivalent conditions...

>>14688763
the latter

>>14688555
Yes, this will actually work provided none of the inputs are 0.Also should be true in the general case when you've got n inputs and the inside lcm function takes the first n-1 inputs.

>>14688593
You don't need symplectic geometry to understand spinors. You just need to have a good understanding of Clifford algebras. Perhaps start with geometric algebra to gain better intuition.

>>14681125
>Worked out Taylor Series using that book with Finite Calculus
Like sequence rules calculated with the rising factorial basis?

>>14687963
[math]\mathbb{C} \ncong \mathbb{R}^2[/math]

>>14688100
That pic looks refreshing. What are they?

>>14689088
Oh there he goes again, the guy who pushes geometric algebra on everyone even though barely anyone does it!

>>14688555
LCM is the join in the lattice of postive integers ordered by divisibility.

>>14688017
At least in the modern theory (last 50 years), the stochastic integral does not come from Riemann-Stieltjes integrals. It can be seen as a special continuous local martingale (actually this is usually extended to semi-martingales with jumps). In fact Riemann-Stieltjes dont really show up anywhere in probability for the same reason Riemann integrals dont show up. When "Stieltjes" integrals do show up they are Lebesgue-Stieltjes integrals. The stochastic integral just extends Lebesgue-Stieltjes integral in the way that you think it does.

The adjoint to the Malliavin derivative, also called the Skorokhod integral, extends the stochastic integral even further.

https://www.quora.com/How-can-one-prove-that-1-+-2-+-dots-+-n-2-1-3-+-2-3-+-dots-+-n-3-without-using-mathematical-induction#!n=12
kino proof right there

>>14689861
Read that recentlt in a Conway book

>>14689750
Ok thanks for the info, sounds like I must have misunderstood my lecturer all those years back when I did the stochastic analysis class.

By the way, is there any difference in terms of applicable functions/ processes for the Stratonovich Integral when compared to the Ito Integral? I assume these are a lot closer together than the Skorokhod one you mentioned.

>>14688748
>>14689088
Well my algebra is pretty damn weak, no wonder I was struggling. I never quite grasped special orthogonal/unitary groups so I guess I'll have to go back to those before I dive into spinors. Thanks lads

>>14684258
>taking classes to learn a language
What a waste of time.

>>14684863
This isn't math, it's experimental physics. You performed an experiment and the results disagrees with theory; now you publish methods, etc so others can ttry to replicate it and so on with the scientific method. Math is concerned with proof, not evidence.

>>14691803
Proof : geometry :: evidence : algebra

This isn't homework. I know all the definitions here, and I would be comfortable carrying out all these computations for any other problem. But I don't know where to start with this one. I am sure I'm missing some very simple observation.

For (a), just show linear independence. Can I divide both sides of the dependence relation by e^t? Can I somehow use the fact that e^t is nowhere 0? A similar question is up on MSE and folks said to take some constant values of t and solve the subsequent homog system. This makes no sense to me. Why would this work? Others said to use the Wronskian, but I'm supposed to only use elementary linear algebra.

For (b), am I supposed to manipulate the abstract operator, like how one would to find the char poly T(A)=A-A^T (take powers), or do I take the matrix of D wrt this basis A?

Where am I fucking in verifying Fubini's theorem? Isn't the integral supposed to be 0?

>>14692849
Could you further clarify the definition of your function in 1? If only x or y is rational is the function zero? And we are only verifying Fubini's theorem for Riemann-integrals, right?

>>14691646
Learning Japanese on your own is next to impossible, it isn't like other languages.

>>14692862
f(x,y) = 1/q whenever both x and y are rationals, and 1/q comes from x = p/q. Otherwise, f(x,y) = 0. And yes, this is using Riemann integrals

>>14684547
is it considered basic in maths class?

>>14692865
How the hell did you come to that conclusion? The process of language acquisition is 99% immersion and there is very little material that makes sense to be taught in a classroom setting. Even for a language like Japanese there is AT MOST a single semester of material that makes sense to be taught in a classroom setting. When one properly self studies they should be done learning kana, basic grammar, and a decent set of vocabulary (around 1000 of the most common words) within AT MOST only three months. From this point forward all that needs to be done is a massive amount of reading as well as listening and vocabulary study. It sounds to me that you think Japaneses is far harder than it actually is which is most likely a result of your teachers shitty teaching and shitty material. I wouldn't be surprised if your teacher is trying to do stuff like compare Japanese aspects of grammar to English or some other retarded shit. I don't understand how people become so misguided when it comes to acquiring languages, the process is incredibly simple.

>>14689483
It does. A Russian anon listed the flavors but I forgot to screenshot it

I've gotten started with 19.) a) twice now and both times I've gotten to a quadratic equation but solving that is only taught in the next part. Am I missing something or is that it?

I'm fine with not getting any hints I just wanna know if I'm missing something or if the book's pedagogy is wonky

>>14691646
a-atleast I get to talk to girls twice a week
but yeah I would be a lot faster if I learned on my own
for japanese you really have to grind hours and with 3 hours of classes a week (+ some homework etc.) it will take ages

>>14693035
japanese is objectively one of the hardest common languages to learn for a westerner
good reasons for a teacher/classroom are imo that they can spot your mistakes that you might overlook and that you get to train talking in person

>>14692849
Wait, I'm a retard. That's not the Dirichlet function, that's Thomae's function and it is integrable

>>14692849
>>14693150
Yes, the upper integral must be incorrect. It should be zero, but I don't know exactly what makes it different from the Dirichlet function in this regard.

>>14671258
They'll be on this one. I can tell the guy in Pic >>14670971 never did an ounce of hard labor his entire life and was a city slicker shuffured around in his fancy German car. Sneed lives in the country and supports farmers.

>>14689483
>>14693043
I know the first two, though(pear, grape). And I never had or
even seen a drink tasting like pine cones before.
Seems rough.

>>14692628
For (a) use the fundamental theorem of operators: [math]dim V = dim Range (D) + dim Ker(D)[/math]

>>14693095
Not sure if this is how they want you to do it, but: at x=2 (the smallest defined value), 0 < ~5.8. Thereafter, 2√x grows faster than √x which grows faster/about the same as √(x-2), so the left side will never "catch up" to the right side.

>>14693095
On that note, the intermediate value theorem is probably sueful for the ones where you *can* find a value. Also, you could solve it by squaring and so forth, but it's probably easier to just graph it and then come up with the proof afterwards

>mfw axler has a video series online going through his book

fucking incredible
what a time to be alive
picrel

>>14685661
Where will I be able to find the results?

>>14693558
oh yeah, that definitely makes sense. I have no idea what the book expects me to do here to be honest

Regarding the OP's title. What do varieties over finite fields look like?

>calculus II
>only two weeks to just barely cover one single type of differential equation and euler's method for vectors field
>"Wow this is the most amazing shit ever, you can make mathematical representations of FIELDS!?"
>immediately change of topic next week, quickly followed by end of course
>can't take diff eqn course until I finish calculus III and linear algebra

this is bullshit why even tease people like this, are you telling me I need to wait another year to get to what seems like the most interesting topic ever brought up?

>>14693744
Check out Serre's A Course in Arithmetic

>Statistic exam
>Some classmate does not how to do a trivial problem
>Since i had already finished my exam a pass him the answer
>Tell him not to copy exactly the same so the teacher doesn't notice.
>Copies exactly the same
>Teacher sent a message saying he will send a letter to my uni to annul my semester and the next one. So I will not be able to study for a year.

>>14694187
>what does this geometric object look like
>bro just check out this book on number theory that has zero pictures

>>14693744
It is instructive to consider the case of elliptic curves, as an example here is the elliptic curve [math] y^2+xy-x^3-100=0 [/math] over the finite field [math] \mathbb{Z}_{701} [/math]


As expected, its just a bunch of points. What they look like is not important, although yes they do in fact look like something.

>>14672180
>>14672810
So does this mean that I should go through Algebra and Trigonometry once more putting priority on doing challenging problem sets?

>>14691646
Unless you're taking a native speaker course, you're gonna be learning a watered-down version of that language-something that you'd use as a tourist or maybe for business. Native speaker courses also cover their curriculum far faster than any regular course, but that's a given.

>>14694257
I’ll have you know it at least includes diagrams of modular forms

I know this is a linear algebra question and not a differential geometry one, but I still don't fully understand why the trace equals contraction with [math]g^{-1}[/math]. I know how to prove it in local coordinates since [math] \mathrm{tr(Hess} f) = \mathrm{tr}(g^{-1}\mathrm{Hess}\ f g) [/math] but I feel like treating them as matrices is cheating even though it's not

>>14694257
Thanks. I remember pics like this. They use elliptic curve cryptography over finite fields in bitcoin, if I remember correctly.

I can't do this shit anymore, how am I supposed to learn all of first year graduate lie group theory in less than a week?

>>14693558
>>14693567
just figured it out.

if x is positive, then the left side is negative, and the sqrt(x) always yields a positive number

if x is negative, then sqrt(x) doesn't work without imaginary numbers

so no real number x satisfies the indicated relation

>>14695310
what is stopping you?

>>14694231
haha
applied nigger gets rekt

>>14694753
[math] \nabla df [/math] is a section of [math] T^*M \otimes T^*M [/math] so you use g to convert one of those factors into a [math] TM [/math] to get a section of [math] \text{End}(TM) [/math] and then take the trace of this thing.

Do tesseracts and quaternions have a known association?

>>14693648
You won't. There was 0 enthusiasm for the project and I'm not doing it alone. Maybe someone else will do something similar.

How do I unbrainlet myself? Today I took way to long for a trivial exercise about topological groups.

>>14673854
I've read Andre Weil's autobiography on the first half of his life and it is genuinely a fascinating life story even if you aren't interested in his mathematical work.

Why couldn't I become a brilliant mathematician? What am I lacking?

>>14695922
don't know about you, but I might not become a brilliant anything because I don't have the autism to keep going with something for 10-20+ years like the true GOATs usually do. don't know if that's a lack or just a normal feature

>>14695922
>What am I lacking?
Probably IQ. In the end, math is always about IQ.

>have trouble with combinatorics
>even elementary
what causes this?

>>14691646
That guy already knows Japanese 1 and English. He will know 3 languages after Japanese 2, and what will you know, anon?

Working through Tao's Analysis, and noticed the absurd lack of exercises. Not sure if this will end up becoming pernicious or not, so I would like to know where I could find more exercises. Both theoretical, and "applied" -- as in not proving a general theorem, but proving a particular sequence converges here.

>>14696371
ya cant go wrong with da baby

>>14696345
not that guy but I know so many languages that I feel like I would dox myself just by listing them. I'm pretty low on math knowledge though, but I'm working on it!

What do I do if I like the concepts of math but I hate the way it is explained or taught to the point it's intolerable?

>>14696505
you are under the severe danger of becoming a brainletism induced /sci/ schizophrenic
please consult professional help

>>14696505
I know that feel. Attending lectures in university made me lose all interest in math. It's awful how it's taught. It took me years to recover from this and now my interest is renewed and I'm reading about math for fun and blogging on /sci/ about it.

>>14696514
Thank you.

>>14696518
what do you mean?

>>14696525
>what do you mean?
huh?

>>14696540
could you elaborate?

>>14695842
You can form a 4D parralelliped using quaternions (should be a tesseract).

Is this basically equivalent to adding Hilbert's epsilon operator? It's from the proof of the completeness theorem in Enderton.

>>14696541
elaborate on what?

>>14696827
Why you say it's awful how it's taught. And what you find fun or blog about, if you want

>>14695496
So what you're saying is that the trace is defined for linear maps [math]TM \to TM[/math] instead of bilinear maps [math]TM \times TM[/math], and as such I need to go from the latter to the former using the canonical isomorphisms? So the metric only arises from applying the definition to the correct object? But then how come one sum where we only consider the diagonal terms equals the double sum with the metric? I think I agree with your argument but my question's less about the technical justification and more about the equality of the sums

>>14696879
Meant to say bilinear maps [math]TM\times TM \to \mathbb{R}[/math]

>>14695326
sqrt(x) yields negative solutions: (-3)^2 = 9 so -3 = sqrt(9)
you also screwed up the middle squaring, it's sqrt(x) = -(3x+11)/12
from there you can substitute y = x+2 and relate the last equation to the first

Hello friends, I'm in college, 23, started late for personal reasons but have always had an affinity for math, I also know how to program very well, better than most, however, I want to make math part of my life, I wonder if math could be like programming, taking on problems and challenges, be it from a project, exercises or some community effort and do it every day, but how would I even work on these things, how would I work on math like I practice piano or like I make a program?

>>14697621
as a bonus question, how do I find the type of math I like?

Hey guy, I'm taking Complex Analysis in the fall. What should I be reviewing these last couple weeks of summer?

>textbook has 20 chapters of undergraduate reminders and 4 chapters of actually relevant content
>those 4 chapters depend on notation and theorems hidden in the 20 first chapters
Fuck you i'm not playing your gay little hide and seek game

>>14697621
if i've understood your question correctly you are asking whether one can do math as a hobby. well you certainly can - you can simply pick up a book or lecture notes floating around on the internet and you just work through it. most textbooks at the undergraduate/beginning graduate level contain exercises you can work through. if what you are looking for are puzzle-like problems, then i guess you could look at contest math problems such as those from the Putnam competition. there are also textbooks which contain only problems, e.g. problems on combinatorics. every now and then anons share interesting problem on /sci/ too. as for community effort, other than /mg/ and /sqt/ threads there is also math.stackexchange which is the platform every student of mathematics uses at some point in their career.
>>14697622
>how do I find the type of math I like?
usually you would actually major in mathematics and take mathematics courses. if you are a hobbyist then you would explore books, such as those you find recommended here on /mg/ (which i dont recommend, too many memes from people who dont actually study) or math.stackexchange. a lot of uni courses put up their course webpage with syllabus, lecture notes and problem sets available to the public which is also very useful.

>>14697150
the book said that conventionally the square root denotes only the positive number whose square is x, I was following that.
oops yeah, I messed that up.
I don't get how that substitution helps sadly

>>14697738
power series

>>14696879
>and as such I need to go from the latter to the former using the canonical isomorphisms?
Exactly. Physicists would say that you're raising an index.
>how come one sum where we only consider the diagonal terms equals the double sum with the metric?
The first equation in your pic only holds when the [math] X_i [/math]s form an orthonormal basis of [math] T_xM [/math]. In an orthonormal basis, [math] g^{ij} [/math] will be the identity matrix, so you can see how the two equations in your pic would be the same in that case.

>>14697871
>The first equation in your pic only holds when the X_i's form an orthonormal basis of T_xM .
But isn't the trace independent of the basis, since it equals the sum of the eigenvalues?

>>14697889
Trace is defined for linear maps, not bilinear forms. For a linear map [math] A [/math] with matrix [math] M [/math], if you change bases, the formula for the trace of A goes from [math] Tr(M) [/math] to [math] Tr(PMP^{-1}) [/math], where P is the change of basis matrix. By the cyclicity property of the trace, [math] Tr(PMP^{-1}) = Tr(MP^{-1}P) = Tr(M) [/math], so the trace for a linear map A is independent of the basis. But if A were a bilinear form with a matrix M, then the "trace" when you change bases would change from [math] Tr(M) [/math] to [math] Tr(PMP^t) = Tr(MP^tP) [/math]. Now this is only equal to Tr(M) if [math] P^tP = \text{Id} [/math] i.e. if P is an orthogonal matrix with respect to the chosen basis. So if you want to define a trace for bilinear forms, you'll have to pick a metric on the vector space first.

>>14697902
>But if A were a bilinear form with a matrix M, then the "trace" when you change bases would change from Tr(M) to Tr(PMP^t) = Tr(MP^tP) . Now this is only equal to Tr(M) if PtP=Id i.e. if P is an orthogonal matrix with respect to the chosen basis.
I didn't know this, I'll have to look into it then but your explanation makes sense. Thanks for the help

>>14670971
How do I start learning math as a complete know-nothing? I find myself getting stumped by even the most basic of counting problems like "what day is it 8 days from now" and the like. I blame it on wasting years just binging on junk food and passing out in food comas but it could just be I'm retarded.

Still hopeful and willing to learn and remember a thread a while back about an anon who went from 90-ish IQ to 130+ by simply grinding math starting with arithmetic

>>14697909
as always start with the greeks

Ok so ;im a celibate male who does cold showers, doesnt fap, and lifts weight.
Within 3 years;can I master pyshics/maths/coding to the point im an "asset" myself and can do reality surfing meditations/stock trade like a pro,etc?
or am I taking the movie Limitless too seriously?

>>14698426
well idk what all that gay shit is supposed to be, or what level of math you define as an asset to you, but you won't master math in 3 years
you can get to a decent level of math assuming you have a lot of time to spend on it, but if you have that much free time you might as well sign up for uni and then if the math itself is not an asset to you, the piece of paper that says you know the math is worth something at least

Is there a way to prove that this function is not integrable over [0,1]x[0,1]? I've proved that it's iterated integrals exist and are equal to 0, and that its set of points of discontinuity are uncountable, but I don't see how that could help me prove that the set of its points of discontinuity is not of measure zero.

>>14697769
what do I do if I live in a third world country with no math programme? I would've studied it in college but there isn't one. There might be some masters and doctorates but it'll be a while before I can do those, so I guess what I can do is just keep at it until then?

>>14698467
OK imma be honest I just want to know enough maths to not feel like a larper when I read /study about quantum immortality
>because if im gonna live hard assuming QI is true,i might a well be well versed in the maths behind it

>>14698569
i hate science so much it's unreal
fuck all of you

>>14698569
to answer your question though, quantum whatever requires math beyond what you would cover in a typical math undergrad, unfortunately most physishits don't even have that much so you'd be in good company if you barely know what a smooth function is

>>14697798
if sqrt(x) = -(3x+11)/12, sqrt(x-2) = -(3(x-2)+11)/12 = -(3x+5)/12
so sqrt(x-2) = 3 + 2*sqrt(x) -> -(3x+11)/12 = 3 + 2*-(3x+5)/12 and you can just solve for x

>>14697798
if sqrt(x) = -(3x+11)/12, sqrt(x-2) = -(3(x-2)+11)/12 = -(3x+5)/12
so sqrt(x-2) = 3 + 2*sqrt(x) -> -(3x+5)/12 = 3 + 2*-(3x+11)/12 and you can just solve for x

error correcting code. i need you to spill the beans now or i'm gonna say it

>>14686025
>the foundations
A foundation*

Hi /mg/, I want to know more about a problem.
The problem is this:
Say you have a polynomial [math]P(x)=ax^n + bx^{n-1} + ... + c[/math]
What can we say about the polynomial? [math]P(x+1) [/math] or [math]P(x+d), d \in \mathbb{N}, d\in \mathbb{C}[/math]?
I have skimmed the MSC and the books mentioned in Praslov's bibliography at the start of his book Polynomials, but nothing has jumped out at me. Does anybody have possible leads to further study of this problem?

>>14699249
A trivial theorem as example:
[math]a[/math] is the same for both [math]P(x)[/math] and [math]P(x+d)[/math] with [math]d \in \mathbb{C} [/math] as [math](x+1)^n = x^n + x^{n-1} + ... + 1[/math] and no other term in [math]P(x)[/math] contains a larger exponent.

>>14677436
letters like "s" or "e" are retarded lmao

>>14698533
do you live in Africa or Cambodia or something?
to answer your question, yeah just keep at it and learn more maths. since you have an internet connection, you can download books off libgen or even just google search for pdfs sometimes. the only difficulty as someone studying on their own is navigating the literature and figuring out /what/ to study. to that end, just simply start somewhere at a level that is accessible to you (say, Lang's Basic Mathematics) and from there you can figure out the next step.

How do I get into automated theorem proving or AI theorem proving? What books, software and publications do you recommend?

>>14698426
>reality surfing meditations
redpill me on this

I've had an idea
could anyone tell me if I'm going in the right direction?

I've had an idea
could someone tell me if I'm going in the right direction?