/mg/ - math general

[Anonymous No.14573570]

TVS edition.
Previously >>14541409
Talk maths; don't whine.

[Anonymous No.14573607]

For some reason my post in the last thread got deleted. Some recommendations for newfags.

Linear Algebra:
Finite-Dimensional Vector Spaces by Paul Halmos

Functional Analysis:
Rudin 2nd Ed.
>In the first edition, a fairly large part of Chapter 10 dealt with differentiation in Banach algebras. Twenty years ago this (then recent) material looked interesting and promising, but it does not seem to have led anywhere, and I have deleted it. On the other hand, I have added a few items which were easy to fit into the existing text: the mean ergodic theorem of von Neumann, the Hille-Yosida theorem on semigroups of operators, a couple of fixed point theorems, Bonsall's surprising application of the closed range theorem, and Lomonosov's spectacular invariant subspace theorem.

[Anonymous No.14573629]

What's a good book on real algebraic geometry? The topic is kind of unpopular, probably cause you actually need to think hard and use analysis when you study it.

[Anonymous No.14573642]

>>14573570
Is this subject anything like general topology?

[Anonymous No.14573676]

What are some simple examples of co-inductively defined sets in mathematics?
I read some stuff about co-natural numbers but I really didn't understand much (might also be because practically all the texts were aimed at computer scientists and used type theory stuff and code from languages like agda, coq, etc)

[Anonymous No.14573682]

>>14573607
>randomly insult people in a slow thread with a resident janny
>why was my post deleted
Call me whatever you want but at least have some self-awareness.

[Anonymous No.14573727]

>>14573682
1. Algebra has an invertible mapping to Trannyme
2. You will never be a woman

[Anonymous No.14573742]

>>14573629
Lang Math

[Anonymous No.14573773]

>newfag hijacks the bake and immediately mentions trannies
the polcel invasion is real..

[Anonymous No.14573795]

>>14573773
>NOOOOOO NOT MY HECKING HOMOLOGICAL MONOIDS NOT THE CHONKERS WHOLESOME ENDOFUNCTORS

[Anonymous No.14573796]

What are your guys' favorite small/silly result from this year so far? Mine is that the diophantine representation of primes has been reduced to 10 variables, which is still fucking hideous
https://arxiv.org/abs/2204.12311

[Anonymous No.14573903]

>>14573795
what’s wrong with Conway?

[Anonymous No.14573973]

Who else here going /monkmode/ for qualifying exams

[Anonymous No.14573985]

>>14573570
Which of you are pure mathematicians and which of you are applied mathematicians? If you're doing applied stuff tell what.

[Anonymous No.14574204]

>>14573973
I tried going monkmode but holy shit I just can't find it in me to force myself to study
Can go about half an hour before I start I game

[Anonymous No.14574427]

>>14573727
1. I'm not an algebraist.
2. I'll never be a woman.

[Anonymous No.14574728]

>>14573985
I did a ph d in a pure math that pretends to be applied math but I don't actually know anything about the supposed application areas. Also didn't do any simulations except to draw pictures of things I proved analytically

[Anonymous No.14574729]

fuck homology fuck reduced homology fuck pair homology fuck anything to do with calculating this piece of shit

[Anonymous No.14574735]

>>14573903
He overcomplicates things, Ahlfors is standard for a reason. My preference for first exposure would be Ullrich, tho

[Anonymous No.14574744]

>>14574735
>My preference for first exposure would be Ullrich, tho
Funny, Ullrich used to post in the sci.math newsgroup all the time. First time I'm seeing his name outside that context.

[Anonymous No.14574877]

>>14573903
Too slow

[Anonymous No.14574887]

Some areas of linguistics such as morphology and syntax are just as much mathematical fields as they are linguistical fields, and I believe they should be taught to students persuing mathematics education. They are a valuable resourse and a good parallel to fields such as formal logic.

[Anonymous No.14574891]

>>14574728
In what? I want to do something like that, almost applied that I can graph

[Anonymous No.14574919]

>>14574891
Pretty much anything that heavily uses differential equations is like this.

[Anonymous No.14574929]

>>14574887
shut the fuck up luke

[Anonymous No.14575046]

>>14574887
Yes. Tableaux methods are basically parsers

[Anonymous No.14575074]

I hate calculus II.
Just feels like busy work calculating particle paths, arc lengths, areas of polar regions. Shit takes almost an hour per problem.

[Anonymous No.14575221]

Bros, i fucking love topology. Although i'm being filtered by it.

[Anonymous No.14575229]

>solve problem geometrically without calculus as the solution is intuitive.
>"Good job, you are correct! But I need to see the work using calculus"
>get 10% credit and test grade drops to a B
AAAAAAAAHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

[Anonymous No.14575240]

>>14575229
Thats none sense, if you solved the problem correctly and the question didn't force you to not use any other method you should have the full credit.

[Anonymous No.14575242]

>>14575229
>write calculus exam
>don't submit any calculus
>wtf where are my marks
based retard

[Anonymous No.14575361]

>>14575240
This, unless you assumed something which solved the problem immediately or were told to use a particular method anyone reasonable would give you full credit.

[Anonymous No.14575378]

Symplectic geometry is bullshit. What a waste of time.

[Anonymous No.14575443]

>>14573642
Yes, it's the study of vector space objects in the category Top of topological spaces.

[Anonymous No.14575517]

>>14575221
fun fact, general topology can be constructed with filters instead of open sets

[Anonymous No.14575535]

Why is literally everything with the word algebra in its name so based?

[Anonymous No.14575590]

>>14575535
Algebra is for NPCs who can't into geometric intuition and only can do symbolic math like a computer.

[Anonymous No.14575734]

>>14575535
>>14575590
The thing I hate about algebra the most is the algebraists who think it's not the worst math

[Anonymous No.14575746]

>>14573629
Try Bochnak-Coste-Roy.

[Anonymous No.14575904]

Why does SL(2,C) pop up again and again in so many seemingly unrelated Lie groups/algebras?

[Anonymous No.14575949]

what's a good (of reasonable difficult and depth) introduction to algebraic number theory, suitable for an advanced undergrad? my algebra background is solid (good grasp of linear algebra + groups, rings, modules over PIDs), but i know very little Galois theory (i know what an algebraic extension is and that's about it, don't know anything of normal/separable extensions and so on)

[Anonymous No.14576039]

>>14575949
A lot of ANT relies on results from Galois theory, read up on at least the basics of GT before attempting ANT.

[Anonymous No.14576042]

>>14576039
fuck, i thought i could avoid this. in that case, what's a good GT resource?

[Anonymous No.14576053]

>>14575535
Algebra is literally the NPC field of Math. Trannies love it for some reason, people who don't like anything that is useful love it.

[Anonymous No.14576135]

>>14574735
>Ullrich
Damn it begins nicely, if you mean "Complex made Simple"

[Anonymous No.14576163]

>>14575904
Double cover of group of Mobius transformations AKA symmetries of Riemann sphere, which shows up everywhere.

[Anonymous No.14576180]

>>14576053
Algebra empowers mathematicians with infinite abstractions, because its fun. It makes category theory possible, because its fun. It has no uses, because its fun.

[Anonymous No.14576253]

>>14576042
https://www.maths.ed.ac.uk/~tl/gt/gt.pdf
Morandi and Stewart are also great.

[Anonymous No.14576266]

>>14575949
https://www.math.toronto.edu/~ila/2018_Book_NumberFields.pdf is a pretty well-known reference. I hear Koblitz is good too.

[Anonymous No.14576310]

There was one anon who posted open university MST125 course.
Is there any way I could get other maths courses from OU without paying?

[Anonymous No.14576635]

>>14573607
What is functional analysis used for?

[Anonymous No.14576643]

just picked up pic related and think i can code a sage clone somebody stop me

[Anonymous No.14576731]

>>14575535
becos algebra is based

[Anonymous No.14576749]

>>14576635
It's heavily used in numerical analysis, in the theory of stochastic processes and in PDE.

[Anonymous No.14576767]

>>14576163
Makes sense when there is a spherical symmetry. But what about higher dimensions and completely different geometries? Why would SL(2,C) be isomorphic to Spin(3,1)?

[Anonymous No.14576811]

>>14576635
Every interesting part of applied math basically

[Anonymous No.14576813]

>>14573570
Anyone able to help me with this >>14576771 ?

[Anonymous No.14576831]

>>14576767
Look up representations of the Lorentz group

[Anonymous No.14576872]

Why is Algebra so boring and soulless?
Analysis and number theory have an incredible amount of soul and history in comparison.

[Anonymous No.14577008]

>>14576872
Algebra is a spice you add to other fields

[Anonymous No.14577014]

>>14573796
>diophantine representation of primes
What's this representation? Why do you represent primes? Primes in N?

[Anonymous No.14577020]

>>14576811
That's a big overstatement. A lot of applied math just needs combinatorics

[Anonymous No.14577052]

>>14576310
Do you have a link to it? I'd love to see, always been curious about the OU's stuff

[Anonymous No.14577088]

>when the second Stiefel-Whitney class vanishes the number of possible spin structure is in bijection with H^1(M,Z/2)
>this can be EASILY SEEN from the Serre spectral sequence
Fuck homological algebra. Fuck homological algebra.

[Anonymous No.14577126]

Is there any literature on numbers with negative modulus?
For example some x satisfying |x| = -a where a is a real number.
If |x| = sqrt(x^2) then there's probably some complex x that yields a negative output

[Anonymous No.14577142]

>>14577126
yeah, just like somewhere there must exist odd numbers that are even

[Anonymous No.14577150]

>>14577142
You can always create an element that doesn't lead to a contradiction, your case leads to an explicit contradiction (x=2n+1=2n implies x=x+1, so there can't be a finite number satisfying your property), whereas mine doesn't but instead just leads to a new mathematical structure.
This is exactly the same way imaginary numbers were born: elements satisfying a logically consistent property.

[Anonymous No.14577162]

>>14577150
>For example some x satisfying |x| = -a where a is a real number.
>"In mathematics, the absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign."
As the other anon said, you want an odd number that is even.

[Anonymous No.14577171]

Is there a high-dimensional rotation that turns left hand into right hand?

[Anonymous No.14577178]

>>14577171
yes

[Anonymous No.14577186]

>>14577162
Sure if you define it that way, but typically, at least in R^1, |x| := sqrt(x^2), I'm wondering if there's any number that would yield a negative using this definition

[Anonymous No.14577196]

>>14577186
If you ignored entirely what the definition is supposed to be, rendering communicating an absolute value pointless entirely, a complex number representing rotation along some axis could give you a negative number.

In much the same way ignoring common definition or convention could let you claim the number 3 is even.

Sure, you CAN choose to communicate badly. Why would you, though? What does it give you?

[Anonymous No.14577197]

>>14577186
it's literally embedded into the definition of [math]\sqrt[/math] that you choose the positive root, otherwise it's not even a function

[Anonymous No.14577259]

>>14577178
Any visualization?

[Anonymous No.14577339]

Can someone be really really good at math?

There was this guy in my graduate level math class last spring who I thought was super good. He came two hours late to our three hour final and I was amazed, I couldn't believe he would finish it that fast.

People were asking each other how they did afterward and when I asked him he just got pissed off and said "I was two hours late, how the fuck do you think I did?"

And I'm not sure. From his tone he sounds like he did bad but I figured he came late on purpose because he was smart enough that he wouldn't need the full time.

[Anonymous No.14577592]

How can I post research anonymously.

[Anonymous No.14577610]

>>14573570
>read math book in English
>text text text, just to say very little
>read math book in French
all relevant info is presented in a concise manner

Is this why the French are just better at math ?

[Anonymous No.14577627]

>>14577052
He uploaded it to some temporary online storage. If you have an idea where could I upload without much hassle I'd be glad to share
I've found some OU stuff on limetorrents, but I've never used that website, so I'm a bit hesitant

[Anonymous No.14577697]

>>14577610
My experience is quite different.
Could you post the books you're referring to?
t. L2 English L3 French

[Anonymous No.14577815]

>>14577126
what do you mean by "modulus"? Modulus in the sense of norm is nonnegative by default. Nothing wrong with generalizing definitions and seeing if you get something cool, but it's not clear how the triangle inequality should function -- should |a + b| be more or less negative than |a| + |b|?

[Anonymous No.14577822]

Any good serious math YouTube channels?

I've technically passed a physics class at community college that required calculus (as it should, but in high school we learned it before calc so it has to be algebra only which was retarded). I got an A minus in said class. That said I never really did calculus properly even though I understand the basic concepts. I want to get into math again and my current manual labor job lets me wear earbuds so I'm thinking of trying to get back into that. But it's audio only and math is visual often. So this would have to be a supplement to actual study. That did are there any good math channels on YouTube that would explain math from calc through stuff like analysis so I could learn it or at least prime my brain for studying it?

Doesn't have to be YouTube but it ahs to be soemthing I can download to mp3

[Anonymous No.14578039]

What are some good books that will help me learn how to formalise ideas.

[Anonymous No.14578211]

>>14577627
Try https://catbox.moe/..

I checked that torrent site, but no one seems to be seeding it. Someone should set up a mega or something....

>>14577822
Maybe put some MIT OCW lectures on? They have calc lectures up, and Francis Su has a good series of lectures up.

>>14578039
Book of Proof is online, free, and good. Try How to Prove It by Polya too.

[Anonymous No.14578216]

>>14578211
>Book of Proof is online, free, and good. Try How to Prove It by Polya too.
thank you

[Anonymous No.14578353]

>>14577697
https://www.libgen.rs/book/index.php?md5=161EC9728BAD602D1C1E95562760CF00
Book on algebraic topology French ~300 pages. Hatcher's nearly 600.

[Anonymous No.14578402]

In a typical university, what does proportion of the budget typically goes to each department, ie what does the pie chart look like

[Anonymous No.14578424]

>>14578353
That french book doesn't cover cohomology. If you discount the additional topics and the cohomology chapter I counted a total of 236 pages in hatcher. So it's not that different.

[Anonymous No.14578462]

>>14578424
True, maybe not the best example. But the french text is more succinct in my opinion. It also has solved exercises that take more space. Hatcher has none.

[Anonymous No.14578474]

>>14577592
Just sign it with a PGP watermark and post it on 4chan or whatever. You have the private key and can prove it's yours.

[Anonymous No.14578477]

>>14575746
>Bochnak-Coste-Roy
thanks!

[Anonymous No.14578546]

>>14577020
He’s talking about applied math useful to engineers and physicists, in which case functional analysis and pde’s are the core of most of what they do that isn’t numerical linear algebra.

t. applied math

[Anonymous No.14578649]

>>14578211
https://files.catbox.moe/92tbsz.zip

[Anonymous No.14578655]

>>14578649
Thanks!

[Anonymous No.14578672]

>>14578655
Yeah no worries
We need to come up with a mega tho

[Anonymous No.14578767]

Brainlet question incoming.

Knowing that each element in the group [math](\mathbb{Z}/7\mathbb{Z})^{\ast} \times (\mathbb{Z}/9\mathbb{Z})^{\ast} [/math] has the form [math]([3^m]_7, [2^n]_9)[/math], how can I, using the natural group isomorphism given by the mapping
[math][x]_{63} \mapsto ([x]_7, [x]_9)[/math]
prove that each element in [math](\mathbb{Z}/63\mathbb{Z})^{\ast}[/math] can be written as [math][2^n3^m]_{63}[/math]?

I know this must have a general group-theoretic answer but I feel satisfied enough solving this example

[Anonymous No.14578815]

>>14578672
To do that we'd probably need other OU stuff, if anyone else has any.

>>14578767
Doesn't this directly follow from what you know? You can take the inverse map of the natural group isomorphism you posted and that gets you what you want.

[Anonymous No.14578832]

>>14578815
Sorry, the conclusion meant to say that each element in [math](\mathbb{Z}/63\mathbb{Z})^{\ast}[/math] can be written as [math][2^n10^m]_{63}[/math], unless there is a typo in my material but it seems to be legit.

[Anonymous No.14578868]

>>14578767
>>14578832
I think your fact is supposed to be that you can write everything as [math]([5^m]_7, [2^n]_9)[/math] .

[Anonymous No.14578950]

>>14576180
everything that is fun has a applications or is modeled by differential equations by definition

[Anonymous No.14580109]

What type of statistical model should you use if your dependent variable is in percentage points and independent variables are also percentage points?

[Anonymous No.14580251]

So I'm a bit confused, according to the Van-Kampen theorem adding a 2-cell to a topological space trivialises the normal subgroup generated by the loop around the boundary of the glueing. More exactly, the fundamental group of the space Y with the 2-cell attached is the quotient of the fundamental group of X by said subgroup. However, say I were to glue a disk to the meridian of a torus, I can't find a single nontrivial loop on this space even though it should be the integers.

[Anonymous No.14580261]

>>14580251
> I can't find a single nontrivial loop on this space
What about a parallel?

[Anonymous No.14580297]

>>14580261
?

[Anonymous No.14580319]

>>14580261
Can't you just homotope it to a loop on one side of the torus?

[Anonymous No.14580367]

>>14580261
Nvm, I think I got where my intuition failed me, essentially, your path can continue through the disk to get to the other side.

[Anonymous No.14580509]

>>14573570
How exactly do Mathematical Physics and Theoretical Physics differ?

[Anonymous No.14580614]

>>14580509
theoretical physics is when you try to apply existing physical principles to situations where they manifestly don't apply
mathematical physics is when you try to apply mathematical principles to situations where they manifestly don't apply

[Anonymous No.14581015]

>>14580614
man I really want to study both. Is this possible? Who would even employ me?

[Anonymous No.14581279]

>>14578815
Isn't the inverse map of that isomorphism
[eqn] ([x]_7, [y]_9) \mapsto [36 x + 28 y]_{63} [/eqn]
?
I don't see how it helps.

[Anonymous No.14581318]

>>14573570
[eqn]\int udv =\begin{vmatrix}
u & \int v \\
du & v
\end{vmatrix}[/eqn]

[Anonymous No.14582394]

Can you learn analysis from a book in 1.5 months, assuming that you spend 25 hours a week?
What's the most realistic plan you should do?
I want to work on some books but my bad habit is that I get autistic about things when I get stuck. There are times when I spend a whole day to understand an equation just to realized that I misunderstood the definition a few pages earlier.
Should I just take an online course instead?

[Anonymous No.14582547]

>>14582394
That's not a bad habit, that's a natural part of learning.

[Anonymous No.14582556]

>>14580109
Nigger tier question

[Anonymous No.14582728]

>its over

[Anonymous No.14582773]

>>14573727
that's not anitranny

[Anonymous No.14582826]

>>14582728
I've unironically once used OpenAI to assist me in finding a proof.

[Anonymous No.14582847]

>>14582728
Do you understand where the network is getting these strings of text from?

[Anonymous No.14582929]

>>14578950
This. Spending your life moving commas around (i.e. category theory) sounds gay af

[Anonymous No.14582941]

if something has an application that usually means that it can help kill people in some way. I don't wanna contribute to that

[Anonymous No.14582966]

Anybody know where I can get books for learning precalc/calc for cheap?

[Anonymous No.14582973]

>>14582966
Libgen/z-lib

[Anonymous No.14582985]

>>14582973
Thanks, anon. I've been trapped in a cult for the
past 25 years and starting my education at 30.
I was so foolish for caving into fear but every day
is a new day.

[Anonymous No.14582993]

Are there any good books on representation theory from a categorical standpoint?
I've focused mainly on algebraic geometry but now want to get into representation theory, any pointers on the best way to go about it?

[Anonymous No.14583030]

Should I study maths or mathematical statistics in undergrad? I feel like pure maths is more interestong for me, but people say that you get basically 0 good jobs if you study pure math.

[Anonymous No.14583034]

>>14582985
Did the cult do sex stuff?

[Anonymous No.14583036]

>>14583030
You can always get a job as a mathematician.
There will always be a programming job or a teaching job for you. At least that's the way it is here in Denmark. But you'll probably never work with any of the stuff you learn as a pure mathematician, don't know if that's the case for statisticians either tho.

[Anonymous No.14583048]

>>14583030
>>14583036
I'll go a bit further than this anon and say that (at least in America) there's essentially no difference at all in job availability between a pure math bachelors and a statistics bachelors. You will still get interviews for all the same stats/business math jobs with a math degree, and any good math degree will contain a few stats courses anyway.
Most undergrad-level statistics jobs are, to be blunt, spreadsheet monkey shit and you shouldn't expect the mathematical sophistication involved to be very high (which isn't necessarily a negative; they're easy desk jobs, generally pay a nice middle-income salary, and are super stable if you find government work, which isn't that hard).

[Anonymous No.14583130]

>>14582728
Isn't this just reading from Stackexchange or something?

[Anonymous No.14583145]

>>14582556
Kek. True

[Anonymous No.14583148]

>>14583030
In the US the correct answer would be to study pure math and get a minor or a double major in statistics. Double major is always better than one of those hybrid programs and for something like math and stats most of the prereqs and the electives are shared.

I'm guessing you're in the UK though and if that's not allowed the mathematical statistics is probably the more useful program all things considered unless you are going into PhD or teaching.

[Anonymous No.14583208]

>>14582728
>>14583130
those proofs are literal gibberish
you'd get much better results if you actually WERE just searching stackexchange and stealing the most relevant answer

[Anonymous No.14583230]

Stupid question, but if we have a connected set (an interval, or a 2D disk), and we say "half of this set satisfy property x", then we are implicitly using some measurement in this statement, right?
For example, without measuring the length of the interval, the statement "a half of an interval" just doesn't make sense to me.
Same with a disk, without calculating the 2D area, it also doesn't make much sense to me.

[Anonymous No.14583272]

>>14577610
>On the other hand, the Grothendieck personality cult had serious side effects: many people who had devoted a large part of their lives to mastering Weil foundations suffered rejection and humiliation, and to my knowledge only one or two have adapted to the new language; a whole generation of students (mainly French) got themselves brainwashed into the foolish belief that a problem that can’t be dressed up in high powered abstract formalism is unworthy of study, and were thus excluded from the mathematician’s natural development of starting with a small problem he or she can handle and exploring outwards from there. (I actually know of a thesis on the arithmetic of cubic surfaces that was initially not considered because ‘the natural context for the construction is over a general locally Noetherian ringed topos’. This is not a joke.) Many students of the time could apparently not think of any higher ambition than Étudier les EGAs. The study of category theory for its own sake (surely one of the most sterile of all intellectual pursuits) also dates from this time; Grothendieck himself can’t necessarily be blamed for this, since his own use of categories was very successful in solving problems.

>The fashion has since swung the other way. At a recent conference in France I commented on the change in attitude, and got back the sarcastic answer ‘but the twisted cubic is a very good example of a prorepresentable functor’. I understand that some of the mathematicians now involved in administering French research money are individuals who suffered during this period of intellectual terrorism, and that applications for CNRS research projects are in consequence regularly dressed up to minimise their connection with algebraic geometry.

- Reid

[Anonymous No.14583290]

>>14583230
It depends on the context, but presumably whatever you're reading it is using it in a colloquial sense. Could be cardinality, measure, probability, or literally (b-a)/2 where a,b are the endpoints

[Anonymous No.14583347]

(a+b)^2 = (a+b)(a+b) = a(a+b)+b(a+b)

I don't understand how you get to the third part of the equality here. I understand that it ends up being correct I just don't understand what rule lets me manipulate it in this way.

[Anonymous No.14583368]

>>14583347
Total nonsence.

[Anonymous No.14583401]

>>14583347
oh, y'know, just associativity, commutativity, distributivity, that whole bag

[Anonymous No.14583402]

>>14583347
Anon, your task in life is to learn, not to understand.

[Anonymous No.14583404]

>>14583034
Jehovah's Witness, anon. I've been trapped all my
life and getting tabs held on me so I couldn't reach
out for autonomy. They told me at an early age not
to even bother coming back home if I went to college
but I think that was my biggest mistake.

[Anonymous No.14583415]

>>14583401
In what order are they applied and how to get this result.

>>14583402
If I don't understand I cannot learn. I've been foiling since I was in the 2nd grade and now that I've seen this it is fucking with my ability to do basic math.

[Anonymous No.14583423]

>>14583415
It's literally just right distributivity
(a+b)x = ax+bx
x is (a+b)

[Anonymous No.14583447]

>>14583423
God bless you

[Anonymous No.14583640]

>>14583130
For the ones in the top left (i.e. established proofs), maybe. But

Find a counterexample to RH: every negative integer is a counterexample

Hopefully isn't, and seems like actual text analysis.

>>14582826
Based. It really seems to struggle with doing actual algebraic manipulations, but it's good for finding initial ideas. What sorts of problems were you successful with?

>>14583208
you're just mad you didn't find a smooth NS solution first, you can have a pity dollar of my prize

[Anonymous No.14583702]

hey anons, i want to teach myself math - can someone post the graph? you know, the graph that tells you in what order to learn stuff

it has some anime girls on it i think, and it starts with a book on logic

i can't find it though

[Anonymous No.14583717]

>>14583702
it's not a graph, it's a flowchart, my mistake

[Anonymous No.14583750]

>>14583717
hey so nobody actually responded but thats fine!! i found it myself

[Anonymous No.14583757]

>>14583750
this is retarded
go to a university you want to pretend to be at
look at their undergraduate math degree pathway
look up past syllabi from those courses
study those textbooks

[Anonymous No.14583773]

Has anyone tried the "topology without tears" book?

[Anonymous No.14583791]

>>14583773
what, munkres? yeah, its good

[Anonymous No.14583799]

>>14583791
No it's this one I'm talking about:
https://www.topologywithouttears.net/

[Anonymous No.14583803]

>>14583773
>>14583791
Is there any good use for topology?

[Anonymous No.14583831]

>>14583803
No

[Anonymous No.14583836]

>>14583803
personal entertainment

[Anonymous No.14583869]

>>14583831
>>14583836
Know of any good guides to useful math?

[Anonymous No.14583884]

>>14583869

[Anonymous No.14583891]

>>14583884
Dover books are based but I'm not sure how helpful that graphic is

[Anonymous No.14583900]

>>14583869
there is one branch of "useful" math, it's called counting

[Anonymous No.14583902]

>>14583750
This chart is absolutely retarded. Enderton and Landau are probably more sophisticated than the books that follow them combined. The Transition to Advanced Mathematics book is a valid alternative to Vellemann or Hammack but completely out of place in the chart. The first book is targeted mainly a first year philosophy students, you're better off reading a Logic book targeted at mathematics students like Mendelson, Rautenberg, Enderton (yes the same one from the set theory book), etc. But starting out with such a formal Logic book without much mathematical maturity is bound to fail so ignore that for now.
Honestly just get the Velleman book and then go from there. The 2nd edition (the one depicted in the chart, because that meme is ancient) is honestly just as good if not better than the newer 3rd one because he scratched some important stuff about closures and instead wrote a half-assed number theory chapter.
Any similar book will do too, like the Hammack one or the Transition to Advanced Mathematics one (both in the chart). Hammack is free to download but Vellemann is far superior imo. After finishing that, you should have enough mathematical maturity to be able to tackle most elementary mathematics textbooks.
Best of luck with your studies anon

[Anonymous No.14583914]

>>14583803
>>14583831
>>14583836
>>14583869
If you study/research geometry (don't laugh), you can still apply a lot of theorems from topology.
Also, more ways to view a certain subject (such as graph theory) is always nice.

[Anonymous No.14583923]

>>14583914
>If you study/research geometry
What is useful in geometry?
>>14583900
Linear algebra?

[Anonymous No.14583924]

>>14583891
alright here's an actually helpful graphic

[Anonymous No.14583926]

>>14583923
counting does not involve made up bullshit like zero or "negative" numbers

[Anonymous No.14583927]

>>14583923
>Linear algebra?
Most you'll ever need is a 3x3 matrix which is essentially just counting. Abstract vector spaces are a waste of time

[Anonymous No.14583931]

>>14583923
>What is useful in geometry?
Machine learning? Statistical analysis? These use a lot of arguments and intuitions from geometry.

[Anonymous No.14583933]

>>14583927
Calculus?

[Anonymous No.14583937]

>>14583931
>Machine learning? Statistical analysis?
Textbooks?

[Anonymous No.14583938]

>>14583924
lol

[Anonymous No.14583944]

>>14583933
Again all you really need is the counting. Epsilon delta shit is the definition of overcomplicating things

[Anonymous No.14583954]

>>14583933

[Anonymous No.14583957]

>>14583954
lmao.

[Anonymous No.14583988]

>>14583954
Based

[Anonymous No.14583995]

>>14583954
Stupid shit like this is why I still come to these threads.

[Anonymous No.14584000]

>>14583884
Shilov is shit, I regret buying this crap but the first chapter is great. Get Paul Halmos Finite-Dimensional Vector spaces

[Anonymous No.14584008]

I got these for 5 bucks at a bookstore.
Are they okay or just archaic? (Written since 1931)

[Anonymous No.14584036]

>>14583048
As an immigrant in the US is it impossible to get a job in the government?

[Anonymous No.14584063]

>>14573570
I've got a math related question. If I can't figure out calculus on my own without a textbook to guide me and teach me, does that make me stupid?

Because I kind of feel like I'm not actually figuring things out the same way Newton probably did when he invented calculus hundreds of years ago. I feel like I'm just copy pasting.

[Anonymous No.14584080]

>>14584063
Do you mean figuring out an exercise or something?
Or do you mean coming up with a definition/new theorem by yourself?

[Anonymous No.14584119]

>>14584080
I'm in actually coming up with a new theorem. I mean, everything I'm doing is just going by a textbook learning a theorem somebody else came up with, and and repeating it. It's like learning any other new language. But am I actually understanding language? I don't think I can call myself intelligent until I come up with an answer myself instead of borrowing it from someone else.

[Anonymous No.14584123]

>>14584080
I'm mean actually coming up with a new theorem. I mean, everything I'm doing is just going by a textbook learning a theorem somebody else came up with, and and repeating it. It's like learning any other new language. But am I actually understanding language? I don't think I can call myself intelligent until I come up with an answer myself instead of borrowing it from someone else.

[Anonymous No.14584130]

>>14584063
Newton was retarded, so if you can't get calculus

[Anonymous No.14584140]

>>14573570
How important is rigorous math for (theoretical) physics (very formal proofs and definitions, etc.)?

[Anonymous No.14584146]

>>14584119
Don't you think coming up with new stuff is a better use of your time than trying to redevelop century old shit?

[Anonymous No.14584150]

>>14584146
For >>14584063

[Pax No.14584153]

200+ IQ medchad here. Is this enough to learn all of math?

[Anonymous No.14584164]

>>14584153
you really need to read chapters 5 and 2 first at least

[Anonymous No.14584239]

>>14584123
If you actually want to come up with a new theorem without having any hint about it before hand then good luck. It would take years for you to reach all of the stuff introduced in a Calculus course in undergrad.
Also about the language thing, it's not like you can always write something truly original either. Think about it, most of your conversation and writing are made of established rules you learned during your school years.
It is true that if you want to satisfy your thirst for math, you need to come up with something new, that's why people do research in math.
For language, I guess that's why modern literature exists? Shits like in search of lost time is a trip.

[Anonymous No.14584361]

>>14583924
lmao I made this like 5 years ago, can't believe it's still being posted

[Anonymous No.14584414]

>>14584063
Although the principle behind thinking this way isn't terrible, your biggest mistake is believing that Newton, or anyone for that matter, developed this stuff in a vacuum.

For starters, Newton most likely received a very rigorous training in Euclidean geometry, and the Greeks, most notably Archimedes, were already doing calculus-like computations to find quantities such as the volume of a sphere. On top of that, these types of things were already being considered by his contemporaries. Gregory and Barrow (Newton's supervisor) were the ones that first stated and proved the fundamental theorem of calculus.

Secondly, Newton had certain goals/motivations that you don't have to develop calculus. Most topics come about first as a shoddy construction to solve a particular problem, and only after its power is understood does it get developed into a full-fledged theory. Most of the time, the prepackaged, clean theory presented to you in books and lectures is a result of decades of teaching, advancement by others, and hundreds of revisions, and has nothing to do with what was originally envisioned. A notable example of this is Galois theory for example, which had nothing to do with fields when Galois did it, but now you take a half-course in field theory before you even touch any of what he did (which is also all stated in terms of field theory).

Lastly, doing this for everything you do will surely give you a stronger foundation, but ultimately will take you nowhere. Moore's teaching method was similar to this approach and was eventually scrapped since the students were left so far behind. You cannot complete 100 men's life's work in your lifetime.

[Anonymous No.14584416]

If I want to pursue a career in mathematics how intuitively do I need to understand the basic rules of math? Basically what I'm trying to ask is in how much detail do I need to study the area from Prealgebra right up until Calculus? I've been out of highschool for 9 years now and I'm trying to feel around for what it is I intend to study, want to know what I need to wrap my head around before I attempt Calculus again having not interacted with it since high school.

[Anonymous No.14584442]

>>14584416
The simplest answer to this is just attempt calculus and try to patch the gaps as you go. If you find you have way too many gaps then you know you need to stop and go back, but you'll also know what you need to review.
I can say you shouldn't be trying to completely _master_ precalc before you start calculus. Good enough is good enough. There's a general rule of thumb that you will never master something until you start using it as a tool to apply to something harder.

[Anonymous No.14584582]

>>14584153
Obviously not.

[Anonymous No.14584788]

>>14583924
here is an even better one
>>14584140
depends what kind of (theoretical) physics you want to do. it has its fringe usefulness, but its not very important in general

[Anonymous No.14584807]

>>14583404
Good on you, man. The peace and freedom
knowledge affords from without challenges the
fear and slavery of ignorance from within.

We're all in a box until one gets a look outside.
That's the fourth dimension for you, I guess.

[Anonymous No.14584856]

>>14584788
Another bad chart

[Anonymous No.14584918]

How do I show that the transitive closure of every class relation R exists? I can't just adapt the proof for set relations to class relations (taking the intersection of all transitive relations containing R). What do

[Anonymous No.14584969]

>>14584918
Use the other way to define transitive closure

[Anonymous No.14584981]

>>14584856
you dont know whats good for you

[Anonymous No.14585000]

Model theory? More like retardel theory

[Anonymous No.14585016]

>>14584969
Hmm I guess. I was hoping to do it without using [math]\omega[/math], I'll keep trying tomorrow

[Anonymous No.14585032]

A book to study maths from scratch?

[Anonymous No.14585037]

>>14585032
real math? try napkin
basic math? start counting your fingers, you'll get it from there

[Anonymous No.14585075]

Can someone please explain to me what is happening in pic related? Context, it is an example from a Norwegian math textbook, it is attempting to show a combination of the product rule and the chain rule.
What is throwing me for a loop is the last three parts, I don't understand how it gets simplified to that answer.
(x^2+1) is one moment raised to the third power, and then suddenly it isn't?

[Anonymous No.14585088]

>>14585075
(x^2 + 1)^3 = (x^2 + 1)(x^2 + 1)^2 = (x^2 + 1)^2(x^2 + 1) = (x^2 + 1)(x^2 + 1)(x^2 + 1)

[Anonymous No.14585099]

>>14585075
They factored out the [math](x^2+1)^2[/math]

[Anonymous No.14585103]

>>14585075
[math] \begin{align}
(x^2+1)^3+6x^2(x^2+1)^2&=(x^2+1)\cdot(x^2+1)^2+6x^2\cdot(x^2+1)^2 \\
&=\left((x^2+1)+6x^2\right)(x^2+1)^2 \hspace{1cm}\text{ via distributivity} \\
&=(x^2+1+6x^2)(x^2+1)^2 \hspace{1cm} \text{ redundant parantheses} \\
&=(7x^2+1)(x^2+1)^2 \hspace{1cm} \text{ since } x^2+6x^2=7x^2
\end{align} [/math]

[Anonymous No.14585127]

>>14585103
I have been staring at it for over 10 min and now I finally get it, thanks!

[Anonymous No.14585171]

>be me
>tranny who stopped repressing this year
>took analysis
>i like it
>start studying abstract algebra in the summer
>incredibly intuitive, already studied up to the isomorphism theorems
>I've never enjoyed anything more

[Anonymous No.14585184]

>>14584981
Best so far

[Anonymous No.14585244]

Schemes seem to be very intricate objects, but it’s one of the coolest definitions I’ve seen in math so far.
Time to do some exercises with these bad boys

[Anonymous No.14585472]

>>14584981
Any good ones?

[Anonymous No.14585476]

>>14583954
schizos btfo

[Anonymous No.14585544]

My course grades show the high, low, and mean scores accurate to one decimal. I know all the assignments haven't been graded yet though, since mine hasn't. How could you calculate the minimum number of assignments graded (since there are infinite combinations of grades that could make that mean, maybe?) given that each score comes in increments of 0.5?

[Anonymous No.14585736]

>>14585171
good for you. how do you eat corn?

[Anonymous No.14585940]

New notation

sc x = cos x
cc x = sin x
tg x = cc x / sc x

sh x = cosh x
ch x = sinh x

[Anonymous No.14585972]

>>14585940
No

[Anonymous No.14585977]

>>14585972
Yes.

[Anonymous No.14586028]

>AI will replace mathematic-

[Anonymous No.14586191]

>>14586028
That's actually a lot more elegant than Godel's original proof

[Anonymous No.14586389]

>>14586191
Anon...that's not a proof. It's just gibberish.

[Anonymous No.14586424]

>>14586028
It's a language transformer. It predicts words. That's it. There is no thinking going on here.

[Anonymous No.14586607]

>>14584918
>>14584969
>>14585016
Ok I think I figured it out. The transitive closure of a class relation is the union of the transitive closures of its subsets.

[Anonymous No.14586633]

>>14586389
I agree (assuming you're talking about godel's paper)

[Anonymous No.14586643]

>>14586633
>filtered by omega consistency

[Anonymous No.14586648]

>>14586633
meyers please go

[Anonymous No.14587025]

>trying to study for calc II exam tomorrow
>cant concentrate on 6 weeks of topics
>practice exam covers everything from integration by parts, trig integration techniques, trig substitution, partial fraction decomposition, improper integrals, comparison theorem, length of curves, rotation washer/disc surface area/volume problems, hydrostatic forces, probability functions, parametric and polar functions and integrals.

Feel like I know only a little bit of everything, but not enough to do 20 problems in 2 hours...

[Anonymous No.14587032]

oh my god
so this is what mg is down to
undergrads complaining about calculus
Jesus Christ the state of this general
at one time this was a viable alternative to stack exchange

[Anonymous No.14587041]

>>14587032
All the graduate students suicided. Now its zoomers turns to go up through the system.

[Anonymous No.14587059]

>>14587041
Honestly higher math is sui fuel, I barely get time to sleep with all obligations and exams
I'll be studying the whole of July and August, no summer break
it's all so tiresome

[Anonymous No.14587069]

>>14587032
>i hate 4chan
>i hate /sci/
at one point in time you were attracted to this board, but now that you've been here for a while, you think the board is garbage. /sci/ was good for you arrived, now its trash.

[Anonymous No.14587083]

>>14587069
no, mg was good, with putnam anon and a bunch of people chatting about math
now they've all went to discord (largo group) and it's understandable why, this place is shit

[Anonymous No.14587099]

>>14587083
>this place is shit
it was good before you arrived and now its shit.
inb4 "correlation is not causation"

[Anonymous No.14587110]

>>14587099
don't you have a calculus exam tomorrow bub?

[Anonymous No.14587156]

>>14587110
/sci/ was good before you arrived, but now that you've been on /sci/ for a while, you think the board sucks balls.
maybe /sci/ will go back to being the way you like it if you stop trying to participate in the discussion

[Anonymous No.14587214]

How many posts will I have to make per thread before you fags stop complaining about thread quality?

[Anonymous No.14587224]

>>14587214
50
or make yukari fag come back

[Anonymous No.14587275]

>>14587224
I don't actually have any way to contact him.

[Anonymous No.14587310]

am i a pseud if i just like watching popmath videos on youtube

[Anonymous No.14587314]

>>14587310
yes

[Anonymous No.14587318]

>>14587275
who are actually the confirmed competent mathematicians who used this thread in the last few years? you, yukari, anitranny on a good day, nikolaj...
some anons too of course

[Anonymous No.14587324]

>>14587318
your avatarfag-vision is antithetical to everything an imageboard is. you don't see the anon, all you see is the famefag. go back to discord

[Anonymous No.14587328]

>>14587314
how can i not be a pseud

[Anonymous No.14587334]

>>14587324
i was just listing some good mathematicians you retarded mongrel. stop pretending there is some sacred board culture that retards like you need to protect.

[Anonymous No.14587350]

>>14587318
>who are actually the confirmed competent mathematicians who used this thread in the last few years?
There was also Colettefag and analytic number theory anon.
Can't remember anyone else I can put a name or description to.

[Anonymous No.14587406]

>>14587334
get it through your thick skull that there are more people who matter than the ones who use a name to look special

[Anonymous No.14587430]

>>14585940
i did this in the middle of a tedious exam problem once

[Anonymous No.14587433]

>>14587406
You don't need to go out of your way, you can just make recurrent posts that have some distinctive aspect like analytic number theory anon did.
Hell the only things we used to tell Nikolaj apart from everyone else were the filenames, the images, the writing style and the subjects, more so the last two than anything else.

[Anonymous No.14587442]

is there a big chart of dependencies to solve not-quite-NP-complete problems anywhere?
stuff like finding a nontrivial square root mod n -> factoring n

[Anonymous No.14587470]

[Anonymous No.14587551]

How can I generate novel math ideas and concepts on demand?

[Anonymous No.14587558]

>>14587551
you dont. math is not created in a vacuum. every super abstract novel thing you wonder how anyone ever came up with was actually just the fruit of years of many mathematicians working on a specific approach to a specific problem.

But you could try mixing coffee and meth.

[Anonymous No.14587562]

>>14587558
>you dont. math is not created in a vacuum.
Wait so why doesn't making something up at random work?

[Anonymous No.14587701]

>>14587025
https://www.youtube.com/watch?v=ZjGb6_uonZk

[Anonymous No.14587753]

>>14587562
Almost all random definitions specify objects which are either trivial or so hopelessly complicated you can't prove anything. Brute forcing math like this is pretty hopeless.

[Anonymous No.14587778]

>>14574735
Both of these are two terse for me. Conway is better, but I really think Stein/Shakarchi is the gold standard. Remmart is good too since it covers a lot of topics in a historical narrative and has good pictures.

>>14575949
The later chapters of Ireland and Rosen would work for this. There's also a book by Paul Pollack that's an easy intro to algebraic number theory that's pretty light on the field theory. >>14578211
Richard Borecherds from Berkeley puts out good content but it's not bite-sized infotainment, just high quality lectures.
>>14578402
I believe you can look this up for many public state university systems. Off the top of my head, California and Illinois do this. Typically math does fairly well, but is just a drop compared to medical and business departments.
>>14580251
The 2 cell that you add to fill the hole will be contractible, so you're reduced to calculating pi1 of a horn torus. Can you calculate pi1 now?
>>14583803
I calculate persistent homology in order to track cell service coverage. It's boring and way OP for this type of problem, but it pays the bills and lets me think about model categories when I'm free.
>>14582993
Serre or Fulton and Harris.

[Anonymous No.14588109]

>>14587778
>I calculate persistent homology in order to track cell service coverage
interesting, are you employed by a provider? is there a big market for jobs such as this?

[Anonymous No.14588123]

>>14587059
lol I wish I could just take two weeks off to study

[Anonymous No.14588125]

>>14587069
You will never be a mathematician

[Anonymous No.14588201]

>>14573570
I want to freshen up my knowledge before taking Real Analysis 3. Tao or Rudin?

[Anonymous No.14588352]

>>14588109
I've done this at internships but am currently dissertating. There is not a huge market for it in industry. Setting up persistent homology to solve industry problems is usually like killing a fly by burning the house down, and there's no ROI. The exception is really the medical field where some people are using it to detect tumors in fancy ways. For the most part, "applied" pure mathematics is only applied insofar as it tricks committees into giving you funding. Such is the state of academia.

[Anonymous No.14588431]

>>14587753
What do human mathematicians do that lead them to good concepts?

If you ever encounter something that involves a number of dimensions, you could turn that into n-dimensional or iterate through different dimensions.

Could someone give a random example of one trivial, and one hopelessly complicated?

What about definitions of intermediate-sounding complexity that can be used, like digital roots?

[Anonymous No.14588475]

>>14587753
I'd like to see a program which generates random definitions and see how complex the objects are.

[Anonymous No.14588592]

>>14588352
i'm nearing the end of my bachelors, after which i definitely want to do a masters (in pure math), but i do wonder at times what the hell i'll be doing after (ideally, i'd like a PhD, but idk if i'm good enough for it). overall, to your knowledge, how is the job market for masters degrees in pure math?
>but am currently dissertating
what's your area/topic (and your school, unless you're worried about getting doxxed)?

[Anonymous No.14588790]

What's the best way to show my work as a hobbyist, a website, a blog, pdfs, a book, videos, or some other medium?

[Anonymous No.14588801]

>>14588790
A blog sounds like the most common thing

[Anonymous No.14588832]

>>14588592
Basically the intersection of algebriac topology and algebraic geometry.

The job market for a master's is dogshit. There's really no marketable skills you learn in a master's in pure math, so you're hardly better off than someone with a bachelor's. If you do applied, you're still competing with people with terminal master's in fields like CS and data science. I'd advice either getting a terminal master's or going into a PhD program, learning math you're interested in for 2-3 years, and then once you get to candidacy focus less on research and more on learning skills and getting internships.

[Anonymous No.14588855]

>>14588832
what's a terminal degree? also i was speaking to one of my professors (i study in Germany) and he claims there is a significant job market, places like Deutsche Bahn, Lufthansa, banks, insurance, etc., and a theoretical degree as opposed to an applied one is not a detriment

[Anonymous No.14589035]

>>14588855
Ahh, I see. I'm in the US, and the situation could very well be different across the pond. A terminal degree is a degree that you get in order to finish ("terminate") your formal education and begin work. Usually these are less academic and more focused on skills, e.g. data science, mathematical finance, software engineering, law, etc. This is opposed to an MS in pure mathematics, which in the US, people usually get with the hopes of eventually joining a PhD program.

Your professor could be right about the situation, though I'd always take real world advice from academics with a grain of salt. What you could do is ask your department to put you in contact with master's alumni who went into industry, and then ask them for anecdotes and advice.

[Anonymous No.14589063]

>>14588790
Usually I don't reply to anitrannies but I would suggest a website. Maybe with a blog part. A good example of a kind of nice but serious hobbyist website would be https://www.lowtechmagazine.com/

[Anonymous No.14589192]

>>14588431
>Could someone give a random example of one trivial, and one hopelessly complicated?
Choose a random finite set of equations in the language of groups. Say you want to find the finite simple groups belonging to the corresponding variety. If you get Abelian groups it's trivial and if you get all groups it's an epic task. In general there is no algorithm for doing this and you won't even be able to decide if the variety is trivial or not.

[Anonymous No.14589203]

>>14589192
>Choose a random finite
I didn't really mean random I just meant a way to iterate relatively simple concept definitions.

[Anonymous No.14589209]

>>14589203
Okay, so iterate through all finite sets of equations in the language of groups. Same difference.

[Anonymous No.14589233]

>>14589209
>finite sets of equations in the language of groups
I'm not familiar with groups. It can't be impossibly unlikely for relatively simple definitions to give good structures if some have already been found.

[Anonymous No.14589239]

>>14587701
what's that guys age?

[Anonymous No.14589247]

>>14589233
>I'm not familiar with groups.
You do not know enough math to understand the phenomenon. It happens everywhere, but this is a basic example.

>It can't be impossibly unlikely
It is. As in the probability of choosing a "viable" definition is 0 in basically any reasonable context. Humans can choose them anyway because we have heuristics which allow us to do so. We don't blindly generate axioms.

[Anonymous No.14589258]

>>14589247
>because we have heuristics
Are there good heuristics to use that you could make a computer use? Is the changing dimensions or changing to n-dimensions or general case usually useful?

[Anonymous No.14589269]

>>14589258
>Are there good heuristics to use that you could make a computer use?
Probably but that's up there with general artificial intelligence. Math is hard.

>Is the changing dimensions or changing to n-dimensions or general case usually useful?
Again, it's a good general line of questioning but this is not a very mathematically mature suggestion. Try learning some logic plus basic algebra, analysis, and topology.

[Anonymous No.14589470]

>>14573570
Just dropped by to say fuck you all, if you want to be a proffessor KYS

[Anonymous No.14589485]

I have never studied an actual rigorous proof-based course. I started one recently and whenever I see an exercise, my mind went blank. I literally have no idea how to proceed.
But when I check the solution it seems really obvious and I should have been able to do that in hindsight.
Anybody feels like this?

[Anonymous No.14589506]

>>14589269
Are additive or multiplicative digital roots neither trivial nor too complex structures?

[Anonymous No.14589510]

What's the math requirements that would get me in a finance company / fintech company?
I already know coding and have some took some engineer courses for statistics.

[Anonymous No.14589523]

Feels like half my department has gone off to work in quantitative finance. Kind of tempting.

[Anonymous No.14589529]

>>14589523
There are some people that make $300k a year working in finance.
If you still love anything else then just make enough money to retire early and then do whatever you like.

[Anonymous No.14589564]

>>14589485
Is it a specific intro-to-proofs course, or is it just your first course that uses them?

[Anonymous No.14589612]

>>14589564
It's my first course that uses them (analysis).

[Anonymous No.14589614]

>>14589485
normal at first, will go away with practice

[Anonymous No.14589700]

>>14589612
Then yeah it's normal to feel that way. My school had a specific intro-to-proofs course which was very helpful. You should probably get a textbook like How To Prove It (never actually read it, other anons might have better suggestions) and work through it on your own time. If the solutions you're reading seem really obvious to you, you're already in a good starting place

[Anonymous No.14589716]

H-Help me solve this... It's an incomplete frequency table

[Anonymous No.14590190]

Any good resources for geometric algebra visualizations?

[Anonymous No.14590325]

Vector Algebra War!!
https://www.youtube.com/watch?v=_AaOFCl2ihc

[Anonymous No.14590331]

>>14590325
100% Hamilton. Fuck the way we teach things. Hamilton was right.

[Anonymous No.14590347]

>>14590325
No worries, Cartan re-connected the universes.

[Anonymous No.14590349]

Is it better to not try and visualize tensors? Right now i just take them for what they are and if i need to use them i think of them as multilinear functionals.

[Anonymous No.14590353]

>>14590349
I can't understand tensors, a visual would help a lot

[Anonymous No.14590359]

Where can I find an English version of Die Lineale Ausdehnungslehre by Grassmann?

[Anonymous No.14590362]

>>14590353
Sorry, the way i know a tensor best is as an element of a tensor product, which is a vector space that arises when trying to associate a linear function to a multlinear one. It can also be seen as a multilinear functional of the dual spaces.

Visually i really dont have a good answer besides they transform in a certain way when coordinates are chosen.

[Anonymous No.14590406]

>>14590362
What does a multilinear functional of the dual spaces look like?

[Anonymous No.14590460]

>>14589523
I really am tempted to just go for it. I have the skillset and unironically enjoy SDEs. I just don't want to be worked hard (I'm a comfy government "worker')

[Anonymous No.14590933]

when did you last hug
https://www.youtube.com/watch?v=lHJxZ7JOEwI

[Anonymous No.14591101]

[Anonymous No.14591104]

>>14591101
Who's right here, fellas?

[Anonymous No.14591486]

[eqn] (a+b)^n=\sum_{k=0}^{n}\binom{n}{k}a^{k}b^{n-k} [/eqn]
Let [math] a=0 [/math] and [math] b=0 [/math]
[eqn] (0+0)^n=0^n=\sum_{k=0}^{n}\binom{n}{k}0^{k}0^{n-k}=0 [/eqn]
Let [math] n=0 [/math]
[eqn] 0^{0}=0 [/eqn]

Fuck your calculus.

[Anonymous No.14591506]

>>14591101
>>14591104
just graph it, they are probably the same and its just mathematica being retarded.
>>14591486
all you said was let 0^0=0. Then 0^0=0.

[Anonymous No.14591531]

>>14591506
>all you said was let 0^0=0. Then 0^0=0.
Technically, let [math] 0^{n}=0 [/math], then let [math] n=0 [/math] which gives [math] 0^{0}=0 [/math]. But all in all, you are absolutely right Watson.

[Anonymous No.14591535]

Do you get other people to draw the diagrams for you, or do you draw them yourself.

[Anonymous No.14591588]

>bomb first calc II exam on trig/parametric/polar/physics shit I don't care about
>mog in class in immediately and intuitively recognizing patterns and sequences, series, and convergence tests day 1 of the topic introduction.

Nice, I don't know why but this is much more fun, like the whole transition to advance math and discrete math courses were.

[Anonymous No.14591622]

>>14591588
I wish undergrads were banned.

[Anonymous No.14591685]

I'm trying to figure out if the following leads to anything more explicit thing.

[eqn] \bigg\{ \prod_{k=0}^{2n-2} \begin{bmatrix}
1 & z_{k+1} \\
y_k & 1+y_k z_{k+1}
\end{bmatrix} \bigg\} \begin{bmatrix}
1 & 0 \\
y_{2n} & 1
\end{bmatrix}[/eqn]

or, which is another form I've found to write it:

[eqn] \begin{bmatrix}
1 & 0 \\
y_{0} & 1
\end{bmatrix} \bigg\{ \prod_{k=1}^{2n-2} \begin{bmatrix}
1+z_k y_{k+1} & z_{k} \\
y_{k+1} & 1
\end{bmatrix} \bigg\}[/eqn]

where [math]z's[/math] and [math]y's[/math] are positive real functions.
I tried to figure out if any pattern comes up inside the product of matrices but so far no luck. My linear algebra is rusty. Any idea on what to do here?

[Anonymous No.14591693]

>>14591685
typo: second product ends at [math]2n-1[/math] not at [math]2n-2[/math]

[Anonymous No.14591773]

Is everything trivial?

[Anonymous No.14591830]

>>14591773
No. Things can be unsolved. Until they get resolved and become trivial.

[Anonymous No.14591838]

>>14591830
What is mathematical maturity?

[Anonymous No.14591883]

>>14591838
It’s a common word you’ll see that basically means experience. There is a kind of experience you accumulate as you, say, complete your first abstract algebra course that can be applied to your further endeavors. The kind of thinking that is applied when proving results is mirrored in many different areas of mathematics.

[Anonymous No.14591900]

>>14591622
Dude you're currently 1 click away from watching scat porn, don't think too highly of yourself.

[Anonymous No.14591941]

>>14591883
I don't really get it. And I don't think I'm going to get it.

[Anonymous No.14592075]

>>14591838
nobody knows. but its real, and its the biggest filter for anyone trying to learn higher math.

[Anonymous No.14592325]

>>14591838
Experience, but it's more than that. Intuition is also experience, but mathematical maturity is bit different. For example, most physicists I've interacted with have incredibly high mathematical intuition in what I would almost call shortcuts and 'tricks' in math especially calculus and differential equations and systems of equations. They typically can 'see' a very elegant and simple path in these sorts of problems.

On the flip side, they typically have no or little 'mathematical maturity'.

Mathematicians typically ascribe maturity to the level and ways you write and explain math. The more rigorous, exact, and tightly you write and explain math is a sign of that maturity. Double checking assumptions and making sure you are allowed to do what you are doing is also a sign of it.

It doesn't mean you are fast though and it doesn't mean you have a high intuition to math. A lot of math undergrads have okay mathematical rigor and maturity by the time they graduate, but absolutely shit intuition.

You really ideally need both mathematical maturity and intuition, but you rarely can grow both in a single undergrad degree. Because of this, math department choose to focus on rigor and maturity since they typically would rather you be right than fast and that you 'know' a few things rather than 'feel' many things

[Anonymous No.14592350]

Need recommendations for a cookie cutter introductory linear algebra textbook that is not Strang nor Axler. I have found both incredibly infuriating. I'm relearning the subject and both are heavily deviating from the standard progression of definitions I saw when I took it. Strang especially is such a mess.

[Anonymous No.14592389]

>>14592350
try Keith Nicholson

[Anonymous No.14592390]

>>14592350
and Grossman

[Anonymous No.14592515]

>>14592389
>Keith Nicholson
Marvelous, thank you x100 anon.

[Anonymous No.14592577]

>>14592515
no problem anon. I'm planning on relearn linear algebra someday again too and not just study to get rid off that class. Is one of those subjects worth learning well and thoroughly.

[Anonymous No.14592582]

>>14592350
Lay, Treil, Lax, Shafarevich, Kostrikin&Mannin

[Anonymous No.14593357]

>>14593356
>>14593356
>>14593356

[Anonymous No.14593912]

>>14574427
holy shit can one man get more based

[Anonymous No.14594084]

I'm running a little imageboard on my home computer where we talk about math puzzles and other stuff.
http://lambdaplusjs35padjaiz4jw2fugdoeutse%3262phqr72uf634s2wdbqd.onion/All/
http://l7jqnz3yfe2wtwietafoieadmgqbu%37dcmzmey63ktbjtxal3he4a.b32.i2p/All/