What are you reading today, /mg/?

# /mg/ - Math general

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Just doing some trig derivative problem sets, not too engaging but better than higher derivatives.

I’m doing an independent study on approximating pi, possibly converting it to hex/binary. Any good books on pi?

Refreshing Geometric Algebra and Calculus.

I plan to use some of its formalism in my next publication.

It's fascinating because I tried just using a Clifford algebra and quickly ran into issues that made it obvious that a discrete exterior calculus or the geometric calculus would be much simpler

I'm excited.

What do researchers here feel is the more popular/standard field? I tend to prefer the exterior calculus since the ties to differential geometry is already well developed, but the notation of geometric algebra appears to be really easy to work with.

Thoughts?

I was reading a parsing theory book and having trouble with a proof on (recursively defined) regular expressions' properties. Not sure if properly applying double induction.

**veekyforums.com**

All you need is basic set theory to get started.

I formally doubt this.**veekyforums.com**

i find algebra to be more fun

You mean abstract algebra?

For those of you who ascribe to ZF(C), would you care if it was proved to be inconsistent, or just continue using it?

If you cared enough to switch, what system would you use instead?

I formally doubt this.

It is true both formally and informally. It's better to start with topology rather than infecting your brain with stuff like "analysis" which you will ultimately have to purge if you wish to continue studying mathematics.

I have a feeling that you're trolling me so I will not follow your advice, sorry.

It being formally true is trivial. Just check any introductory book on topology. Some of the shittier ones use examples from "analysis", but that's about it.

Why do you doubt it? The only reason to """""need""""" anal before topo is that you can then say

oh this is why it works instead of some ridiculous inequality farce i saw earlier

when you see claims familiar from anal proved in a more general sense. It follows that is correct. Have fun studying topo!

I took an applied math thing but it's all Lagrangian and Hamiltonian systems and I keep getting bogged down in the physicsy things I don't need to know about. I'm becoming one of those people who can regurgitate enough to solve problems but can't understand what's going on.

I'm becoming one of those people who can regurgitate enough to solve problems but can't understand what's going on.

Congratulations! You are becoming a true applied "mathematician".

lmao category ""theorists"" eternally fuming out their arse because the analyst will get employed after their degree whilst they sit on Veeky Forums all day crying. HAHAHAHAHAHHAA

lmao category ""theorists"" eternally fuming out their arse because the analyst will get employed after their degree whilst they sit on Veeky Forums all day crying. HAHAHAHAHAHHAA

cringe

qê wants to be employed by the bourgeoisie

No wonder you can't handle the deep insights of category theorists.

Did you know category theorists were once banned(informally) from receiving NSF funding because they were huge cunts?

Sorry for misgendering.

a sociologically defined class, especially in contemporary times, referring to people with a certain cultural and financial capital belonging to the middle or upper stratum of the middle class: the upper (haute), middle (moyenne), and petty (petite) bourgeoisie (which are collectively designated "the Bourgeoisie"); an affluent and often opulent stratum of the middle class (capitalist class) who stand opposite the proletariat class.

Yes it is.

an affluent and often opulent stratum of the middle class (capitalist class) who stand opposite the proletariat class.

Not well-defined.

because

Your reasoning doesn't seem to make sense here, I'm assuming that's just on the surface level. Could you elaborate how you came to this deep conclusion?

The proletariat (/ˌproʊlJˈtɛəriət/ from Latin proletarius) is the class of wage-earners in a capitalist society whose only possession of significant material value is their labour-power (their ability to work). A member of such a class is a proletarian. In Marxist theory, a dictatorship of proletarians is for the proletariat, through the proletariat and by the proletariat. This, in Marxist theory, will lead to proletarian self abolition and, thus, communism.

Take the complement of this set.

This is just a bunch of gibberish, not a well-defined set. Some authors have even gone as far as to call it a "fictional set".

Some authors have even gone as far as to call it a "fictional set".

Is that like a "fictitious force" (i.e. actually not fictitious)?

Yes it is in anarcho-primitivist mathematics.

Is there not a set of humans? Is there not a set of people living in a country? Is there not a set of people living in a country and not owning the means of production?

The proper class of humans doesn't contain things which are fictional and not well-defined, i.e., terms/objects/entities such as "proletariat" and "means of production". It also doesn't contain "communists", but the only known proof of this uses "biology" which we don't discuss here.

The class of humans is in bijective correspondence with a subset of natural numbers, and thus a set. It follows that all those sets are well defined.

I'm trying to find a formula for the number of elements in P1(Z/nZ)

The number of elements in P1(Z/pZ) is obviously p+1 as you have p elements of the form (1:k) and then 1 element (0:1)

It's also obvious that Pn(Z/pZ) has 1+p+...+p^n elements for the same reason as the above.

If I can get a formula for just P1(Z/p^kZ) then I'm done as I can use the Chinese Remainder Theorem to get the answer for all n, but I'm lost trying to get any formula for this.

Any help?

modern algebra lecture

professor asks class to define the characteristic of a ring

classmate flips to the page in the book with the definition and paraphrases "It's the least positive integer n such that nx = 0 for all x in the ring."

I chime in and say that nx is not necessarily the same thing as n · x, nx is multiplication while n · x is summing x with itself n times.

professor says I'm being pedantic, multiplication is repeated addition. We move on.

as I'm sitting through the rest of the lecture, I think of the ring [math]M_{2}(\mathbb{Z}_{2})[/math].

you can sum the matrices in [math]M_{2}(\mathbb{Z}_{2})[/math], but you cannot multiply them by an integer.

didn't ask professor about this case because too much of a pussy.

Am I being autistic and pedantic, or was the definition given by my classmate valid? I usually don't win when I disagree with professors, but I would like to make sure that lies are not being taught in class.

nx is multiplication

In a ring this is usually written as x^n.

n · x

This is just the [math]\mathbb{Z}[/math]-module action on your ring, usually it is written as nx.

Follow up to this:

it seems the formula is p^k+p^(k-1)

or p^k(1+1/p)

This has confused me somewhat as for Z/4Z I think I can make 9 distinct elements, not 6:

(1:0) (1:1) (1:2) (1:3) (0:1) (0:2) (2:0) (2:1) (2:2)

Any help?

you can multiply the matrices in M2 by integers, that is scalar multilication. it's the same thing as adding a matrix to itself n times (or the additive inverse of that matrix)

Mathematics is (by definition) the study of TQFT and string theory and maybe some AQFT over exotic spacetimes.

seems like 0:1 and 0:2, 1:1 and 2:2 aren't distinct. 2:0 and 1:0 also but I don't know how you justify it

and maybe I just don't understand your terminology but if 2:2 != 1:1 aren't we talking about a cartesian product instead? i.e. Z X Zn

What scares me is that he is even talking about "multiplication" in a group theory context.

The operation nx of the ring isn't necessarily multiplication in the trivial sense.

That Prof is confusing his class.

yes it is, it's often not well-explained though. well-defined things just fit the labels you use for them, e.g. checking if a map is well-defined is the same as checking if it's actually a map.

How do you define the projective line over a commutative ring that is not a field?

Set theory student here. No one except philosophers and babies first logic class care about the consistency of ZF. The reason is that if ZF is inconsistent everything follows, so the only interesting case is when ZF is consistent. Thus that assumption is implicit when working ZF. Very few set theorists actually care or work with axiomatics, I took a grad set theory course with someone who did work with axiomatics and it was fucking painful. Hurr durr does this set exist well take the power set of the power set of the power set of this set and cut down with comprehension. I do work in effective theory so I could restrict ZF down to Kripke Platek (KP) set theory + omega and everything would carry through.

Ok, I see. The problem with the (algebro-)geometric definition is then that [math] \mathbb{P}^1(\mathbb{Z}/p) [/math] already has infinitely many elements - there are not only the points rational over [math]\mathbb{Z}/p[/math] but also other points. But if you restrict yourself to rational points, the question over [math]\mathbb{Z}/n[/math] for general n is somehow weird.

These are the rational points. But the Proj-construction generally gives more (closed) points (whose residue field is a proper extension field of the ground field).

But if you mean rational points - what do they mean over arbitrary Z/nZ.

Or do you mean something else by Proj? If you mod something out (set-theoretically) of some kind of R^2 you might get the correct object.

Does it matter where you get your undergrad degree? I go a decent public Uni and I am thinking of transferring to a more rigorous private school or an IV league.

some "decent" public universities have abysmal math programs, especially if you stay off the graduate track

this of course means transferring from such a school would be really hard, because everyone around you would have underlying knowledge that you lack

is right.

I go to what would be considered an ivy league school if it were in the states and the math program I'm in is a total joke. The honours stream is legit though and will actually prepare you for grad school. Research thoroughly the program you want to be admitted to regardless of the reputation of the uni.

I went to a pretty shitty undergrad institution but got into a Group I school for grad school. Get good letters of rec, and try to get your name on as many papers before you graduate as you can. I'd also recommend self-studying your dream school's curriculum if your current one isn't challenging you enough.

How did you cope? My courses are terrible so I self study the material from proper books, but having to do all this computational bullshit in the actual class is brutal.

I haven't started the math program at my school yet. I've completed all the Calc courses and am currently taking Differential Equations. At this point I'm a mathlet. Which is why I was wondering if I should transfer out before I even have the chance to be aware of how shit my school's curriculum is. I plan to self study anyway and to review Spitvaks Calculus book since my school uses Stewart. Could I still lack crucial underlying knowledge if I haven't even seen a real math course yet?

Thank you.

If you're not being challenged by the material, use it as an opportunity to work learning a new skill into it.

I took a cryptography course at my old school that wasn't hard, but it was extremely computation heavy. So I taught myself how to code and wrote methods to do all the long calculations for me.

Plotting on how to overthrow my upcoming calculus classes.

Algebra 2 person here, freshman, the only freshman in my class of all sophomores. I already raised the pits of Satan himself upon the class by smoking everyone, which is fun until our teacher counts everything off for not showing work, but hey, I might consider studying pre calculus over the summer just got the heck of it, that way I'll send the class into oblivion.

Then I'll just enjoy senior year.

What am I doing.

yes it is

That remains to be shown.

well-defined things just fit the labels you use for them

This is not well-defined.

you have to be 18 to post here I thought. If this isn't b8 tho just realize now that you aren't special and chances are you won't amount to anything like the overwhelming majority of the rest of us so try to understand that now so you don't end up being disappointed in the future.

Showing your work is what mathematics is. Don't be a brainlet by thinking you aren't one

apparently he talks about high school math (algebra/precalculus), not actual mathematics

Thanks for the recommendation. I'm taking a class in this and this book is really confusing.

take a look at the GRE's, that should give you some idea what you are supposed to learn. analysis and algebra are typically 3 semesters each.

How did you guys learn numerical/computational math? Any good books? Youtube?

This is the mathematics general. If you would like to discuss engineering please direct yourself to the engineering thread(s) on /toy/ and elsewhere.

Hey, can someone here answer my question? (**veekyforums.com**

Thank you!

Start with Spivak's calc on manifolds and Schutz's geometry in physics.

Kuhnel's curves surfaces manifolds, Spivak's differential geometry vol 1-2, Lee's smooth manifolds, Milnor's differential topology, Guillemin and Pollack's differential topology, Schlichenmaier's Riemann surfaces algebraic curves moduli spaces, Naber's gauge fields, Nakahara's geometry topology, Baez's gauge fields knots gravity, Gockeler and Schucker's differential geometry

Isnt Algebra 2 and Trigonometry precalculus? Trig is very easy if you can remember and visualize the unit circle and understand it. Precalc algebra is harder than trig

Schlichenmaier's Riemann surfaces algebraic curves moduli spaces

That book tries to cover way too much material and ends up not really giving any detail at all.

How can I show that every ideal is maximal in the non-standard integers [math]\underline{\mathbb{Z}}^\infty[/math]?

No one in engineering you mean? Why are you posting about that here?

tangible results

Try asking in the physics threads if you want "tangible" (i.e. understandable by the mentally impaired) results such as the existence of blacks holes and so on.

No need to get mad user.

I meant tangible in an abstract sense, as in lacking results within the field. How many useful connections have actually been made that weren't previously known though other techniques?

That's true. I included it because its short and gives a fair intro to complex geometry with good references. I thought about including Bott and Tu and Bredon as well but I think they're too involved.

Hey guys I'm a real brainlet when it comes to maths and am having some trouble trying to solve this problem I have. I want to find the coordinates of B and D in pic related. I have the coordinates of A and C currently and have calculated the length of each edge and the diagonal length.

The problem is it's a 3 dimensional object and it's on a reasonable angle such that A is much deeper than C.

If anyone could point me in the right direction of what they'd do next that would be super appreciated.

**amazon.com****amazon.com****amazon.com****amazon.com****amazon.com****amazon.com****ntrs.nasa.gov**

as in lacking results within the field

That's understandable since it's not a field about "results" in the usual sense.

How many useful connections have actually been made that weren't previously known though other techniques?

What is "useful" to you? Is pretty much the entirety of algebraic geometry, algebraic topology and homological algebra somehow not "useful" and "tangible"? In that case, maybe you should start using the physics threads over at /toy/? Although even their kind would laugh at you for openly claiming such things. So maybe /g/ would be a more suitable place?

Dugundji's

An old dusty Topology book. I knew that you were a troll, you can't do Topology without Analysis.

you can't do Topology without Analysis

No. You in particular can't do topology (with or without an*lysis) and that's understandable given the limits of your brain.

old dusty

Not an argument.

i knew that you were a troll

How am I a troll?

you can't do topology without anal

Yes you can. Anal serves as a source of examples of how topology can be applied to certain cases, but it is not needed for topology. You can't do linear algebra without analysis either because differential operators are linear?

This.

You say this as a person who did topology before analysis or are you just speculating because you feel like your mathematical maturity didn't play a role because you fail to realize it's importance and just focus on the analysis-aspects?

Not him, but he's completely correct and I'm saying this as someone who has never touched any branch of engineering (including analysis).

We used some anal stuff as examples when doing metric space stuff, for example Lipschitz continuity. Otherwise we had no use for anal.

Reddit spacing and reddit frogs are not welcome here. Try using proper websites for your kind, one example would be /r/catalog#s=eddit%2F.

"unironically"

Refer to the message above .

Errrrrrrrrrrrrr, nope.

If you can't pronounce shit like "homotopy" using only the fact that it's derived from Greek, you are not welcome here.

Reddit spacing and reddit frogs are not welcome here. Try using proper websites for your kind, one example would be /r/catalog#s=eddit%2F.

(You)

"unironically"

Refer to the message above .

(You)

Errrrrrrrrrrrrr, nope.

If you can't pronounce shit like "homotopy" using only the fact that it's derived from Greek, you are not welcome here.

No one gives a shit faggot. Go drink your soy milk you pathetic kike. You can play all the nintendo switch you want you limpwristed faggot no mudslime yuro or shitskin spic will ever accept you into their commie nigger club

I'm interested in Logic, Number theory, Proof theory and to a certain degree Probability theory.

I'm a physics major.

Using the common division, Algebra, Analysis and Geometry/Topology. Would Algebra be the right way to go?

Would Algebra be the right way to go?

In what sense are you interested in number theory if you have to ask this?

Suppose epsilon is smaller than 1 (otherwise, the set is empty or has very few elements). Then there is by archimedean property of the reals, there is some natural number q such that [math]\frac \epsilon 2 q>1[/math]. Hence [math]\frac{1}q<\frac \epsilon 2[/math]. Now, how many natural numbers p(and hence rational) are there such that p/q is smaller than 1? Hint: it's finite

All the things you are interested in are completely unrelated, and hence they require literally all the fields you mentioned

Studying for a functional analysis test and reading Rick Miranda's Algebraic Curves and Riemann Surfaces along with Milnor's Characteristic Classes. Miranda's book is a gem.

Vilfredo Pareto’s Manual of Political Economy.

Not mathematical enough desu senpai. I liked Irving Fisher’s mathematical investigations a bit more

Is pretty much the entirety of algebraic geometry, algebraic topology and homological algebra somehow not "useful" and "tangible"?

Of course those are not useful or tangible.

In what sense are you interested in number theory if you have to ask this?

Presumably the analytic sense.

Perhaps to a "computer ""scientist""" such as yourself. Refer to the /g/catalog#s=hetto%2F.

analytic

And why would he be posting about that in a mathematics thread? Presumably he has read the subject.

True. They're too abstract and untangible for me. I'm a black person by the way.

Mathematics is that which is studied in Mathematics departments in non-profit academic institutions

kys

old dusty

do you think theorems change over time, faggot-kun?

dust is also topologically invariant so just discard it

this fucking thread

We should just call it /shit/. Do you autistic losers EVER discuss mathematics? The thread is literally solid shitposting from post 1 to here.

Do you autistic losers EVER discuss mathematics? The thread is literally solid shitposting from post 1 to here.

Hey guys. What are some good algebraic topology books for black people? I find the usual references too hard and abstract for some strange reason.

What are some good algebraic topology books for black people?

It's not a book, but **freevideolectures.com**

the complement of the middle class is not the proletariat

unless you consider people like Gates, Trump, and Weinstein to be proles

you know what, fine, i like this definition

leftists are so funny sometimes

Is there not a set of humans?

no. there are only sets of sets. formally all that exists are sets. your entire premise is ill-conditionned

The class of humans is in bijective correspondence with a subset of natural numbers, and thus a set.

Dunning-Kruger: the post

it's in a ring context; they're talking about characteristics of rings

it's honestly perfectly fine

The Black Body is an ONTOLOGICAL condition. Ontology here is not in the Heideggerian sense of Dasein, but a social formation in which Being, as such, is determined by the system which produces it. Being, then, is defined by the outside. Who you are, or who you think you are, is irrelevant against the condition of Blackness. Blackness is the condition of a body which is labelled as inhuman, uncivilized, etc, and is the figure by which Civil Society is defined against. This opposition of Civil Society being everything which is NOT the Black Body is the way racism perpetuates itself in the status quo, and comes from a long tradition of slavery.

Middle class = petty bourgeoisie, high class or w/e it's called in English are the capitalists. Combine those and you get the non-proletariat.

Are we not sets of atoms in the end? Are atoms not sets of smaller stuff? Eventually we get down to some primitive notion.

What do you mean? There is an injective class function from the class of humans to the set of natural numbers.

petty bourgeoisie

high class

non-proletariat

all ill-defined

ESL

oh that explains it, you're just retarded.

Are we not sets of atoms in the end?

no, faggot

of course the literal communist posting in the math general has never been exposed to the most fundamental branch of mathematics

kindly kys

There is an injective class function from the class of humans to the set of natural numbers.

no there isn't. if you'd studied even the most rudimentary set theory or type theory you'd know this to not be the case. instead, you're content to copy and paste buzzwords from wikipedia to impress anonymous faggots on the worst thread on the worst board on Veeky Forums

the set of natural numbers.

The natural numbers object in "[math]\mathbf{Set}[/math]" can be shown to be a proper class.

He is actually correct if you assume that LEM is false.

you can't do topology without analysis.

this is kind of true in a sense, but really it's more like they're both intertwined.

think of the Jordan curve theorem for example. most of complex analysis is virtually impossible without it but you have to prove it topologically.

I wish. They are by @omnisucker (twitter). These three are the only ones which exist as far as I know.

no there isn't. if you'd studied even the most rudimentary set theory or type theory you'd know this to not be the case. instead, you're content to copy and paste buzzwords from wikipedia to impress anonymous faggots on the worst thread on the worst board on Veeky Forums

cringe

oh that explains it, you're just retarded

Speaking the same language as British island monkeys and Amerimutts makes you the retard here.

faggot

Why the homophobia?

of course the literal communist posting in the math general has never been exposed to the most fundamental branch of mathematics

You mean TQFT? That is not mathematics.

How is there not an injective class function? Collect all humans in a line and label them with consequent positive integers. What you end up is a function mapping every human to a unique natural number, and thus a function from a class to a set. Since it is injective, the class of humans must be a set.

he

Did I permit you to assume my gender?

this is kind of true in a sense, but really it's more like they're both intertwined

False. Anal is an application of algebra and topology.

The category of [math]\mathbb{R}\text{world}[/math] can be used as an example. Read Bourbaki's critique on Proudhon.

He is actually correct if you assume that LEM is false.

no he is not, as the "class" of humans is not a class of any type, neither a proper class nor a set

Literally this. Actually, you can even prove a meta-theorem that the definition of an exact sequence depends in a crucial way on analysis.

Speaking the same language as British island monkeys and Amerimutts makes you the retard here.

he said, in English.

Collect all humans in a line and label them

hahahahahHAHAHAHAHHAHAHAHHAHAHAAAAAAAAAAA

It's provably a type in the topos [math]D(\mathbf{Ho}(\infty\mathbf{Type}))[/math] which is definable if and only if LEM is provably false.

, you can even prove a meta-theorem that the definition of an exact sequence depends in a crucial way on analysis.

What do you mean?

I am not reading anything. I am doing a really tedious partial derivative Webassign before Spring Break.

It states that the notion of an exact sequence in an abelian category is undefinable without having the deep prior notion of an "integral".

I am doing a really tedious partial derivative Webassign before Spring Break.

Why did you decide to tell us about your non-mathematical activities?

I'm currently teaching myself abstract algebra.

Is it just me or do all of the interesting results in this field come from other, superior fields? number theory, polynomial algebra, combinatorics, etc.

superior fields

number theory

polynomial algebra

combinatorics

Nice b8, m8. I r8 8/8.

number theory

That's a branch of algebra.

polynomial algebra, combinatorics, etc.

Haven't heard of those. Not an expert in engineering.

Refer to /lit/ for the proper place to discuss such topics.

Refer to /x/ if you are unable to provide proof of your claims as per the burden of proof.

most of the less-obvious stuff to me, at least so far. e.g. the structure of a cyclic group is essentially derived from number theory. it's obvious that every group is isomorphic to a permutation group, but the features of permutation groups (e.g. parity) are much less obvious and are proved with more outside math.

compared to those kinds of results, stuff like lagrange's theorem seems really basic

I know I'm still in baby land but I wanna know if this pattern continues -- does most of the insight in abstract algebra stem from concrete examples?

Do you know what makes abstract algebra abstract? You abstract away redundancies like numbers.

structure of a cyclic group

lagrange's theorem

features of permutation groups (e.g. parity)

""results""

It's funny how high-schoolers always seem to be the ones writing such laughable posts and yet with a serious tone. I wanna know if this pattern continues -- do most of these people ever become self-aware enough to realize their own retardation?

not every group is isomorphic to a permutation group

every group *embeds in* a permutation group

consider: the order of a permutation group on a set of cardinality n is n!, but there are groups of each prime order

don't listen to the other anons. Group theory is trash. Better speed up to get to the juicy ring/module theory

Seconding the Lee recommendation, gr8 book altho it doesn't cover some areas of non-directly-manifold-related point-set topology, if you care about that)

Group theory is trash. Better speed up to get to the juicy ring/module theory

Oh, the irony...

Pure maff student here --any tips for an aspiring hs math teacher? I know it sounds gay, but I want to give kids the education I never received.

Where(which book) can I find levi civita tensors demonstrations in vectors? Like Ax(B.C), determinant, trace, det(I + kA), something like that, not the definition of index.

Not really mg material, but don't be that "cool" teacher. That shit killed my desire to show up for geometry. I might be biased though since I was a loner.

speed up

What do you mean? Are you implying that finite group theory is somehow a prerequisite for studying rings and modules?

I've often felt the same way but if I'm being honest with myself most people probably wouldn't appreciate the kind of education that I wish I'd had (i.e., most people are not autistic)

The books the topology guys are recommending you are find, though I would say they're probably going to be too advanced if you're fresh off Spivak (it's not there there's a formal prerequisite for lots of this, it's just you want more mathematical maturity first). It also makes some sense to do a good analysis book first, because such books will do some point set topology in a more simple concrete context, which helps when you generalize later when studying topology properly.

But before you do all that, it's really crucial you do some linear algebra next. It just shows up everywhere and it's a good way to build more mathematical maturity. Hoffman and Kunze is the best linear algebra book in my opinion, but there are lots of good options out there.

After this, for analysis, I think Pugh's book is excellent. Rudin is a more terse alternative with no pictures, so I like it less for self study (it does have good problems though). Since you mentioned Tao, Analysis I covers very similar material to Spivak, so you'd really want to start on Analysis II. After any of these you'd be more than ready to read a point set topology book if you want (Mendelson or Munkres for example).

There's lots of options out there for algebra, like Aluffi, Artin, or Dummit and Foote. I have no strong feelings on these, maybe someone else will.

I would say they're probably going to be too advanced if you're fresh off Spivak

Post disregarded. Try recruiting people into your organization elsewhere.

I have no strong feelings on these

You don't have any strong feelings on actual math and yet you seem to be an expert in "undergrad" "analysis" as you guys call it. Maybe you shouldn't be giving advice?

it's just you want more mathematical maturity first

And how exactly is someone supposed to develop it by doing engineering problems?

It also makes some sense to do a good analysis book first, because such books will do some point set topology in a more simple concrete context, which helps when you generalize later when studying topology properly.

He didn't state that he was a brainlet who requires crutches to understand simple concepts.

But before you do all that, it's really crucial you do some linear algebra next.

Linear algebra (the mathematical kind) requires basic ring theory and module theory, so it's advisable to learn those first.

After any of these you'd be more than ready to read a point set topology book if you want

He would be more than ready even without reading any of the poisonous garbage you recommended.

anime poster

Not even worth reading your shitty post. Why don't you fuck off to /a/ and stay there?

Not even worth reading your shitty post. Why don't you fuck off to /a/ and stay there?

Do you need to swear?

Your kind is not wanted here, simpleton. Proceed to /r/catalog#s=eddit%2F if you dislike the fact that this website is based on anime discussion.

Not necessarily, but if he's taking the usual abstract algebra sequence, then they always start with group theory

if you havent read all 9 volumes of dieudonne's treaties on analysis what exactly have you been doing with your time? hint: wasting it

someone mentioned that pic was good. pdf on author's website.

none, which is why you want a basis so badly

But what good is assuming you have a basis if you can't do anything else except assume it exists?

Every vector space has a basis by the AoC, I don't know what your problem is? you want an explicit basis?

Every vector space has a basis by the AoC, I don't know what your problem is?

So every vector space has a basis only if you assume it has a basis. What's the point in making such an assumption?

it is a useful one. Turns a "suppose you have a basis", to "let this set be a basis"

it is a useful one. Turns a "suppose you have a basis", to "let this set be a basis"

Useful for what? "suppose you have a basis" and "let this set be a basis" are functionally equivalent if you can only say "let this set be a basis" by assuming a basis exists.

Another poster interrupting - you might define "finite dimensional" without a basis: just take "generated by some finite subset" as your definition. Then definite "infinite dimensional" as "not finite dimensional".

Another poster interrupting - you might define "finite dimensional" without a basis: just take "generated by some finite subset" as your definition. Then definite "infinite dimensional" as "not finite dimensional".

I am not sure what you are trying to imply here.

All vector spaces are infinite dimensional which is why "infinite dimensional vector spaces" is redundant, and "generated by some finite subset" is not remotely equivalent to the definition of a basis.

Ok, I misunderstood your statement.

Can you give a proof that all vector spaces are infinite dimensional?

proof

Refer to /lit/ for the proper place to discuss such topics. I am sure you can find one in any of the standard references (e.g. proofwiki, vixra).

Can anything which is not "well-defined" be lifted to something "well-defined"? For example the function [math]f: \mathbb{Q} \to \mathbb{Z} [/math] defined by [math] f(\frac{a}{b})=a [/math] which is not "well-defined" since [math]\frac{1}{2}=\frac{2}{4}[/math] but [math]f(\frac{1}{2}) = 1[/math] and [math]f(\frac{2}{4})=2[/math], but can be lifted to a "well-defined" function [math] \tilde{f}: \{ \frac{a}{b} \mid a\in \mathbb{Z}, b\in \mathbb{Z}\backslash \{0\} \} \to \mathbb{Z}[/math].defined by [math] \tilde{f}(\frac{a}{b})=a [/math].

The formula you gave does define a relation, just not a function. What you can do is show that given an appropriate into the "domain" of the relation, the relational composition of that function with your relation is itself a function; this is your "lift". The function you'd compose with in this case would be (a, b) |-> a/b

Maybe look into applied math about something you care about? I am an electrical engayneer who likes machine learning so taking advanced linear algebra with someone who researched applied problems in signal processing/control theory was pretty cool. Of course if you don't give a shit about anything then pure math is cool too.

Things like this:

This is just from the first half the of the thread and I definitely skipped some. Basically, lots of trolling and elitism about branches of mathematics (inb4 somebody replies in a way that implies analysis isn't "true math"). I just wanna talk about math without 5 trolls responding to every post.

The set [math]\{(a^2,a^3,a^4) | a \in \mathbb C\}[/math] is algebraic since it's the vanishing of [math] (x^3 - y^2, x^2 - z) [/math], right? It's an exercise to find the Zariski closure of this set, and based on how far into the section it is it feels like it shouldn't be this obvious.

Ok, let's try this and see what happens.

I'm taking a geometric measure theory seminar this coming semester. Does anyone have any book recommendations, and have there been any recent interesting results to give me some idea of what's being worked on right now?

Does anyone have any book recommendations

The most boring kind of question, are Amazon reviews not enough? Especially when you can download nearly any book instantly

what is analytic number theory

what are elliptic curves

the absolute state of algebraists

the definition of a vector space nowhere implies the existence of a basis

go retake undergraduate linear algebra for the third time; maybe you'll learn something this time

All vector spaces are infinite dimensional

every day i browse this site i more quickly converge towards suicide

geometric measure theory

sorry, i thought you wanted to talk about math?

anyways guys what's you're favourite functor/co-functor pair?

Because of a failed jewish biologist spamming. He doesn't even understand what people are talking about here, but tries to act cool by "knowing" abstract non-sense.

Yeah, just take the equivalence class of being a certain number and project it down to the quotient, but don't expect it to be a homomorphism or anything

So is this the homework help thread?

Because I need some help with a statistics question.

I have to use the maximum likelihood rule to determine which classification and object belongs too.

There are two classes of objects, and each object has two measured features.

The question asks you to use the "Naïve Bayes classifier" which is no problem, but all of the examples I have for applying this have the constraint:

Objects are equally likely to be in class 1 or class 2 and are normally distributed.

For this question though, objects are still normally distributed, but objects in class 1 are twice as likely to appear as class 2.

my set of data looks something like:

class 1:

object 1: x=3.4 y=2.3

object 2: x=4.5 y=2.1

...

object 10 ...

class 2:

object 1: x=2.4 y=1.3

object 2: x=3.5 y=1.1

...

object 10 ...

where both sets are the same size. My question is just what do I need to adjust in my calculation to reflect the increased likelihood of being in class 1 vs class 2 if the data sets are the same size?

your reddit spacing and retarded way of explaining things makes it hard to understand what you want

I have never done anything like this before so you should have clarified some more

Objects are equally likely to be in class 1 or class 2

My question is just what do I need to adjust in my calculation to reflect the increased likelihood

my guess is you simply multiply with the probability

what exactly is the formula you use? I dont know what naive bayes means. so when you have a new object, to guess its class you compare the probability that it belongs tto class 1 or class 2. now if twice as many appear in class 2, you simply add the respective probability multipliers 1/3 for class 1 and 2/3 for class 2 and then pick the one with the higher probability for maximum likelihood

when both are equally likely both are multiplied by 1/2 and since it is the same you can ignore this factor

class 1 are twice as likely to appear as class 2

read that wrong

ultipliers 1/3 for class 1 and 2/3 for class 2

should obviously be switched, 2/3 for class 1 and 1/3 for class 2

Ok lads, I wanna be ready for the start of my PhD next September on algebraic number theory/geometry. Recommend me books or a certain progression to be absolutely prepared for anything by the time I get there. Assume I'll work all day starting June.

For Naive Bayes with Gaussian class conditional you need

a) priors for all classes given by b) Estimate the class conditional for each class by estimating the mean of the feature vectors. Since its Naive Bayer you don't need to estimate a full covariance for each class but only the variances for each feature in each class

so [math]dx[/math] is a purely symbolic representation and not an actual division of differentials?

Why does this work then?

[math]\dfrac{df}{dg} \times \dfrac{dg}{dx} = \dfrac{df}{dx} [/math]

Why does this also appear to work?

[math]f(x) = y[/math]

[math]f(x+dx) = y+dy[/math]

[math]f(x+dx) - y = dy[/math]

[math]f(x+dx) - f(x) = dy[/math]

[math]\dfrac{f(x+dx) - f(x)}{dx} = \dfrac{dy}{dx}[/math]

You need to think of it as an arbitrary change in value locally then all that makes sense

you can turn it into an actual division if you work in non-standard analysis

ultrapowers are neat

how hard would it be to learn multivariable calc on my own? ive just finished integration at uni.