/mg/ math general

Have fun bruh. I struggled with topology, too until we had to prove that RP^2 is homeomorphic to a disk glued to the boundary of a Mobius strip. Then something clicked and I started doing really well for the rest of that course.

youtu.be/8dKTYIJK5ek?t=3150

probably best to copy paste the url

Just started multivariable calculus today. Its cool

/out/ fag here. I've been messing around with the growing degree days concept in the garden. For those who don't know what I'm talking about, G.D.D. is a cumulative measure of temperature used to predict the life cycle of plants & animals.

I recently discovered that it takes around 190 G.D.D. for a sweet potato to form root nodules and to extend roots. Next, I want to track how many G.D.D. it takes for an alpine strawberry flower to become a ripe fruit. Hopefully, I can use the results to predict when I'll need to harvest without having to physically check the plants constantly.

Wouldn't you still need to check periodically to make sure there aren't any issues with development, insects, or soil conditions, I imagine there would be some extra unknowns that would fudge things a bit. What might be nice and fairly easy to do is make a program to keep track of local weather conditions (you could make a basic setup as well, get a some basic equipment to measure moisture, temperature, sunlight, and soil conditions in your garden, then have your computer track these variables to predict when the veggies should be ready to harvest and if there are any unforeseen issues.)

No it's not

recommend LA books for a retard pls

Go on and me about your superior intellict because youre studing graph-knot-ring-bullshit-fag theory and how much of a brainlet I am

Classical Mechanics is pretty much all symplectic geometry/topology at its roots.

Nope. Pretty retarded, right? It's because we have a prestigious med school so everything public health is top-tier and well-funded.
We're just now getting a data science program starting in Spring, and you can apparently use Biostats courses as electives for that. So that's what I'm gonna do I think.
Maybe I won't know as much about theoretical stats/probability (which is where my heart is) but I can graduate fast af and make a ton of money eh.

tell him you took the course and that you're better than his students

i have to take out of department classes in my grad school and you have to bully around the non math brainlets

>Classical Mechanics is pretty much all symplectic geometry/topology at its roots.
Mostly the symplectic geometry, the topology is the background material in which the stage is set. Topology does come up more in electrodynamics though, with the subject being likely the first intro to gauge theory/cohomology for most physics students.

I've been studying language theory and mathematical logic.

I seriously doubt authors on language theory books know how to prove a language has certain property because none of them writes a single proof of what they affirm; for instance, one author defines a language and then states that in each word of that language the number of a's is the same as that of b's and his two lines proof basically restates what he is supposed to prove.

>Mfw I see one of those "proofs"

Seeing this thread every week just reminds me of how much of a brainlet I am

I wish I could take maths but my passion is in mechanical engineering

Personally least favorite of all math courses for me and my lowest grade by far lol. Best of luck

youtube.com/watch?v=Ww4r9lN-2Xo

I'm trying learn about modal logic, multimodal logic, and epistemic logic.

It's basically about multiple agents having different knowledges about the same world.

Shit gets crazy when you get statements like A knows that B knows that A knows...

Then a temporal parameter is added where agents can exchange knowledge.

Most of the theory is built around having idealized agents that are perfectly logical and always truthful.

I'm trying to see what happens when you allow the agents to have imperfect logic and also allow them to lie because, let's be real, people can be dumb and people can lie.

From the ytmnd days
youtube.com/watch?v=2h6seJ3xjWA

How do you use it in classical mech? The only way is to use symplectic manifolds but that seems pretty stretched for an introductory class.

yeah but you need to define all sorts of things like tensors, differential forms, differential manifolds and so on to get to cohomology to get to the homogeneous Maxwell's equations [math]dF=0[/math].

Need some hints on proving that:
>G is a group with |G|>1 and the only subgroups of G being {G, {e}}
>Prove that |G| is a prime and thus finite
I CANNOT use cyclic groups in the proof.

>I imagine it's not TQFTs, GR, or condensed matter theory so seeing topology in physics seems a bit odd if not those subjects.
Topology plays a role in string theory, but then again what doesn't?

Can you use Lagrange's theorem?

Strang

...

There is a lot of years of pure math you can do that are still applicable to the real world. Algebraic geometry applied to coding is one that comes to mind, or topological optimization.

nope

t-thanks

WHY can you not use cyclic subgroups in the proof?

take any element [math]x \neq e[/math] from G
[math]\{ e, g, g^2, g^3, \dots \}[/math] is a subgroup of G

he said no cyclic groups

it's not if it is infinite
there are no inverses

The axiom of choice implies that |G| is actually not finite.

My professor specifically asked us to prove it "using everything we learnt this semester so far"
And we just started on abstract algebra

which did not include cyclic groups at the date the question is posted

how about you start listing the topics you've learnt so far you retard

see

cyclic groups are literally the first example of groups, are you meaning to tell me in this class you've only covered the definition of a group?

This question was posted 1 lecture before we started on cyclic groups

maybe so you could have scratched your head and derived it yourself, or so that you would do it after you did that lecture
well it's basically going to implicitly use cyclic groups, but:

Suppose G has more than one generator. Then each generator alone can create a different subgroup by multiplying it by itself. But the only subgroups are 0 and G, so either the generator is [math]e[/math] which by definition is not a generator, or the generator generates the whole group G. Therefore there is only one generator by contradiction.

Now if G is infinite, then if g is the generator, then g^2 is another generator. We can't have that so contradiction to G infinite.

So obviously, since g generates G, we have that |g|=|G|. Suppose |g|=pn with p prime. Then we can form a subgroup using the element g^p. But this subgroup must be either G or 0. If 0, then |G|=p, a prime. If G, then n=1 and hence |G|=p.

QED

Suppose first that [math]|G|= \infty[/math], and choose [math]g \neq e[/math] such that [math]g^2 \neq e[/math], and define [math]H = \{ g^{2n}\ |\ n \in \mathbb{Z} \}[/math] to get a subgroup [math]0 < H < G[/math], thus contradicting the assumption, so [math]|G| < \infty[/math]. Let then [math]p[/math] be a prime number dividing [math]|G|[/math]. We can then use Cauchy's theorem:
>Given a finite group [math]G[/math] and a prime number [math]p[/math] dividing the order of [math]G[/math], then there exists a subgroup of order [math]p[/math] in [math]G[/math]
Let [math]H[/math] be the subgroup given by Cauchy. Clearly [math]0 < H[/math], so we must, by assumption, have [math]H=G \Rightarrow |G|=|H|=p[/math].

...

Well, you learned about subgroups.
Show that for any g in G, Cg:={g^n ; n in Z} is a subgroup.

Now for g=/=e (you can do that since |G|>1) you obviously have that Cg is different from {e}. Therefore, from the hypothesis it must be that ****** Cg=G *****.

If G(=Cg) was infinite then you get that for k=/=0,1 Cg^k={(g^k)^n ; n in Z} is a proper and non-trivial subgroup of Cg(=G). From the hypothesis, this cannot happen. Therefore G must be finite.

Now let |G|=:n for some n>1.
Suppose n was not prime, say n=st with both s and t different from 1.
Take the element g^s.
{(g^s)^i ; i in Z} is a subgroup of Cg(=G).
Show that this subgroup is different from G and {e}.
.
.
.

Consider the set of all 6x6 complex matrices such that they have 2 eigenvalues λ and μ, where λ has algebraic multiplicity 4 and geometric multiplicity 2, and μ has algebraic multiplicity 2 and geometric multiplicity 1.

How does one clasify these matrices up to similarity?

My attempt:
We find the possible Jordan forms.
The μ part can be either {{1,1},{0,μ}} or {{μ,0},{0,μ}} and the only acceptable one is the first one because the second one gives geometric multiplicity 2.
Therefore, the number of similarity classes, are completely determined by the λ part.
Now for the λ part we have 5 possible cases:
a 4x4 block,
a 3x3 block and a 1x1 block,
a 2x2 two 1x1s, two 2x2s,
four 1x1s (diagonal).
The diagonal case gets rejected for the same reason as {{μ,0},{0,μ}}.
But, what about the other cases?

So recently one of the exces at IBM talking about watson and that in the future there wont be programmers or people who program computers, instead they will teach and train computers like students.
Anyways, I've been meaning to learn more about what they use to be able tho do things like this and wondering would I if I work through one of the popular textbooks with either "machine learning" or "data mining" in the title or is there something more to it besides that?

Someone answered
thanks anyway

From the last thread:
What is the value of [math]^ii[/math]

Research grants.

What does that notation mean?

tetration

Hey guys, [math]\mathbb{Z} _{12}[/math] (mod 12) is NOT a manifold right? just making sure..

Z_{12} with what topology?

well idk...how would you define open sets on [math]\mathbb{Z}_{12}[/math]? Can you even do that?

Trivial or discrete topology for example.

It is a zero dimensional manifold with the obvious topology.

Coinduced by the projection [math]\pi \colon \mathbb{Z} \to \mathbb{Z}_{12}[/math], [math]n \mapsto [n]_{12}[/math]. You can show this makes it a discrete space of 12 points, so it is
>Hausdorff
>second countable
>every point has a nbd homeomorphic to [math]\mathbb{R}^0[/math]
making it a 0-manifold.

wow...so it can even be made into a smooth manifold?

im asking because i wanna know if its possible for [math](\mathbb{Z}_{12},+)[/math] to be a Lie group.

Thermodynamics in biochem

Pretty much plug and chug

>free energy

What do you lads think of Khan Academy? I've been using to to learn differential and integral calculus while supplementing the lack of proof and whatnot with books and I find it's going well. I'm preparing for 1st year of uni in a few weeks and I'm supposed to be familiar with diff and integral calculus as well as basic proofs. Is this the right route?

khan academy is great for proofless math so its certainly a good tool for learning calculus
my gut tells me that analysis is not a good entry point for learning how to prove stuff
at my uni our discrete math class served as a de facto intro to proofs, a subject much more managable at least in it's elementary phase

please respond

It's cumbersome but worth it as it gives you info on the properties of the solutions of your equations
[math]^ii=e^{-\frac{1}{2}\pi}[/math]

Trying to get some intuition for Kan extensions. They subsume pretty much all of algebraic mathematics and that makes them really fun

How much point-set topology should I know before starting out with algebraic topology? I should be mostly fine on the categorical/algebraic part, but I haven't studied topology yet.
And what are some good introductory books on it?

Faggot

You should know about continuity, homeomorphisms, compactness, and connectedness. I would suggest reading Munkres chapters 2, 3, and 4 for this.

>Faggot
Why the homophobia?

This, although topology is like linear algebra, it never hurts to know more random topology facts.

Also don't skip the quotients section/chapter. It's not optional if you're doing algebraic topology.

9185692

what is i^i?

Book recommendations for stochastic processes? (Nothing super advanced, intro grad level)

that is [math]i^i[/math] if i'm not mistaken

Bump

found the anti-intellectual conservitard

Fuck off to

>tfw going to switch over to study stats and probability instead of pure math
Too worried about getting a job and earning money

Trying to wrap my head around Igusa local zeta functions. Its difficult, cause with these kinds of niche topics there's not a lot of literature. Also the lit. that exists is written for those 'in-the-know', so you have to piece things together from multiple sources.

This year ill finish my master and submit for publication a combinatorial style shit-paper on representation "theory" i got sick of already. What kind of math should i pick for my phd that rather deep and beautiful but have as lowest amount of calculations and hand-work as possible? Some ncatlab/homotopy stuff? Or more geometr-ish fields will do better?

Algebraic geometry.

number theory or mathematical logic, particularly model theory

>Number theory
>low number of calculations
?

can [math](\mathbb{Z}_{12},+_{\mathbb{Z}})[/math] be turned into a Lie group?

Sub-group of the circle group consisting of the 12th roots of unity?

wait what?

Of what kind?

why not just applied math?

holy shit could you be more assblasted?

Aww yeahhh, just bought Stewart's "Calculus: early transcendentals." Very stoked. Never took calc in undergrad.

i'm teaching based on that text right now. gl!!

Isn't Steward's book too handwavy?