/mg/ - Math General

In this case the requirements are various linear algebra, calculus, abstract algebra, analysis, discrete math and some theoretical statistics. Then for electives you can take stuff like combinatorics, cryptography, differential equations, topology, optimization, stochastics, etc.

What are /mg/'s plans for the future? I'm in my last year of undergrad and because of how the system works here, I'm used to everything being streamlined for me and not having to make any decision, but now I have to start thinking about getting a master's and I'm pretty fucking scared.
Also, I don't know what my proffessional future holds, because I don't know if I'm cut for academia, so I don't know what master's to pick. So what about you guys?

I'm going to get a job and do a masters in statistics part time. Hopefully I can get a job somewhere that will pay for my masters. Don't care about academia.

Read 'the Secrets of mental math".

>What are /mg/'s plans for the future?
I will never discover anything interesting, I will never prove anything impressive, I will never amount to anything. I think my plans have been made for me, and the choice is simple: live like a dirt-eating maggot, or suicide.

>I will never discover anything interesting, I will never prove anything impressive, I will never amount to anything. I think my plans have been made for me, and the choice is simple: live like a dirt-eating maggot, or suicide.
cringe

kek
I like this guy

>using the word cringe
cringe

Shit weeb artstyle and autism

/wild/ edition of /mg/

user, do you realize what you've done?!

I feel as a physicist completely down when I read a physics book. I mean, it's even that hard to learn real anal, but in something like electromagneticism, they just go and do whatever they want with notation and formalism. Heck, I had to properly derive a formal description for the electric field. I feel like this shit isn't for me, but I love physics more than math, still, I can't stand how physicists go about it. Wat do Veeky Forums?

It's not even*

brehs what is this

Cave-mathematicians

They were here.

If you like physics for the pretty and elegant formalism and theorems then you probably shouldn't be a physicist, do learn physics, but the cutting edge of research isn't beautiful theorems, concepts, or elegant formalism, it's dirty and messy and cutthroat. When it comes to physics you'll rarely have exact solutions, rarely have nice, well behaved equations that are easy to analyze (nonlinear pdes will fuck you up), the systems can and will be horrendous, and it's possible all your ideas will be bunk or people just won't give a shit. Look, physics can be hard, really hard, jackson's EM book is proof of that (basically a shit load of pdes that are really difficult to solve), you've just gotta have the stomach to get your hands dirty and swath through pages and pages of calculations. This is not to dissimilar to mathematics, though since math has no need to be subordinate to reality there are more elegant structures at the forefront ready to be explored, some of these do have relevance to physics, (this is mathematical physics for the most part, or at least fields interacting with this discipline) some of the fields connected to math phys are harmonic analysis, operator theory, algebraic geometry, diff geo, representation theory, number theory, dynamical systems/ergodic theory, functional analysis, complex analysis, algebraic topology, homological algebra...actually most math can be made relevant to physics in one way or another, so you might as well go the route of an applied mathematician or working in analysis/geometry.

> applied mathematician
No such thing.

What do you mean?

That "applied mathematics" is a vacuous, ill-defined term. Not going to have this discussion again. Read through the previous thread.

>That "applied mathematics" is a vacuous, ill-defined term
What? It's a pretty standard term

en.wikipedia.org/wiki/Applied_mathematics

What else would you call what applied mathematicians do?

>reddit

>spacing

Is this better?

What? It's a pretty standard term
en.wikipedia.org/wiki/Applied_mathematics
What else would you call what applied mathematicians do?

is there a good online degree/course for number theory?

it's a list of the genders you fucking bigot

Much better.

So what would you call what applied mathematicians do?

See

I didn't ask about applied mathematics, I asked what you would call what applied mathematicians do.

Or was quoting that post of yours meant to imply that you would call it applied mathematics but just don't like to?

I wouldn't call it anything, because the set of "applied mathematicians" does't exist. Membership in that set is ill-defined.

What's wrong with the definition here?

bls.gov/ooh/Math/Mathematicians.htm#tab-2

>Some mathematicians apply theories and techniques, such as mathematical modeling, to solve practical problems. These mathematicians, sometimes known as applied mathematicians, typically work with individuals in other occupations to solve these problems.

>double

>new line spacing

Who are you quoting?

You appear to be blind. Please go see an ophthalmologist.

>You appear to be blind.

Who wrote "double" or "new line spacing"? I don't see it in any posts you replied to.

Is this better?

What's wrong with the definition here?
bls.gov/ooh/Math/Mathematicians.htm#tab-2
>Some mathematicians apply theories and techniques, such as mathematical modeling, to solve practical problems. These mathematicians, sometimes known as applied mathematicians, typically work with individuals in other occupations to solve these problems.

What's wrong with the line spacing? It looks like he/she is formatting the same way you are?

>I am so dumb I cannot parse mock-paraphrasing and satiric explications

What did 'double' and "new line spacing" paraphrase?

And why do you use quotation arrows when you're not quoting anyone? It seems it would just take extra effort to type your message that way

First day on Veeky Forums huh

See
(nice plebbit spacing btw)

I've been here quite a while, but I just don't see what 'double' and "new line spacing" were 'mock-paraphrasing'.

Nor do I see what this has to do with your confusion about applied mathematics and applied mathematicians.

What exactly makes a gap between paragraphs 'plebbit spacing'?

This formatting is common on probably every board on Veeky Forums you take a look at, and has been for years, it just increases legibility.

There's a reason there's a rule against
> indecipherable text (example: "lol u tk him 2da bar|?")

Go back to already.

Why do you make claims about applied mathematics and post formatting that you don't want to explain?

Who is a member of SIAM (Society for Industrial and Applied Mathematics) if not applied mathematicians?

siam.org/

>ftw don't want to ask the following in /sqt/
Let [math]\phi:G \rightarrow H, \psi: H \rightarrow K[/math] be morphisms in a category of products and let [math]\phi \times \phi: G\times G \rightarrow H\times H, \psi \times \psi: H\times H \rightarrow K \times K[/math]
I need to conclude that [math](\psi \phi)\times (\psi \phi) = (\psi \times \psi)(\phi \times \phi)[/math]
So, [math]\psi\phi:G \rightarrow K[/math] uniquely determines morphism [math](\psi \phi)\times (\psi \phi)[/math] as [math]K \times K[/math] is a product in this category. Since [math](\psi \times \psi)(\phi \times \phi): G \times G \rightarrow K \times K[/math], can I conclude that uniqueness of morphism from [math]G \times G[/math] to [math]K \times K[/math] forces [math](\psi \phi)\times (\psi \phi) = (\psi \times \psi)(\phi \times \phi)[/math] ?

How do I become a human calculator to impress my friends? Brainlets like it when I can multiply triple digit numbers in under a minute. Any resources to do faster mental math?

Due to the UMP of [math]K \times K [/math] as a product this morphism is indeed unique, I think

Let [math]p_H\colon H\times H\to H, p_K\colon K\times K[/math] be projections onto the first object. We then have these equations: [math]p_K((\psi\varphi)\times(\psi\varphi)=\psi\varphi=\psi p_H(\varphi\times\varphi)[/math] and [math]p_K(\psi\times\psi)(\varphi\times\varphi)=\psi p_H(\varphi\times\varphi)[/math], by commutativity. The same holds for the other projections, so the same unique arrow makes the whole diagram commute, but so [math](\psi\times\psi)(\varphi\times\varphi), (\psi\varphi)\times(\psi\varphi)[/math].

[math]p_K\colon K\times K\to K[/math] and [math](\psi\times\psi)(\varphi\times\varphi), (\psi\varphi)\times(\psi\varphi)[/math] I'm retarded

Nice latexing retard.

Any good guides for writing actual morphism diagrams in [math] \LaTeX [/math]?

I know.

make them in paint then add the .png file to your latex workspace

No, I mean native support. I can always draw them in inkscape and add the .svg to the document but that's not what I'm interested in.

>What are you S T U D Y I N G today?
I'm studying mathematics without "real" numbers right now.

What happens when the unstoppable mouse runs into the immovable kitten?

I am stuck on a question about the number of walks between two distinct vertices in a complete graph. The answer according to the book is n^2 - 3n + 3 but I can't for the life of me figure out how to get there.

n being?

Amount of vertices, sorry forgot to mention that, and probably n>3 or something, dont have the book open right now

tried induction?

mfw user trolled the fuck out of the "that's reddit spacing!" /pol/nigger by using an /s4s/ meme

objectively wrong

You can't do it within [math]\LaTeX[/math] directly (i.e. without a package for commutative diagrams). There's a few old guides if you look around. However you should be aware that a lot of the older guides mainly talk about older crappier ways of generating commutative diagrams (and you should also know that said packages still have a userbase due to old mathfags who got used to them).

The modern way to do it is through the commutative diagram package for tikz. Just add:
\usepackage{tikz}
\usetikzlibrary{cd}
To your preamble. The manual can be found at:
ctan.math.washington.edu/tex-archive/graphics/pgf/contrib/tikz-cd/tikz-cd-doc.pdf

The concept and syntax format looks complicated at first but it's actually really simple. Basically:
>Imagine the objects in your diagram as sitting in a matrix.
>Then imagine your arrows starting at one cell and going to another one (e.g. from the cell of object A go right, right, and down for the end cell)
>Arrows have options on them that allow you to give them a label (text that will appear next to the arrow) and an orientation (which way the arrow curves) among other things).
So in the syntax your matrix is column separated by & and row separated by \\ then in each cell you write the object that lives there and a list of arrows starting there, eg.
>A \arrow[d, "f"] \arrow[rd] \arrow[rrd] \arrow[r, "g"]
is a cell with an object "A" and four arrows going to different cells (rrd means "right, right, down"), some containing labels.

Advanced options allow you to do fancy arrow paths, name objects and create arrows between them, name arrows and create arrows between arrows, etc...

Don't do this.

Daily reminder that "applied mathematician" is vacuous and ill-defined.

Frickin' cute!

I'm having a problem with a question in a graph theory entry level book, I already made a thread but I figure it'll be twice as fast posting it here. Anyway, in case there are some experts (though I doubt you need to be one), here goes.

How do I go about proving that a graph with order n and minimum degree (n-2) has VERTEX connectivity (n-2) as well?

I mean I know, intuitively that if I delete a certain number of vertices and end up with 2 or more components, then each component must contain a vertex u that had degree n-2 in the initial graph, and one other component must contain the one vertex v that wasn't it his neighbourhood. And since these two vertices have the same neighborhood with n-2 vertices, you'd have to delete all of them for there not to exist a path between u and v.
However this seems far fetched and I don't really know how to write the first part formally.
Is there a simpler proof I'm missing? The exercise is literally at the beginning of the book and all the proofs seem much easier.

But since there are like 5 people on Veeky Forums currently, I'm guessing I'm gonna get the same people anyways.

>Daily reminder that "applied mathematician" is vacuous and ill-defined.
applied mathematician: one who works in the branch of applied mathematics

applied mathematics: mathematics applied to non-mathematical domains

>vacuous and ill-defined.
youtube.com/watch?v=yetwdpsiM8Q

>applied mathematics
No such thing actually exists.

but who are you quoting?

see

>No such thing actually exists.
What is biomathematics then?

en.wikipedia.org/wiki/Mathematical_and_theoretical_biology

>Mathematical biology aims at the mathematical representation, treatment and modeling of biological processes, using techniques and tools of applied mathematics.

>What is biomathematics then?
Apparently something which "uses" something nonexistent.

It sounds like Wikipedia could make great use of you as an editor

Many articles mention this allegedly fictional area of study

I don't use websites such as "Wikipedia" so I wouldn't know.

Do you read any math journals?

scirp.org/journal/am/
> Applied Mathematics

I do, but I simply ignore the parts where they talk about fictional stuff. I'll just read some fiction if I'm interested in that.

So can we define applied mathematics as the mathematics you consider fictional?

>mathematics applied to non-mathematical domains
is not mathematics. Mathematics is the study of mathematical structures. Applying the results obtained by studying mathematical structures to non-mathematical domains is not a study of mathematical structures, hence not mathematics. Or in short, applications of mathematics [math] \neq [/math] mathematics.

You cannot define applied mathematics as a subfield of mathematics for any sensible definition of mathematics.

Errata: applied mathematics [math] \not\subset [/math] mathematics.

>You cannot define applied mathematics as a subfield of mathematics for any sensible definition of mathematics.
What do you mean? 'Applied' is just a modifier, it separates mathematics into applied mathematics and non-applied (pure) mathematics.

What sensible definition of mathematics do you propose?

Now, say, [math] if [/math] you think about mathematics as a practice, concretely, as the application of results obtained by studying mathematical structures, then [math] all [/math] mathematics is applied mathematics.
You're spouting words but you're saying nothing. Define that separation. What does "applied" modify and how does it modify it?

>What does "applied" modify and how does it modify it?
It modifies mathematics, specifying the subset of mathematics dealing with applications of mathematics to fields other than mathematics

How can you define mathematics in terms of 'mathematical structures', a term which depends on mathematics?

>applications of mathematics to fields other than mathematics
is not a
>subset of mathematics

pure mathematics
>Mathematics which yield applications within mathematics (i.e. mathematics for the sake of mathematics).

applied mathematics
>Mathematics which yield applications outside mathematics (i.e. mathematics for the sake of something else).

Heuristically speaking pure mathematicians care about more general results (at a higher level of abstraction) while applied mathematicians care about more specialized results (at a lower level of abstraction).

How so?

You either apply mathematics techniques within the context of mathematics alone or you don't, when you don't it's applied mathematics.

>Mathematics is the study of mathematical structures.
Define 'mathematical structures'.

A mathematical structure is an object whose essential properties are exhausted by its formal definition. Synonymic terms: a platonic Form or Idea.

>A mathematical structure is an object whose essential properties are exhausted by its formal definition.
How does one prove something is a mathematical structure?