What are you learning, /mg/?

# /mg/ - Math general

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What are some applications of vector spaces which do not have a basis?

everything i should have in the last 2 months since my exams are next week

>want to keep working on first semester modern algebra homework

>can't because too fucking worried about my operations research grade

>professor assigned our second exam online last week

>exam was open book, open notes. instructions were to print, complete, scan, submit in a 2hr 15min period.

>finished on saturday morning (two days ago).

>received grades this afternoon

>0/100

>my 98.8% average dropped to a 64.5%.

>have no fucking clue what went wrong.

>there is no way I missed every single question on the exam

>either I submitted the wrong pdf (I don't think I did that, I remember double-checking) or I am suspected of cheating (which I didn't do).

>worst case scenario, it was a bug in our open source online homework platform

>I have fought against such bugs before, it rarely ends in my favor

>swear to fucking god I'll withrdraw from enrollment and join the navy if this doesn't end well. I am tired of playing the online student game as a resident student.

I have no fucking idea what I should do, short of talking to the prof during his office hours tomorrow. Should I talk to my advisor? He's respected in the department. Would he be able to help if this goes south?

Every vector space has a basis.

On the other hand, not every module has a basis (i.e. not every module is free).

>asking Veeky Forums for irl advice

He's a subhuman shitposter. Don't reply to him.

People like you are why sci sucks.

/mg/ is not the same as /b/, my dude. I've received solid advice from Veeky Forums before.

no u

Lurk or read the archive before posting, idiot.

Theorem: Proof.

QED.

∎

Email the professor ASAP.

Don't reply to the spammer.

congesting /mg/ with pointless arguments

What are you learning, /mg/?

not >Crucify the shitposter and repliers, /mg/

this

especially if you can remember your answers, if even one is right, it means you hit a buggu

Yes I just barely passed my calc 1 class and am barely passing calc 2

>Every vector space has a basis.

ZFC + ¬AC begs to differ.

Fugg I meant ZF + ¬AC lol

to be fair, ZFC + ¬AC also proves that some vector spaces don't have bases (:

Even in ZFC most vectorspaces don't have bases unless you assume they do

One of the biggest sources of difficulty in math is bad learning habits. People get used to not actually understanding what they're doing, and then they forget what actually understanding something is like in the context of math, and then their ability to learn math at all atrophies, because learning requires you to be able to actively engage in a process of fixing what you don't get.

Semirelated quote:

>Don't just read it; fight it! Ask your own question, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical special case? What about the degenerate cases? Where does the proof use the hypothesis?

Working in the context of ZF, the axiom of choice is provably equivalent to the statement that every vector space has a basis. Therefore, it is true in ZFC that every vector space has a basis—the assumption you mention is precisely the C in ZFC.

>Therefore, it is true in ZFC that every vector space has a basis—the assumption you mention is precisely the C in ZFC.

Right, like I said, they don't have a bases unless you assume they do

Yes, you are correct.

I think you meant ZF and not ZFC then buddy

Don't feed the trolls.

thank you user, I'll think about that

>I think you meant ZF and not ZFC then buddy

Choice and existence of bases are equivalent in the category of axioms (i.e. isomorphic objects), just labelled differently like [math] \frac{1}{2}=\frac{2}{4} [/math]

Good luck!

>ksi

dropped

PDEs

I'm glad this is the last pure math course I ever have to take ;_;

Category Theory**github.com**

I'm confused user. What do you think happens in applied math?

What's a good source to learn finite calcul us?

Numerical solutions, what else?

Seperating math into "applied", "pure", "whatever", was a bad idea imo. Applied math is mostly considered to be anything that is concerned with PDEs and of course numerics. But numerics is not just using big calculators, the theoretical aspects of it are usually more complicated than a lot of "pure" stuff since you need a lot of different concepts from other fields like analysis, (metric) topology, combinatorics, graph theory...

Unless you don't study proper math, then yes, applied math is literally using calculators.

What is categorized as pure math

Am I an applied math or pure mathematician

>Seperating math into "applied", "pure", "whatever", was a bad idea imo.

You can't separate something which is not well-defined.

>Unless you don't study proper math

I'm an engineer

K, then you can probably relax a little in your applied math courses.

Really brings my neuronal schlongers into swinging motion. Also yes.

>What is categorized as pure math

Usually everything that is not PDEs, numerics, stochastics, statistics. It's stupid though.

My rule is that if the professor uses the word "theorem," it's pure math.

Please respond

>applied math

No such thing.

>math

No such thing.

This is a legal game of Connect Four. After some experimentation, I found a sequence of play (encoded as the natural number 2167127614743451375325622663157315723654) which ends with the second player (yellow) winning.

What's slightly interesting about this is that it illustrates how a /legal/ (although certainly not typical in "normal" play!) game may conclude with multiple "fours", obtained all at once, by the winning player. It also calls attention to the central importance of the game's center column, and especially the board's central two cells. Consider that in principle, either such cell may participate in one of thirteen game-winning four-in-a-rows; here, the winning move simultaneously generates eleven distinct fours in the same blow. The result is the more interesting in that upon inspection the board-state given happens to show the conclusion of a legal game (which may be reached by multiple distinct games, of course).

I've stopped using khanacademy as a learning tool and I've found myself at a faster pace by using just a textbook, Paul's Online Math Notes, Professor Leonard and profrobob's youtube tutorials.

How long would it take for me to get to calculus? I am currently on Algebra II factoring.

Does a functor mapping spectra to (to the equivalence classes of) their Postnikov towers serve any purpose?

Math simply, platonically, Is. Xie doesn't exist to entertain you.

That's retarded.

>you guys are fucking lucky.

must be why people here talk about killing themselves so often huh

>must be why people here talk about killing themselves so often huh

That's just one of the female regulars

Applied math is math being used for real-world applications. Pure math is math for its own sake. The latter often grows out of the former, for example geometry came about because of a practical need in construction and land measurement, but when Euclid wrote his elements the primary concern was the mathematical objects and structures themselves.

It's so tempting~

pure maths is for smart people

applied maths is where brainlets are redirected by default when they have less than a 4.0

>What are you learning, /mg/?

Not a single thing in mathematics implies intelligence. I wouldn't be surprised if the regulars here were mostly people who just memorize theorems and definitions for exams and then forget them, never understanding the stuff. This would explain why these threads are full of failures posting about categorical stuff and thinking they are cool, but really their posts are just barrages of buzzwords without any real content. An example of such a post would be as a reply to a legit question. These failures come together to these threads to post the same stuff every time, and some unlucky and innocent people fall for their traps every time, or are the other losers and start a shitpost fest by replying to them just for the sake of shitposting. Smartness isn't just having a high IQ, but also about being able to use it for something. These people may have almost 120 points as their scores, but for all mankind they have contributed nothing. This should itself prove you don't need to be smart to study math. On the other hand, your submissive attitude makes me think it is better for you to simply stop trying or even breathing, as you would only get trampled by people with stronger wills.

>Not a single thing in mathematics implies intelligence. I wouldn't be surprised if the regulars here were mostly people who just memorize theorems and definitions for exams and then forget them, never understanding the stuff. This would explain why these threads are full of failures posting about categorical stuff and thinking they are cool, but really their posts are just barrages of buzzwords without any real content. An example of such a post would be as a reply to a legit question. These failures come together to these threads to post the same stuff every time, and some unlucky and innocent people fall for their traps every time, or are the other losers and start a shitpost fest by replying to them just for the sake of shitposting. Smartness isn't just having a high IQ, but also about being able to use it for something. These people may have almost 120 points as their scores, but for all mankind they have contributed nothing. This should itself prove you don't need to be smart to study math. On the other hand, your submissive attitude makes me think it is better for you to simply stop trying or even breathing, as you would only get trampled by people with stronger wills.

cringe

then why do math and physics graduates have higher average IQ than other fields?

lang basic math

sometimes, it's better to ask anons on Veeky Forums, then friends and family. Actually Veeky Forums is a great place to ask irl questions, bc, literally there are thousands of people, who definitely know more than your family,who are much smarter, who work and study in many many different professions, who can unselfishly give you a good irl advice, and answer probably all of your questions.

Irrelevant. That is not needed to get a degree.

Someone is jealous.

Jealous for what?

>lang basic math

Lang is a meme.

it's a good meme

What's the geometric intuition for projective transformations?

jealous of that hot 2D body

Your entire life is a meme, yet you are alive somehow. Why haven't you killed yourself user?

>gpa

>measure of intelligence

Die whore

I talked to him today. He gave everyone a zero on the exam because he hadn't finished grading them(!). Apparently, I was the fifth person to ask him about it since he posted the grades yesterday morning. You thought he would have posted an announcement or something on the class website?

Can someone please tell me why would someone in it's right mind prefer to define the tangent space in terms if derivations? Just so you can justify abuse of notation? I thought mathematicians weren't like this.

I cannot think of a good explanation, but you might want to look into some "mathematics for open gl" book. This might be a good source of intuition.

Give me some simple but tricky problems.

U just got troled!

Currently I'm trying to understand the classification of semisimple Lie algebras and their representation theory. Humphreys presents this pretty well, in my opinion.

Because it works for any locally ringed space. i.e. Manifolds, Analytic Spaces, Varieties, Schemes

>PDEs

Eh PDEs can definitely be pure math.

Here's one that I came up with for myself. It's rather easy but you need a slight idea:

Let [math] n [/math] be and even, positive integer and let

[math] \pi: \mathbb{Z}/n\mathbb{Z} \to \mathbb{Z}/n\mathbb{Z} [/math] be bijective.

Show that there are [math]x,y \in \mathbb{Z}/n\mathbb{Z} [/math] with [math] x \neq y [/math] and

[math] x - y = \pi(x) - \pi(y) [/math].

Then why it's also used in more practical textbooks designed for physicists? Lie brackets make no sense with that formalism.or maybe I'm just a brainlet idk.

your professor is a moron

Lie brackets in that formalism are essentially just the commutator. Nothing really confusing there.

The derivation definition is also often more convenient for actually computing tangent spaces.

How does one go about actually computing concrete tensor products in practice?

I mostly understand how they're defined and what they do but I struggle to figure out on my own even very simple examples of them because there doesn't seem to be any obvious way of "solving" for it

how irresponsible of him, hopefully you end up doing well on the exam in that case

Put them in a basis and distribute the sum, but besides quantum entanglement and information, it's really not something done in practice I believe

Mathematical Statistics and Real Analysis. I've finished chapters 1-7 of baby rudin, and gonna start doing chapters 9 and 11 next. I've heard it's shit though. What's a good book to learn about the Lebesgue integeral/measure theory?

Also no one here knows any good stats books, huh

Not long. I would finish your algebra 2 stuff and then just dive right in with calculus. I did pre-calculus before calculus and I honestly dont know if it was necessary at all. Just make sure you learn some trigonometry as you do algebra 2.

Don't be scared of calculus, the operations are actually pretty easy. You'll be fine if you do well on the algebra 2 material.

tensor products of what

There are no good stats books. Statistics is a dung heap of a subject kept alive by it's practicality.

As for measure theory, there's a book by Robert Ash called Probability and Measure Theory that I really like.

I think it's a really good idea to teach measure and probability simultaneously, it's the easiest way to see that rigorous integration isn't just pointless autism but is actually good for something. Most other places where it's worthwhile to ditch Riemann are difficult to show to undergrads.

Crammed through 200 pages of linear algebra textbook without sleep

I just want to die

and tomorrow you will remember 15% of it

studying only because I have a test on it tomorrow

>Statistics is a dung heap of a subject kept alive by it's practicality.

lmao, yeah its a weird subject. Somehow nothing is rigorous even in "mathematical" statistics. Thanks for the book rec, will check it out.

Tensor product of vectors could be made in the next way. You have a vector $a = (a_1, a_2) \in A$ and $b = (b_1,b_2,b_3) \in B$ . Vector $c \in C = A \otimes B$ will be $c = (a_1 b_1, a_1 b_2, a_1 b_3, a_2 b_1, a_2 b_2, a_2 b_3)$. I dunno what are you afraid of.

Tensor product of vectors could be made in the next way. You have a vector [math] $a = (a_1, a_2) \in A$ [/math] and [math] $b = (b_1,b_2,b_3) \in B$ [/math]. Vector [math] $c \in C = A \otimes B$ [/math] will be [math] $c = (a_1 b_1, a_1 b_2, a_1 b_3, a_2 b_1, a_2 b_2, a_2 b_3)$ [/math]. I dunno what are you afraid of.

I did. I felt fucking destroyed yesterday.

He's sharp when it comes to statistics and operations research related things. I get the feeling that he isn't so sharp with other things, mostly technology. He does most of his lecturing with this digital whiteboard and he fucks up the most basic shit (screenshots and copying-pasting images in Windows 10). I'm sure giving us all zeros was a quick-fix to a "bug" he ran into while grading. Who the hell knows.

Anything is better than a 0/100 after this shit, and it was only worth 20% of our final grade. Can't wait for this class to end desu. Operations research without spreadsheets is just fucking tedious.

Im currently majoring in Mathematics and I feel like im not hitting the potential that I could with amphetamines. My smartest friends use adderall, vyvanese etc. but I used to use meth as a young teen so I feel that I could relapse if I do this. Anyone here use Kratom as a performance-enhancer for mathematics?