I'm in the process of teaching myself undergraduate level mathematics.
I've done basic algebra, calculus and real analysis and next I'm looking to learn Number Theory, Group Theory and more advanced Differential Equations.
Is there a logical order to learn these in, or does it not really matter?
I've heard number theory builds on group theory, but does it do so enough that I need to know group theory before I can learn number theory?
>>7688245
why?
Math higher than basic arithmetic is a huge waste of time to learn unless you plan on actually using it for something other than doing taxes.
>>7688367
as a passion project because I'm interested
>>7688245
>high school level knowledge tattoo
>>7688388
>not my tattoo
>just some random pic because i needed one to make the thread
I'll give you an answer but first prove you're not full of shit.
Prove the following:
i) nZ = mZ iff n|m (hint: use groups homomorphisms)
ii) the induction principle is equivalent to the principle of well ordering of the natural numbers (this should be very easy)
Let's see if you really understood what you taught yourself.
These is first semester of the first year stuff.
>>7688388
Please find me a single high school that teaches the Schrödinger equation or PDEs in general.
>>7688367
>Math higher than basic arithmetic is a huge waste of time to learn unless you plan on actually using it for something other than doing taxes.
I feel very bad for you. There is a huge, vast, beautiful universe out there which requires no spaceships, no engines, no machines, nothing, only your brain to explore. And your close mindedness is preventing you from discovering it. I will always feel nothing but deep sadness for people like you. I still hope you can have a good and eventful life, but you are truly missing out. I'm sorry man.
Yeah I'll give you an answer too but only if you can solve my homew... i mean this test to see if you are smart enough to deserve an answer:
What is the radius of convergence of the following sequence:
[math] \sum_{k=0}^{\infty}{k^3(z+4)^k}[/math]
>>7688475
Is z a complex number? I thought OP said he studied real analysis.
>>7688453
mine too bad you live in america lol
>>7688479
z is a real number, k is a natural number. and is it just me or did the math code not embed even though i put it in math tags
>>7688480
lol fucking nerd, who wants to learn that shit. we should have more useful classes at high school like a baking class, or a wash laundry class, eww disgusting nerds
>>7688483
whatever that series is not convergent anyway.
>>7688480
Regardless of which nation you live in, it's stupid to explain such a complex theory to a high school student since he/she doesn't have the mathematical background. Don't think you're special because some teacher wrote a long formula on a black board and you know what the symbols mean.
>>7688446
I'm still waiting OP.
>>7688446
Dont you mean mZ is subset of nZ
>>7688511
Yes. mZ is a subset of nZ and nZ is a subset of mZ. In fact, they are the same set but if and only if n divides m.
>>7688518
Take m=6 , n=3
Then 3 is element of nZ, but not mZ
-> not equal
>>7688523
You are suppose to know what you're talking about before telling us your opinion.
>schrodinger eqn tattoo
lol i'm going 2 get the dirac eqn XD
>>7688527
We're talking about subgroups of Z arent we?
>>7688485
Friendly reminder that ironic shitposting is still shitposting.
>>7688541
You are correct, I'm stupid. mZ is a subset of nZ.
I suck cocks. You are free to offend me.
>>7688547
Anyway I am not OP, I just wanted clarification
Another task would be:
Show that all groups Z/pZ (multiplication and without 0 ofc) are cyclic if p is prime, lagrange makes it nearly a nobrainer
>>7688563
Definitely. Proving it without lagrange seems unreasonable. Primes are very useful.
>>7688472
>I will always feel nothing but deep sadness for people like you
Shut the fuck up you pontificating reddit user. What math do you know that is vast and beautiful? The Banach-Tarski paradox?
Fucking memer
>>7688574
You should really consider sticking to /b/. This is supposed to be a board for people who are at least intelligent enough to not make baseless assumptions.
>>7688580
I guarantee that I've forgotten more math than you've ever know in your life, and I have a pretty good memory.
>>7688584
Ok. Try me then.
>>7689070
Let F and G be formulas (in first order logic).
Prove the following equation is valid:
[eqn] \forall x(F \land G) \equiv (\forall xF) \land (\forall xG)[/eqn]
follow this list in the described order:
http://www.superstringtheory.com/math/math1.html
http://www.superstringtheory.com/math/math2.html
http://www.superstringtheory.com/math/math3.html
>>7689116
>the goal of arguing with you was to make you do my homework
topkek m8
>>7689116
def is the same as bicond
prove left -> right, right -> left
left -> right:
forall x (f & g)
x fresh
(f & g)
f
forall x f
x fresh
(f & g)
g
forall x g
forall x f & forall f g
left -> right
right -> left:
forall x f & forall x g
forall x f
forall x g
x fresh
f
g
f & g
forall x (f & g)
right -> left
left <-> right
left := right
qed
>>7688453
>>7688472
How do I make math fun anon? I know up to intermediate algebra.
>>7689429
This guy has no clue about the development of human logic and reasoning. Children at an early age are only capable of grasping naive physics, there's no way an average kid could grasp some of these concepts, despite how easy they may seem now. I know this must be bait but this is Sci and some people honestly do believe everyone is autistic as they are.
>>7689706
>This guy has no clue about the development of human logic and reasoning
Jean Piaget (like Freud) is a fucking quack that has been disproven over and over. Stop repeating his bullshit.
>>7688453
I try not to bother you guys with my posts often, bit I feel like I should tell you that I'm beginning PDEs right now as a (18yo) high school senior for my E&M class.
American private school.
>>7689772
post notes fool
