>mom and dad are maths teachers >see that I've got

What textbook did you get? Which subjects?

What do you mean i doesn't exist?

>>8573707
One book on exercises in upper-undergraduate analysis.
One book on general exercises of undergraduate maths, covering mostly all topics.
One book in maths history.
One book called "Treaty in Algebra".

All of them are extremely good, but I just took a glance at the analysis one.

>Nature of the series [math]\sum_{n=1}^{\infty} a_n[/math] where
>[eqn]a_n = \int_{1}^{1/n} \frac{cos^2(t)*Log(1+\sqrt[3]{t})}{\sqrt[3]{1+t} dt[/eqn]
Wew lad

>>8573716
[eqn]a_n = \int_{1}^{1/n} \frac{cos^2(t)*Log(1+\sqrt[3]{t})}{\sqrt[3]{1+t}} dt[/eqn]
Whoops.

>>8573717

I don't get it tho. Its a sum of definite integrals. Are you supposed to figure out what is equals or something?

>>8573704
how old are you

>>8574074
B&

>>8573704
This is what you're looking for anon. Great and FREE intro book to higher level mathematics.

https://usamo.files.wordpress.com/2016/11/napkin-2016-1107.pdf

>>8573717
>>8573716
That obviously diverges, just show that a_n > a_2 for all n, then show that a_2 > some positive number.

>>8574074
Not me, by the way

>>8574484
Thanks.

>>8573704
>the algebraic closure of the reals "doesn't exist"

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>>8573704
>kid gets interested in math, what do?
>just throw some books at him, he can read, right? What else would he need to learn math?
>Nothing else, obviously, and we know that because we're math teachers

So, your parents are terrible math teachers and terrible parents, huh? Guess what you're gonna be, anon?

Hint: Not a fucking genius

>>8574659
This, just what the fuck? I get that at some stage your learning will come down to your own discipline and independence but come on, you can't just throw books at someone when they're just starting out.

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Everyone writing books on math seem to revel in giving everything the most strictest definition they possibly can, rather than writing something that can actually help people get an idea about the subject before diving deep into said strict definitions. Every time things go slightly advanced it starts to sound like a fucking voodoo magic and trying to look up what any of this means only leads to even more voodoo magic, until you forget what did you want to know in the first place and give up.

>>8574803

this is true

however I find that some papers that actually have something to say (actually are trying to share some knowledge) sometimes cut through the bullshit

>>8574659
I have a bit of level already, but I think they went too far on that one.

>>8574139
Not OP but I'm definitely going to read it, thanks.

>>8573704
Some nice books for beginners are Hoffman and Kunze or Axler's linear algebra and Rosenlicht's intro to analysis. Once you feel comfortable with most of those books look at Rudin's two books on analysis, principles first. Abstract algebra from Artin, Herstein, or Dummit and Foote. Or Topology from Munkres, Gamelin and Greene, or Willard.

>>8573704
>mom and dad are math teachers
Fucking lucky. My mom is a bipolar drunk and my dad is a criminal. At least I didn't inherit that shit.

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>>8573704

>>8573704
i^i = e^(-pi/2)