/sci/ - Science & Math

When is the "right time" to learn category theory?

I see its language thrown all over the place casually, sometimes without any explanation - functors, initial/terminal objects, inverse limits, etc. However, last time I tried learning about it, it was over my head.

I want to study enough category theory to be able to understand the terminology when I come across it, but my end goal is not to study pure category theory. I guess it's sort of like the modernized version of set theory - ubiquitous in the language, but not too popular to study directly.

Does anyone have any good recommendations for sources to learn with my goals in mind? Thanks.

I've been thinking a bit about the so-called "Local to Global Principle" and was wondering if this could be considered a basic example of it in action:

If <span class="math"> x \equiv a \mod p[/spoiler] for every prime number, then <span class="math"> x = a \in \mathbb{Z}[/spoiler].

My questions are:
1. Is this true? (It seems like it)
2. If so, how does one prove this?

>>5830853
pic related

>>5607157

I miss based Brosef.

>>4810243

/sci/, can you share some of your favorite abstract algebra problems at the undergraduate level? Anything from groups to rings/fields, and anyone can try to solve them (using LaTex - pic related).

LaTex is used by many mathematicians to write papers, and can also be used on /sci/. Let's have a practice thread so that in the future we can better communicate with each other.
>see pic for a quick tutorial

>Practice
<span class="math">a_n = sqrt(1+a_(n-1))[/spoiler]

correct

>>4719064
LaTeX is great, but it's kind of arse here on /sci/ if you can't preview it. The odds of making mistakes are somewhat high, and there's no way to edit posts to fix them. In usual texts, I use the \Sum command because it's clearer, but apparently that one doesn't work here and I have to use \sum. Tiny typographical difference, but every such typo can already fuck up the entire .tex sequence.

>>4719058
I showed both the (simple) matrix and scalar derivation, so hopefully you should have the answer now.

>>4564267
pic related

>>4539922

>>4536912
pic gives a guide to writing in latex on /sci/

Im going into grade 11 and I am in higher mathematics. I have to choose from one of the following options. I plan on majoring in physics. Would series and differential equations be the most useful?
Further Statistics and Probability
Sets, Relations, and Groups
Series and Differential Equations
Discrete Mathematics

pic related

you prob don't need this, but for others interested, pic related

>>4320129

Pic for LaTeX.

>>4320081 has the algorithm for solving a derivative of a function raised to a power. If you're still unsure,

http://www.wolframalpha.com/input/?i=d%2Fdx[x^%28-2%2F3%29]

Also, learn to use parenthesis.

>>4276157
This one?

A sticky! On /sci/! How bizarre.
Let's post something useful then.