How can I develop mathematical understanding? I never paid attention

>>8833850
I told you on /g/.
See the wiki: http://4chan-science.wikia.com/wiki/Mathematics

bumping for interest
how to regain grasp on calculus?
what comes after that?

>>8833916
>how to regain grasp on calculus?
Read calculus books. As a first one I recommend Stweart but the board meme is T. Apostol.
>what comes after that?
In that branch of mathematics? Analysis. But there also is algebra, geometry/topology.

>>8833941
>in what branch
which is the most useful?
what are the applications of analysis?
how hard is topology?
and what more is there to algebra that they don't teach you in school?

>>8833954
>which is the most useful?
This question doesn't make much sense.

>what are the applications of analysis?
Analysis is the larger branch that contains what most brainlet engineers like to refer to as "muhh calculus". So, basically all the applications of calculus.

>how hard is topology?
As hard as anything else if you go deep enough.

>and what more is there to algebra that they don't teach you in school?
Oh boy. I don't even know where to begin.
The first things that occur are number theory and the entire field of computer science.

>>8833974
shid i'm intimidated my all of this
which one do you personally find most interesting?

>>8833996
Algebra. More specifically Number theory. More specifically cryptography.

>>8834008
i know a man who works in that field and makes absolute fucking bank

what professions could i go into based on different fields of mathematics?
i don't want to get stuck working in finance, however lucrative it might be.

>>8834049
It's not very hard to go from one area of mathematics to another.
There isn't anything that you can do with a branch and not with another. The division is simply to make things easier.

You can work with basically anything.

Anything in computer science, such as data mining, machine learning, security, computer graphics and computer vision, all of which are rapidly growing fields.(and also buzz words)

In engineering most people I know work with fluids, more specifically stuff related to oil and drilling. It pays insanely well.
Aerodynamics also pays very well.

Physics, in the development of materials and high precision equipment that engineers are too much of monkeys to build. Such as medical equipment.

In any decent sized or transport company you can work with operational research which pays even better than oil stuff.

Communications. You could fit it into engineering or computer science but i prefer to treat it on it's own. I don't know about the money.

Statistics and actuary(Calculating the probability of shit happening.) The last is said to be one of the most rewarding and well payed professions.


Most people I know are uni professors and work in one or more of those fields as contractors. I frequently work in the computer science and physics fields.

>>8834049
Also don't forget that you can always be a professional shitposter shilling for companies.

File: pepe smug.jpg (27KB, 600x600px) Image search: [Google]

27KB, 600x600px

>>8833941
>I recommend Stweart

>>8834008
>>8833996
>>8833850
I was in a similar situation to you OP. Born and raised in a shitty ex commie hell-hole of a country, I was taught mathematics in a really bad way. We were just manipulating symbols, basically.

This year I finished "mathematics for computer science" (by eric lehman, you can get it for free) and it was a great read, taught me basic logic and number theory and most of the undergrad math that you need, besides calc and linear algebra.

In the book there was a small chapter about logic and it's very important to realize that everything in math is pure logic, everything is a set that's manipulated and built on a set of basic axioms and rules that let you create new rules from those axioms.

Most math proofs just use modus ponens (google it) which works like this: We need to prove P implies Q (which means IF P THEN Q) which is also written as P=>Q. We know that if P is true in that situation then Q has to be true, at all times, in order for that implication to be true. Cool. Let's assume P is true, let's just guess. If in this case P=>Q is true then it means that our initial assumption of P being true was true and Q is also true, because Q HAS to be true when P=>Q. This is the most basic form of truth.

And from these simple rules of logic you basically build up and create new truths.

Let's say you have natural numbers. Then you axiomatically declare that A+B is the sum of A and B. From this you end up with a ton of rules that are true because the axioms are. They have to be. It's not that you make them true or that when you discover them they're true. They are from the moment you say the axioms are true.

How do you build up from those axioms? With logic, of course. The upside down A ("for all", "each", etc), the mirrored E ("exists", "there is") are part of logic too. Everything is a set connected by logic, in most branches of mathematics, at least the ones you will start learning about now, at the beginning.

That's math. imo

>>8834246
Why people here don't like it? I didn't have any problem with it.

>>8833850
Algebra by Gelfand and Shen
Functions and Graphs by Gelfand, Glagoleva, and Shnol
The Method of Coordinates by Gelfand, Glagoleva, and Kirillov
Trigonometry by Gelfand and Saul

Basic Mathematics by Lang

How to Solve It: A New Aspect of Mathematical Method by Polya

A Transition to Advanced Mathematics by Smith, Eggen, and St. Andre

>>8834502
thanks my dear, dear friend

my geriatric and labial friend

i love you man, you really care about me, you helped me a lot
I appreciate me. A friend is someone who helps you unconditionally, right? You were capable of doing that for me and therefore you are my friend. Thanks man. What's your name?

>>8833850
You already understand math. Everybody does. The only hard part is writing it down.

>>8834536
Dylan Roof

>>8834546
that's my favorite thing about math. everyone already knows it we just have to learn the rules and operations.