Flow charts are the bane of my existence.

This isn't much of a flow chart, but I'm not much of an artist. So, here's my best rough outline of what subjects you should pursue based on your interests.

Ideally, you'd learn all of these subjects (because to be quite frank, in the world of mathematics most of the ones listed here are beginner/intermediate level).

The best course of action is to start from the beginning: Algebra. But if you have a pretty solid understanding then Calculus I (single variable), Calculus II (integration & series) and Calculus III (multivariable calculus) are the real core courses, in my opinion.

Here are the definitions of the courses list (in order of difficulty, ish):

**Algebra**- this is the introductory of mathematics, really. It can be divided into 2 different levels, but you'll need to start here before moving on to anything else in mathematics.**Geometry**- shapes and shit. You'll need this as an introductory course as well. It's helpful for artists, architects, or really anyone that likes to work with their hands.**Statistics**- considered a not-real-math course to math snobs, stats is essentially the study of human behavior. You'll need if for psychology, finance, and medicine. Basically, if a human is involved, stats can help explain it.**Calculus I**- calculus is usually divided into 3 different levels at university. Calc I is single-variable calculus. It's as easy as college math gets. Enjoy it while you can. Calc I is a requirement for not only every STEM course ever, but for economics as well.**Calculus II**- integration & series is pretty important for technology careers, especially computers. If you want to pursue engineering or tech, you'll need this. Most of us agree Calc II is harder than Calc III.**Calculus III**- multivariable calculus. Calc on crack. You'll need this if you want to pursue cryptology or physics.**Discrete**- Logic math. Discrete is used by anyone who needs to quantify logic. Which is basically computer engineers, philosophers, and analysts. You will be uncomfortable by how easily summarized every thought you've ever had is.**Linear Algebra**- A requirement for computer engineers (I'm sure you've noticed the pattern by now computers = math). Vectors, matrices. You saw some of it in Calc so it's an easy enough transition.**Topology**- Advanced geometry. This was my favorite subject in school. Outside of mathematics and physics I'm not 100% on who needs it, but I'm told animators and video game designers utilize topology.**Linear Analysis**- this class can blow me. You learned the basics like differential equations in Calc, but this course just takes it to a whole other level. Usually only math majors or computer engineers take this course.**Pure Mathematics**- It's not fair to list this as a course, because it's not. Pure Mathematics is its own degree. It's the study of math for the sake of math. So, if you like numbers and sitting down with a piece of paper to solve math problems that no one understands, this is the course for you.

So, where do you go from here?

First -and I cannot stress this enough - you need someone to check your work. Let me say it again: YOU NEED A HUMAN TO PHYSICALLY CHECK YOUR WORK.

It is very easy to learn it all wrong. You need someone to check every step of your progress. A teacher is the norm, a tutor is ideal. But don't think you can just buy a book on multivariable calculus and walk away understanding it. You need human interaction.

But if you don't care all that much and you're in it as a casual observer, then here are some sources that are free to varying degrees:

__Khan Academy__- personal favorite. What started with math eventually branched off into science and history. The videos are comprehensive and easily available.__edx.org__- these are university courses from bougie joints like Berkeley and Stanford, and have way more subjects than just math. I used to be addicted to this page__Brilliant (app)__- the app is interactive for both science and math, which is a great way to engage in your own learning, but only the first few courses are free, eventually they make you cough up money: $24.99/mo or $149.99/yr.__Symbolab__- a giant calculator. You have to know your shit before using this page. It checks your work, even up to a complex level, but you have to know what you're doing or it will probably give you a wrong answer.

There's a lot to it. The learning curve is years long, but why not, right?

You got nothing to lose.

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