Infinitybyzero said:
I hope you're ready for a very long, grueling process to get to the level you're looking for...
You cannot tell others how their journey will be. If something is difficult for you, that doesn't mean it will be for them or even that they will follow the same route as you. Even as a beginner, it's definitely possible to test into pre-calculus perhaps even calculus at some colleges. However, I cannot comment on obtaining the knowledge of a professor of mathematics by self effort.
I left UCSD as a political science major, only to have taken stats/algebra as my highest maths, to finish pre-reqs for a physics degree. It took me 2 months to relearn/understand arithmetic-pre-algebra, 1 month for algebra 1, 1 1/2 months for algebra 2, 3 weeks for trig., and I tested into pre-calculus. So, from arithmetic - pre-calculus took me about 5 1/2 months. Mind you, I worked 25-35 hours and once I finished my algebra 2 review, I started to tutors others. Not only was this FUN, but it took not long at all.
p.s. I got an A in calc 1 and I am tied with 4 other people for the highest grade in calc 2 ( about 2/3 through the course).
FishBowl44 said:
Need some kind of outline to learn math from beginner to an advanced level. Where should I start and how should I progress through the different subjects of mathematics? I want to be on a really advanced level in mathematics. Like a mathematics professor level/higher.
Also, some book recommendations/learning sites/videos would be great too.
Fishbowl, IMO, I would get at least two books for each math course. Be it physical or ebook. One that focuses heavily on concepts and the other for application. Once you are introduced to a new concept, do enough application so that you can explain to a young child how the concept works. ALWAYS look up words you don't understand and keep a word journal/notebook. If a mathematical definition looks daunting, break it down each symbol/letter at a time and translate it until it makes sense to you. I remember the first time I saw -1<= sin(x) <= 1, I had to graph it, review the definition of the sine function, etc. Mind you, I was self taught until pre-calculus - so no tutors/teachers to easily explain things.
Here's how I started out:
pre-algebra: conceptual book: pre-algebra for dummies ebook; application: Pre-algebra by McDougle/Littel 2005 ed. ebook
geometry: conceptual book: Geometry by Jacobs 2nd ed. textbook, Euclid Elements by Euclid (you don't need this one, I just love math and he's the OG for geometry), Geometry Schaum's Outlines; application: (some random Common Core book from my library).
I would email a professor at a local college that is teaching the class you're in and ask for a syllabus. You will not need to cover everything in your review. There are the "main components" for each math class and a syllabus can help you find out what those are. Don't be a afraid to review/re-learn a lower level math concept if you forgot/missed it. Some of the students I've tutored are resistant to this, especially the ones that have a lot of pride in their math ability. As a calc 2 student, I had do a solid 1 week review of the double angle and other trig identities, because I simply forgot them!
GL
edit: I believe questions like this have been asked already on this site. Have you tried doing a search?