First post, I'll try to make it clear and concise. I've been spending the past few weeks watching all sorts of space and science documentaries and it's ignited my eagerness to learn more about these subjects. I've begun to search the web in all sorts of science topics and any deep learning will require a solid understanding of math.
This leads me to problem, I don't know where to begin. How does one begin to learn about a subject without knowing a pre-requisite or requirement… I've had this problem my entire life. I work in IT and a couple of years ago enrolled in cs. I completed 2 years worth and quit because I started to get interested in ee. After some self studying in ee, I found I was interested in physics. Soon though I got discouraged because I found I was in this loop of being interested in the whys and the foundation. How does one begin to get a better understanding of a topic without knowing the underlying why?
Which brings me to this forum. Im always finding that the whys Im trying to figure out always have a basis in math. Although I have no advanced studies, I have always been interested in the topic. I just worry that my main interests are in computing and sciences, Ive come to this realization too late in life and to develop any real knowledge in the topic, I will need real knowledge with math. So now I need to start learning the core of math and building upon that, I just worry I will get discouraged and lose sight. I worry about topics that are used as building blocks but I do not see the applications for. I worry about not understanding math but wanting to understand space or electronics or anything else
I worry about where to begin I guess. Anyway, its 3 am and I have been spending the past few weeks wanting to be a true academic and not knowing how I should go about doing so. Im in my 30s with a full time job and would love to start.
Thanks for reading my ramblings and sorry for the writing, Ive been using me phone.
Best Answer
Sounds like you are in for quite an adventure.
Mathematics is a huge, vast forest of knowledge. The choice of foundations to master and the path towards advanced topics depends to a great deal on precisely what it is that interests you. It sounds like you are not sure yourself what precisely it is that interests you so here goes some general advise to self-learning mathematics, assuming that you are interesting in understanding it all and not just memorize some techniques.
Disclaimer: These are only my humble opinions.
The language: Mathematics is written (mostly) in English augmented by set theory and/or category theory. The former is indispensable while the latter is only highly recommended. There are plenty of books on naive set theory (since you certainly don't want to start with formal set theory until you become seriously interested in logic and set theory). Halmos' "Naive Set Theory" is old but very very good. There are also various texts on category theory (including notes on category theory for CS which you might prefer). Category theory might be hard to digest so you might want to take it slow with categories and read on it while you are reading other things.
It is safe to assume that for the topics that seem to interest you you will certainly need a good dose of analysis. To save time and if you are up to a bit of abstractness look for textbooks that talk also about general metric spaces (e.g., Larussens' "Lectures on Analysis").
Linear algebra is also certainly going to be required. The book "Linear Algebra Done Wrong", despite its name, is a good text.
You should probably set this for yourself as a first goal. As you won't have plenty of time to put into it it might take you a good year to reach that milestone, if not longer. Once that is done you can think about how to proceed.
One thing to remember is that even if it will take you a very long time to get where you want to get to, the things you will learn on the way are very likely to assist you not so much on their own right but rather due to the analytic skills you will develop when working on challenging mathematics problems. Good luck!