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In the past I have only been driven to learn mathematics to stand on the top of my class but after I started programming in python I realized the importance of mathematics and it's beauty. After passing high school I had a determination to learn mathematics all the time realizing all I could do with mathmatics that I learnt over the past 17 years was addition, subtraction, division and multiplication.
Yes, I learnt calculus, I learnt theorems of limit, I learnt linear programming and statistics when I was in high school but the real mathematical ideas were not presented in the high school study. It was more of a horse race, if you back down on the 'parrot- study', you lose your future. So, I did it along with all others. I don't understand the most base concept of mathematics and I want to learn.
As I've mentioned above, I have only 4 skills in mathematics addition, subtraction, multiplication and divisions.

How can I self-study my way for maths but a complete understanding of the subject.
I did find a book that I thought I would try, was an open content by Thomas w. Judson, but after learning a few pages I found out it required knowledge of matrices. After acquiring a book on matrices(linear algebra), and reading a few pages it said it required calculus. And I thought a similar problem would round up.

So how should I start the very first brick in mathmatics after all these years?

Sorry, if this question sounds pathetic, while I know similar questions have been asked It isn't specific towards this one. If you think of closing it as an off topic question please provide a link that I could ask elsewhere because I've already inquired in the places I could besides in websites and am unaware of other sites that involve such question and answering interaction.

BumbleBee
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  • There's something I'm unsure of here... Are you in university or self studying? That makes a huge difference. You might want to emphasize this – Brevan Ellefsen Oct 10 '16 at 13:13
  • @Brevan Ellefsen, I've just passed high school. I'm going to join college but I'm waiting for the results. So I want to utilize the time and grasp every ounce of time I have left. – BumbleBee Oct 10 '16 at 15:05
  • alrighty. In that case I would review the calculus and Algebra you know and make sure you have them down pat. After that I would begin working on whatever undergrad work interests you. If you really liked calculus you could begin working on calc 2/3 directly. I might recommend studying a linear algebra course, as the foundations are so vital to so many fields of math (calculus 3 for me was a lot tougher until I studied some linear algebra to understand what was happening). Linear algebra generally doesn't require much calc if any (perhaps for application, but a knowledge of calc... – Brevan Ellefsen Oct 10 '16 at 15:21
  • ... 1 should definitely suffice). On the whole, the question of what you should study is more up to you.... What are you interested in? What do you enjoy doing? What have you studied prior? Just make sure you know everything you've learned well enough to teach it to someone else, and them study to your hearts desire. As far as texts to read through, that sorta depends on the topic you want to study. – Brevan Ellefsen Oct 10 '16 at 15:23
  • @BrevanEllefsen, Do you think starting from fundamental properties would be good like [knowing how a.(b+c) would be actually an application of distributive law]. I know how such operations work but I didn't know it were an application of distributive law. Do you think such understandings are crucial towards mathematical knowledge. I mean like knowing about the jargon along with knowing how to apply theories. – BumbleBee Oct 11 '16 at 12:29
  • yes and no. You should absolutely know that $a(b+c) = ab+bc$ for any real (or complex) a, b, and c. However, knowing the jargon is a lot less important than knowing how to symbolically do things. You need to really understand why things work. I recommend trying to prove everything you learned in calculus class (or at least as much as you can). Practice with vectors and really understand what's happening with them. Prove the quadratic formula and make sure you know how quadratic functions work forwards and backwards. Challenge yourself to ask questions about material from a... – Brevan Ellefsen Oct 11 '16 at 12:44
  • .... Class you took years ago and to read justify what you learned. Why does the exterior angle of a triangle equal the sum of the two, opposite interior angles? Why is it that I can simplify a repeating decimal by making the period the numerator of a fraction with a denominator of all nines? Why does $ab = ba$ but $a^b \neq b^a$?? Start asking and answering questions like these. Like I said, it's really important to understand all the material well enough to teach it. (and again, the jargon is secondary. Make sure you understand the math first, then learn the English phrase for it) – Brevan Ellefsen Oct 11 '16 at 12:48
  • @BrevanEllefsen, I started off with abstract algebra and found i required a knowledge of matrices, so I went there and found I needed calculus, and again there i needed functions – BumbleBee Oct 12 '16 at 10:38
  • @BrevanEllefsen, So I thought maybe I should go from the tail: functions, then matrices, then linear algebra and then abstract algebra, (i don't know if it's a good combo), then I'd like to continue with number theory and discrete maths. Do you have any recommendations to sources.? – BumbleBee Oct 12 '16 at 10:39
  • Does this answer your question? Learning mathematics as if an absolute beginner? – user1147844 Apr 29 '23 at 05:50

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Hum, I'm not sure this will answer your question but imho the very first brick in mathematics is to accept things as true. The very core of mathematics is to suppose something as granted and see what happen (this granted things are called axioms). Of course in any subject you can always go "deeper" and question every things. Like you said that you know how to do an addition but what does that mean, how do you define an addition? Addition on what by the way? addition on matrices are well defined, ...

Because of this reason I don't think there is any book (or anything else) that start with very few axiom and confer the whole mathematics, because that would require to go again trough the millenary of previous mathematics.

In all books you have some knowledge required to understand the book, you can see it as axioms. If I admit that this properties are true then the content is true. However each time you question this claims you will have to "re-do" all the history of mathematics

wece
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