recommend math books So i completed an year ago my schooling and i am pretty good at maths well at my level and i am very interested in maths and want to learn as much maths as possible and i like stuff like number theory. what got me really fueled up is the fact that i watched a video on numberphile (its a youtube channel on math stuff) about prime numbers and i got goosebumps when i heard that they have a formula that approximately calculates n'th prime number i thought prime numbers follow no pattern and bad thing i did not understand that formula ....
well not to go with the story and all so the thing is i want to study more of mathematics by my own so i need you all to recommend me good books to get firm hold of every topic in math i not very hifi stuff that i want to start low and then become a jedi that does not mean i need books for noobs to understand what my math level is consider these things so that you may help me in a better way to recommend books 


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*i do know $e^{iθ}= \cos θ + i\sin θ$ and its proof using expansions of $\sin  x, \cos x$ and $e^x$

*i do have basic knowledge about parabola, circle, straight lines(and pair of straight lines), ellipse and hyperbola(although i don't like them idk why)

*basic trignometry


now my thinking levels 


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*i once tried to calculate a algorithm or formula that would give equation of circle that would have maximum overlap with a parabola and passes through its vertex(failed miserably)


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*tried to calculate function that would give distance(not displacement you have to follow along curve) between any two points on curve of sine graph(not failed actually a computer would be able to calculate using that infinite sum to some accuracy but still failed)



well that should be enough i would ideally like books that would assume i know basics and then follow up but books that do start from very basic and get to pro are good to but not the ones that do not tell me what i already know but are just filled with much difficult problems based on what i do know i want although problem solving is must for math and i am not saying i don't want that in  books you recommend i do want them and lots of problems but you get it what i am trying to say well go for it !!!!
 A: You say you like number theory so, try A Friendly Introduction to Number Theory as a start. If you like this, follow it up with Elementary Number Theory, David M Burton.
Also you may be interested in Linear Algebra, and this would be a good step into more advanced maths. For this you can try Linear Algebra and Its Applications, 4th Edition.
A: A good starting point, covering lots of topics in first/second year college math, are the various lecture notes by William Chen. Well written, clearly explained.
Kenneth Bogart's "Combinatorics through Guided Discovery" is a nice introduction to it's topic, geared towards self-study.
If you want to be dazzled by a broad variety of ingenious reasoning, perhaps Aigner and Ziegler's "Proofs from THE BOOK" (Springer, 5th edition 2014) is what you are looking for. You need some higher math to fully understand it.
If you want a flavour of how math became what it is today, Dunham's "Journey through genius" (Penguin Books, reprint 1991) could be a good starting point.
In any case, "I want to learn more math" is awfully broad. Today's mathematics has splintered into dozens, if not hundreds, of subtopics, each of whose detailed exploration can (and does) take a lifetime. Do you want to get a leg up for college? Go for Chen's notes. Want to learn more in depth, explore some types of stuff that aren't in high-school main fare? Go for Bogart's. Both available for free. You might also check out open culture's textbooks.
