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I'm have a solid high school math bases and I'm a Mathematics enthusiast. I want some good books suggestion to progress even more and be able to have a scientific career.

Jaideep Khare
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Oneriste
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    Reaching a scientific career from a high school understanding (no matter how solid) will take more than a book or three, even if you are a one-born-every-century mathematical prodigy. There is just so much that has been done that you would need to catch up on. – Arthur Dec 04 '17 at 18:30
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    I think you don't understand my question i search some book that can help me in my formation in mathematics and acquire good knowledge – Oneriste Dec 04 '17 at 18:31
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    I guess it would depend on what branch of science you want to pursue. The skills that are useful for a computer scientist are not the same as those for a physicist. –  Dec 04 '17 at 18:34
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    To what extent are you interested in "pure mathematics" as compared to "applied mathematics"? Do you have ambitions of being more of a theoretical physicist or a mechanical engineer? – eepperly16 Dec 04 '17 at 18:35
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    It's good that you are interested in mathematics that is certainly something that this community should promote instead of disappointing people. :) Maybe a bit more information about your background and your interests can help people better to give you more appropriate recommendations. – stressed out Dec 04 '17 at 18:38
  • I think that there are some foundations of mathematics that should be mastered before you goo deper so i search some books to master this foundation – Oneriste Dec 04 '17 at 18:40
  • University math usually starts with analysis and linear algebra, so you can probably start with a book on those subjects. Another possibility would be abstract algebra. If you are interested in doing calculations then take a look at scripts from physics courses called something like "mathematical methods" . – klirk Dec 04 '17 at 18:44
  • My suggestion is to take a look at standard book used in the first year of University of a Mathematics degree. Something about Linear Algebra or Analysis or Logic or Arithmetic depending on your taste. – Overflowian Dec 04 '17 at 18:47

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I suggest you an excellent book: What is mathematics by Courant and Robbins.

szw1710
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I highly recommend Judson's Abstract Algebra: Theory and Applications. On top of being totally free, I think it does a good job of introducing you to advanced undergraduate math without assuming you've taken a bunch of other courses on linear algebra and set theory and logic.

Linear algebra is also essential to learn for pretty much any field. If you have ambitions of being a theorist, the "abstract vector space" approach is probably better than the "matrix approach" (in e.g. Strang)--though eventually it is good to see the material developed both ways. I first learned out of Friedel, Insel, and Spense and found it to be good.

If you've already done Calculus, I cannot highly enough recommend Real Mathematical Analysis by Pugh. This is a very challenging book and it may very well be too advanced for you right now. But I read a bunch of it in high school and I really credit it to forming my mathematical intuition, so if you have the background for it, it can be a good experience. A gentler introduction to real analysis is Lebl's Basic Analysis.

Ultimately, more than anything, mathematics is about solving problems. Whatever books you choose, make sure you are solving problems that are interesting and challenging to you. Challenging should not mean impossible though so make sure you pace yourself. If something is too challenging, try and "back up a few steps" to something that isn't like hitting your head against a brick wall. Best of luck and happy mathing!

eepperly16
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  • Thank you i will try Judson's Abstract Algebra: Theory and Applications – Oneriste Dec 04 '17 at 19:57
  • I finished a bachelor a physics before turning myself to mathematics. Judson's book educated me greatly during this transition. Strongly recommend it too. – aadcg Dec 04 '17 at 21:11