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1.My question:Could you please recommend the resources and structure of learning maths from algebra to higher level like calculus and beyond?Mainly books please. Something like books for Algebra I-geometry-Algebra II-trigonometry-precalculus-calculus I-calculus II-Linear algebra --and advanced

2.Motivation:Learning physics and computer science and of course the enchantment of maths itself.

3.Background:A little bit of algebra,Trigonometry utmost basics and basic geometry

4.Why it is interesting and why it should be answered? Honestly it would be of great help to anyone wishing to learn mathematics but are unable to find resources.

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  • $\begingroup$ I'd suggest looking at the classes you are interested in from a local school and picking up their required textbooks. If you're self-learning you can get older editions - mostly the same but a fraction of the cost. $\endgroup$ May 21, 2020 at 15:02

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These are some useful books on some of the topics you cited:

College algebra and trigonometry plus, by R. D. Ferguson

Precalculus : Mathematics for Calculus, by J. Stewart

Algebra and Trigonometry With Analytic Geometry, by J. A. Cole

Geometry and trigonometry for calculus, by P. H. Selby

Precalculus: A Concise Course, by R. Larson

These are some books on more advanced topics, which answer the part 'calculus and beyond':

Real and Complex Analysis, by W. Rudin

Real Analysis, by J. M. Howie

Algebra, by T. W. Hungerford

Linear Algebra: Step by Step, by K. Singh

Abstract Algebra: An Introduction, by T. W. Hungerford

Real Analysis: Measure Theory, Integration, and Hilbert Spaces, by R. Shakarchi and E. Stein

Functional Analysis, by K. Yosida

Classical Fourier analysis, by L. Grafakos

Modern Fourier Analysis, by L. Grafakos

Since there are various versions of these books, I have not written the years of publication.

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    $\begingroup$ The OP wants "Algebra-geometry-trigonometry-precalculus-calculus I" which sounds like basic high school math to me. These would be far more advanced than that. $\endgroup$ May 21, 2020 at 14:58
  • $\begingroup$ Thanks for noting this. I focused too much on 'calculus and beyond'. I will now add some books more related to such topics. $\endgroup$ May 21, 2020 at 15:00
  • $\begingroup$ Thank you very much. $\endgroup$
    – Neelesh V
    May 22, 2020 at 7:35
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Your best bet for pre-university Mathematics is probably to look at Khan Academy. https://www.khanacademy.org/math

I'm sorry that I can't give you a better answer than this, but a single book to structure all your self-learning would be huge. The upside of using Khan Academy is the learning is very structured, with videos, problems, and explanations, and it should carry you until you can begin with the book list posted by Manuel Norman above.

I would also recommend for that list "Linear Algebra Done Right" by Sheldon Axler. It is a short book, and is a nice introduction to Linear Algebra and can be your gateway into the rest of abstract algebra.

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  • $\begingroup$ I did'nt ask for 1 book for all.But a collection of different book that complement each other $\endgroup$
    – Neelesh V
    May 22, 2020 at 7:36
  • $\begingroup$ thank you very much for your suggesttion $\endgroup$
    – Neelesh V
    May 22, 2020 at 7:37

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