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I am looking for a book recommendations for learning algebra for high school.

Usually my exams(national level competitions) may even ask some of the things that are a bit beyond the syllabus, and have really hard problems. So I want a book that goes over both theory in some detail and also contains hard problems and maybe a few tricks.

I am looking for a book in algebra that goes over topics like:

[This is the prescribed syllabus]

Algebra

Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations.

Quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots.

Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic means, sums of finite arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n natural numbers.

Logarithms and their properties.

Permutations and combinations, binomial theorem for a positive integral index, properties of binomial coefficients

Please can someone help me ?? :)

Thank You

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  • $\begingroup$ There are good resources listed here quora.com/What-are-the-best-resources-for-preparing-for-the-IMO $\endgroup$ – Vatsal Limbachia Aug 10 '19 at 4:32
  • $\begingroup$ @VatsalLimbachia I'm looking for books that are difficult , but not specifically for imo. Eg I believe complex numbers are not used much here ( correct me if I I'm worng, because I'm not really sure. $\endgroup$ – RandomAspirant Aug 10 '19 at 13:20
  • $\begingroup$ @VatsalLimbachia I have edited the question, so that it becomes more clear now $\endgroup$ – RandomAspirant Aug 10 '19 at 16:37
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There exists the relics from the past which go from the very beginning to such topics as complex numbers in deep. $$.$$ G Chrystal, an elementary texbook volume 1 and 2.$$.$$ Hall and Knight, elementary algebra volume 1 and 2. (though it's also named as "elementary algeba for schools") $$.$$ For an advanced standpoint, you can read B.D Bunday and H. Mulholland "Pure mathematics for advanced level", though in my opinion you should read Chrystal's algebra first for it is one of those books that never age and deals with many interesting topics (even series, interesting identities and so on) so you should do fine just with it, since the book is kinda old you can find it online.

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  • $\begingroup$ Sorry to say but these books are not that good and even lack advanced theory. Eg in G Chrystal , the complex number don't go over Euler form and the geometric discussion is too brief. $\endgroup$ – RandomAspirant Aug 10 '19 at 13:22
  • $\begingroup$ Refer to Titu Andrescu's books for challenging problems in different fields plus Hungarian problem books. $\endgroup$ – muhammad Aug 10 '19 at 16:43
  • $\begingroup$ This link refers to many books for every subject which I have found most helpful. imomath.com/index.php?options=347&lmm=0 $\endgroup$ – muhammad Aug 10 '19 at 16:44

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