What would be the best textbook you can ever recommend to achieve algebra skills?

Question

I think that I'm not familiar with algebra, which consequently made me look for a book to achieve algebra skills. Do you have any advise?

Here are given what I'll be asked

Polynomials, Logarithmic functions, division, Rational Numbers, Inequalities, Absolute values, exponentials, radicals, Factoring, first degree equations, sets, functions, second degree equations, parabolas, complex numbers.

Regards!

Answer 1

I would highly recommend the Little Mathematics Library series of Mir Publishers. Some of the titles in the series that will be particularly relevant for you are:

1. A. G. Kurosh - Algebraic Equations of Arbitrary Degrees
2. A. I. Markushevich - Areas and Logarithms
3. P. P. Korovkin - Inequalities

They do cover more material than may be required from the point of view of your exams, but they are wonderful to read nonetheless.

Since you mentioned that you want to learn as much as possible, I wouldn't mind adding a few general references that will surely interest you. Try:

1. Courant and Robbins - What is Mathematics?
2. Ian Stewart - The Foundations of Mathematics
3. Ravi Vakil - A Mathematical Mosaic: Patterns and Problem Solving

In fact, it was largely thanks to Ravi Vakil's book that I decided to take up mathematics for my higher studies when I was completing high school.

All the very best.

Answer 2

Discourses on Algebra, by Igor Shafarevich might be a good idea. At a more elementary level, you also have Algebra, by Israel Gelfand and Alexander Shen.