Best textbooks for different intro math subjects

[Thomaz]

What are the best intro math textbook for these subjects below? The level is for a advanced high school student/ National math Olympics/ or preparation for a difficult College entrance exam like JEE.

1) Sets
2) Functions
3) Logarithm
4) Trigonometry
5) Sequences and Series
6) Matrices/Determinants/System of linear equations
7) Combinatorics
8) Probability
9) Complex Numbers
10) Polynomials and Polynomial equations
11) Analytic Geometry
12) Euclidean geometry in the plane
13) Euclidean geometry in space
14) Descriptive Statistics
15) Commercial Math
16) Number Theory

 

[symbolipoint]

Each of us has our own experience to inform ourselves of which books were or are the best for any topic or specific course. Any answer which someone gives may or may be different from what the other person would want. An example of the set of authors for a College Algebra book is Aufmann, Barker, & Nation, which gives good or very good instruction about Functions, Logarithms, Polynomials & some of their equations, parts of Analytic Geometry, and a few other topics.

 

[symbolipoint]

The listing #15,
What is "Commercial Math"?

 

[Thomaz]

Each of us has our own experience to inform ourselves of which books were or are the best for any topic or specific course. Any answer which someone gives may or may be different from what the other person would want. An example of the set of authors for a College Algebra book is Aufmann, Barker, & Nation, which gives good or very good instruction about Functions, Logarithms, Polynomials & some of their equations, parts of Analytic Geometry, and a few other topics.

This book is suitable for high schoolers?

 

[Thomaz]

The listing #15,
What is "Commercial Math"?

it's basically math applied to common commercial situations

from wikipedia:
"Business mathematics, sometimes called commercial math or consumer math, is a group of practical subjects used in commerce and everyday life. In schools, these subjects are often taught to students who are not planning a university education. In the United States, they are typically offered in high schools and in schools that grant associate's degrees; elsewhere they may be included under Business studies. The emphasis in these courses is on computational skills and their practical application, with practical application being predominant.

A (U.S.) business math course might include a review of elementary arithmetic, including fractions, decimals, and percentages. Elementary algebra is often included as well, in the context of solving practical business problems. The practical applications typically include checking accounts, price discounts, markups and Markup, payroll calculations, simple and compound interest, consumer and business credit, and mortgages and revenues."

 

[symbolipoint]

This book is suitable for high schoolers?

Maybe. It depends how well the high schooler understands intermediate algebra. The three typical algebra courses follow a natural progression of difficulty, and a student could very well take the order as

1. Algebra 1 (Introductory)
2. Algebra 2 (Intermediate)
3. "Algebra 3" - or College Algebra

A 'more advanced' course in high school may be called "Mathematical Analysis" or maybe "Pre-Calculus", but at the high school level, the course could be weak or incomplete, compared to a "College Algebra" course in college or university. Other than that, Algebra 1 and Algebra 2 are much more comparable between high school and college.

 

[mathwonk]

1. Euclid: the Elements
2. Euler: Elements of Algebra
3. Shilov: Linear Algebra
4. Allendoerfer and Oakley: Principles of Mathematics.

if you read these you will have superb introductory preparation in most of your areas.

After these, I recommend Courant's Calculus, and Lang's or Cartan's Complex analysis, and Hardy and Wright Number theory. This is work for several years. or more.

 

[verty]

Try "Elementary Geometry" by Roe if you like. I assume you have some knowledge of high school math already.