What books are there to read demonstrations?

Question

I have been searching in the web for books with logic demonstrations of equations, formulas, theorems, etc. The problem is, I have found them, but they include too much calculation. I would like to read a book where you can find an explanation and logical demonstrations of formulas, equations, etc. By this I mean, for example:

In the formula of permutation, is $n!$, because when you choose the first element, you only have left $n - 1$ elements, after when you choose the second, you have only left $n - 2$n, because you have already chosen 2 elements. This is what I want, a demonstration and logical explanation, to really understand a formula / theorem / equation, and not just replace variables.

So, could you recommend books? where there are logical explanations of many formulas?

Answer 1

I would just look through elementary books on probability and combinatorics in a library until you find what works best for you. A fairly well known such book written for strong high school students is Mathematics of Choice by Ivan Niven (see here also).

This online reference might also be helpful.

Answer 2

You may have difficulty finding books that that do not include "too much calculation," as you stated. Often the author of a text on combinatorics is a combinatorialist, and they generally enjoy calculations.

That being said, a book that lets you figure out many of the calculations is Bogart's Combinatorics Through Guided Discovery. The text is freely available online, and recommended by the American Institute for Mathematics as an open text.

Answer 3

Given the very broad context of your question, I recommend "How to prove it. An structured approach." by D. Velleman. It teaches about mathematical reasoning and demonstrations in general.