# Intro Math A book on arithmetic that doesn't treat you like a baby

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1. Aug 10, 2015

### Ankel

The state of arithmetic today is disgusting. The textbooks on it are absolutely repelling, the authors treat it like a subject that will be of concern to only babies. They don't show any love, they treat the subject like a dirty rug. It's been two years since I majored in mathematics, since then, I have been programming very wildly and would like to relearn arithmetic in a way that Leonhard Euler and Euclid would personally enjoy.

Arithmetic is actually very rigorous, there exist theorems on even the most basic of the components and it's a very beautiful topic, if you're being taught by the right author.

I seek a complete book on arithmetic, how old it may be, that deals with it in an elegant manner and covers the following topics;

And if possible...

What I am describing is a treatise on arithmetic and I do not want a book on Calculus because it covers some of the topics above in it's first few chapters. I want a book that deals with arithmetic only. And no, I don't want a number theory book. I have been suggested this many times before and the books are not at all elementary, they discuss many advanced topics and all I am asking for is the very basics, the very very basics.

The book also must:

1. Show why things are the way they are (why are they true).
2. Be succinct as possible.
3. Contain no annoying images and distractions (which are everpresent in 99% of today's textbooks on arithmetic)
4. Be lucid.
5. Contain zero fluff.

That's it! I hope such a book even exists.

2. Aug 10, 2015

### micromass

So on the high school level, you should look at Gelfand's Algebra book and Euler's algebra book.
If you are looking for a more advanced treatise, then you will have to start from the Peano axioms and work up from there. A good book that does this is Bloch's real numbers and real analysis. It doesn't quite cover everything you mentioned though.

3. Aug 10, 2015

### Ankel

Doe
Do Gelfand/Euler cover up all the topics I mentioned, including equivalent fractions?

4. Aug 10, 2015

### micromass

I have no idea what you mean with equivalent fractions since it lead to exponentiation. Do you just mean $a/b = c/d$ iff $ad = bc$. Then yes, they cover this.

5. Aug 10, 2015

### micromass

6. Aug 10, 2015

### Staff: Mentor

7. Aug 10, 2015

### micromass

In my opinion, if you're interested in doing arithmetic in a very rigorous setting, then you have no other choice but to start from the Peano axioms. Gelfand and Euler both do not start from the Peano axioms.