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;
Order of operations Addition Sum Additive inverse Subtraction Multiplication Multiplicative inverse Multiples Common multiples Least common multiple Division Quotient Fraction Decimal fraction Proper fraction Improper fraction Vulgar fraction Ratio Common denominator Lowest common denominator Factoring Fundamental theorem of arithmetic Prime number Prime number theorem Distribution of primes Composite number Factor Common factors Greatest common divisor Fractions Equivalent Fractions and Elementary Continued Fractions Square root Cube root Properties of operations Associative property Commutative property Distributive property
And if possible...
Real number Rational number Integer Natural number Irrational number Odd number Even number Positive number Negative number Prime number Whole number Natural number
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:
- Show why things are the way they are (why are they true).
- Be succinct as possible.
- Contain no annoying images and distractions (which are everpresent in 99% of today's textbooks on arithmetic)
- Be lucid.
- Contain zero fluff.
That's it! I hope such a book even exists.