Rational Mathematics

Contents

My aim here is to try to provide a simply expressed course on mathematics as the study of structure, concentrating on finite systems. I am putting these notes together to clarify ideas in my own mind, but I hope others will find it useful, and will not find too many mistakes. There is much more to be included in due course.

1 – Generalities Introduction Reason Symbols Systems and Sets Sequences and Arrays Quotations and Sources

2 – Algebra Operators Relations, Equivalence, Order Operations, Groupoids Dualised Algebras, Lattices Boolean Algebras Logic Algebra Set Algebra Inversive Algebra: Permutoids, Groups Rings and Fields

3 – Arithmetic Numbers Numerical Order, Finiteness Addition and Subtraction Multiplication, Quotient, Remainder, Congruence Powers Forms, Power Series Factorials Combinations Divisibility, GCD, LCM Prime Numbers Infinity