Rational Mathematics

by G. P. Jelliss

© 2005, layout revised February 2013

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


Comments from readers will be welcome to: george . jelliss @ virgin . net (close spaces).