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Rational Mathematics

by G. P. Jelliss

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

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