Notes

Note 1 Notes on algorithms : 1

Updated Sec 2.3.1 February 2021

This note covers several topics relevant to modulo arithmetic :-

1 Division giving quotient and remainder

2 Highest Common Factor, hcf, alias Greatest Common Divisor, gcd

3 Modular multiplicative inverse (x^-1 in modulo arithmetic)

Algorithms and proofs of their correctness are given for the latter two, both for Integers and for Natural Numbers.

Note 3 Notes on algorithms : 3

This note describes a general class of structures that includes Lists, Trees, Well-Founded Relations, and more. It then describes the use of Induction to prove properties and of Recursion to define functions on the structures.

The general structures are called Well-Founded Multigraphs for want of a better name. The note finishes with a mathematical definition of the class and rigorous proofs of the Induction Principle and Recursion Theorem.

Note 4 Notes on algorithms : 4

This note is about a problem associated with the Chinese Remainder Theorem : Given a set of divisors and associated remainders, what is the lowest number that when divided by those divisors has those remainders ? The note derives the conditions needed to ensure that there will be a solution, and describes an algorithm to find the solution.

Javascript Some features of javascript

This note describes the key features of the javascript (ECMAScript) programming language. The note is aimed at people who are familiar with another programming language and want to know what is different about javascript. After reading it you will know that javascript and Java are different languages.

Many new features have been introduced into the original language and many more will continue to be. This note concerns itself with the fundamentals - they haven't changed.