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What is an axiomatic system?
In Math, an axiomatic system is any set of axioms (propositions that aren't proven or demonstrated but are assumed to be true) from which some or all axioms can be used in conjunction to logically derive a theorem.
Is mathematics a logical system that exists devoid of application or is it a problem solving language?
Mathematics has lots of practical applications, if that's what you mean.
What is the contribution of bertrand Russell in mathematics?
Bertrand Russell coauthored a book in the early 20th Century, called Principia Mathematica, in which he tried to show that all mathematical theorems could be derived from a well-defined set of axioms. The only tools to be used were those of logic. Unfortunately, in 1931, Godel proved that it was an impossible ambition except in very trivial cases. Using any axiomatic system you could find statements that could not be proven to be true or false from within that system.
What kind of mathematics is used in the merchant navy's navigation system?
trigonometry
What is pure math?
Pure Mathematics is the branch of mathematics that deals only with mathematics and how it works - it is the HOW of mathematics. It is abstracted from the real world and provides the "tool box" of mathematics; it includes things like calculus. Applied mathematics is the branch of mathematics which applies the techniques of Pure Mathematics to the real world - it is the WHERE of mathematics; it includes things like mechanics. Pure Mathematics teaches you HOW to integrate, Applied mathematics teaches you WHERE to use integration.
