Concepts & Conventions

Math is a concept-laden discipline. Its concepts are based on other accepted concepts. Acceptance of a concept depends on whether that concept is a result of the strict application of the logic of mathematics, as judged by fellow mathematicians.

Math also has conventions which are “rules” which have been accepted by fellow mathematicians for mathematical reasons. The difference between concepts & conventions should be brought out very clearly.

There are two kinds of conventions – those related to the mathematics itself or those related to the communication of mathematics.

Mathematical Conventions

Since math is built on logic, conventions adopted for mathematical reasons are very few.

The most important mathematical convention is related to the order of operations. This convention known as BODMAS or PEMDAS arose out of the necessity of getting the same result when multiple operations are present in an expression.

There are two other conventions - the definition of 2 as a prime number and 1 as a non-prime. In chapter 8.7 on the Fundamental Theorem of Arithmetic, we have dealt with these issues in detail.

Communication Conventions

Math is also a discipline about which persons share documents related to math, written partly in daily language and partly in symbols. So the symbols should be understood internationally. The work of standardising mathematical symbols has been going on for centuries. Researchers who study old manuscripts in mathematics realise the difficulty in understanding them.

Each topic in math uses many symbols common to mathematics and some symbols which are unique to that topic. Any new topic will introduce symbols of its own. Let us see some example of symbols used in arithmetic, algebra & geometry that we have studied till now.