Definitions in Mathematics

Introduction

Definitions per se are not something specific to the field of mathematics, but are rather prevalent in almost all subjects (for example English Grammar). An obvious need for definitions is to express a new term using already existing vocabulary. In mathematics however they have much more importance than in any other subject. Definitions in mathematics are rather precise and clearly express what a thing is or is not. From now on we will restrict ourselves to the form of definition used in mathematics.

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On Mathematics Education: Algebra vs. Calculus

This time I am going to take a break from heavy use of $ \mathrm\LaTeX$ like I used to do in my earlier posts. I will focus on the education of mathematics as is being provided to students in India. My sources of information in this regard are:

• memories from my school/college days (which are still relevant in current time)
• interaction with current school/college students
• mathematics books (both Indian and foreign, old and new) available on the market

The subtopic of the post should not be taken too literally, rather it reflects two approaches in the teaching of mathematics: 1) algebraic approach which I don't like and find unsuitable for any serious teaching of mathematics, and 2) the calculus approach which is the way mathematics teaching should be, but is currently not being practiced anywhere as far as the books show.

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