Mathematics is a fascinating world – a world full of mysteries and wonders, a world full of joy and excitement – a world full of divine beauty and grace. No other area of human activity is as glamorous as mathematics and yet as depressing. The dawning of the mathematical training really starts at the college level inasmuch as the real rigour of mathematics is learnt by the students only at this stage. The strength of logic unveils itself through the study of the real numbers, functions and limits, continuity and differentiability on one hand and abstract algebra and linear algebra and linear algebra on the other. In fact, analysis, both real and complex, and abstract algebra are the two main pillars of this subject. It should be kept in mind that the study of mathematics is never complete unless one applies what one has learnt in solving problems of real life.