BMTC-133

About the Course

This is the third semester course through which we aim to introduce you to the branch of mathematics called “analysis”. The word ‘analysis’, in general, means a detailed examination of the elements or structure of a substance or statement of a result. In mathematics, analysis involves the study of the structure of sets having different types of elements such as the set of real numbers, the set of rational numbers and also the set of certain functions. Real Analysis is the branch of mathematics that studies the structure of real numbers and the behavior of functions defined on the set of real numbers. You already have some idea of the structure of the set of real numbers, and of functions defined on it, from the 1st semester course, Calculus. In that course you were introduced to many concepts such as limit, continuity, differentiability and integrability for real-valued functions, though more from an algorithmic and computational aspect. However, when you apply the algorithms, it is important to know the logic behind them. The study of analysis provides the reasons behind these computation rules. The study will also help you to develop “analytical thinking” and the ability to apply mathematics more precisely and confidently. The analysis of real numbers and real functions played a fundamental role in the development of mathematics. Though many mathematicians like Newton and Leibniz contributed to the development of analysis, the origin of analysis took place in early 19th century with the work of Cauchy, who gave precise definitions of concepts such as limit and continuity. The convergence criterion introduced gave a path way to the techniques of approximation which led to the development of the theory of integration theory by the mathematicians, Riemann.