COURSE NAME AND CODE:  Introductory Linear Algebra and Analytic Geometry (MATH 1141)

LEVEL: I

SEMESTER: I

We consider the limitations of the Riemann integral, and show that it is necessary to develop a precise mathematical notion of `length' and `area' in order to overcome them. Thus we develop the more abstract concept of measure, and use it to construct the more Lebesgue integral, and to investigate its properties. Finally we look at the role played by measure and Lebesgue integration in modern probability theory. This course is intended to develop the ability of students to work with abstract ideas.

This course considers the limitations of the Riemann integral, and shows that it it necessary to develop a precise mathematical notion of ‘length’ and ‘area’ in order to overcome them. Thus we develop the concept of measure, and use it to construct the more powerful Lebesgue integral, and explore its properties. Finally we look at applications of measure and Lebesgue integration in modern probability theory.