MAA301 is devoted to the modern theory of integration. After first constructing the Lebesgue integral, and explaining how it improves the Riemann integral, a major part of the course will be devoted to discovering the power and ease of use of this tool.
Applications in probability theory will then be briefly described. The course will finally provide an introduction to Lebesgue spaces and the Fourier transform, in order to demonstrate the usefulness of the theory for applications in physics and economics.
After constructing the Lebesgue integral, and explaining how it includes the Riemann integral, a long part of the course will be devoted to discover what a powerful and easy to use tool it is. First applications will be given to probability theory. Finally, Lebesgue spaces and the Fourier transform will be introduced to demonstrate the usefulness of the theory in applications such as physics and economy.