The aim of the course is to introduce a variety of standard statistical methods used to analyze multivariate data. Emphasis will be placed on developing the theory of these methods as well as the various interpretations of results derived from applying these methods. The (free) R statistical computing package will be used for data analyses.

This course is intended to introduce and give an understanding of numerical methods for the solution of ordinary and partial differential equations. The methods will be derived and the convergence and stability of the methods will be analyzed. The applications of these methods in solving real world problems will be emphasized. Students will be exposed to modern mathematical software for the practical use of the problems and for better visualization of the convergence and stability of these methods.

The aim of the course is to teach students the tools of modern analysis as it related to further study in mathematics, especially numerical analysis, differential equations, functional analysis, topology, stochastic processes. This course is intended to develop the ability of the students to work with abstract ideas.

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.

The course gives an up-to-date and modern overview of the main concepts in Functional Analysis. Functional analytic properties and several examples of Banach and Hilbert spaces arising in several branches of mathematics are studied to show how functional analysis is a unifying theme in different mathematical fields.