Available courses

Real Analysis 1
Bernd Sing

Real Analysis 1

This course exposes students to rigorous mathematical definitions of limits of sequences of numbers and functions, classical results about continuity and series of numbers and their proofs. A major emphasis is placed on the proper use of definitions for the rigorous proof of theorems. The following topics will be covered: The real number system, topological properties of real numbers, sequences, continuity and uniform continuity.

Metric Spaces
Bernd Sing

Metric Spaces

This is a first course in point set topology. The subject of topology grew out of the study of geometric and analytic properties of the real line and Euclidean space. In particular, topology studies generalizations of the concepts of union, intersection, open intervals, closed intervals, limit points, and continuous functions. The material of topology is a combination of ideas from algebra, analysis and geometry.

In this course on metric spaces, topological concepts already met in MATH2321: Real Analysis 1 and MATH3550: Real Analysis 2 will be discussed in greater detail and generality. Besides the necessary abstract theory, applications are also pointed out, e.g., Picard’s Theorem that is so fundamental in the study of differential equations, or the how GIS (geographic information system) stores information about the relationship between spatial regions. Thus this course on metric spaces could be considered an applied topology course.

This course is compulsory for all students majoring in mathematics. It is also of interest to students that deal with objects and data in higher-dimensional spaces.