This course aims to provide a basic understanding of selected Mathematical concepts that many branches of science relies on. The topics will be explained at an abstract, post graduate level.

Target group and learning outcomes

The structure of the course is designed for PhD candidates. Yet I am certain that prospective MSc students would benefit from it. After successful completion of this course, participants should have a better understanding of: 

• The importance of paradoxes in mathematics, and logic. Several famous paradoxes and Gödel’s incompleteness theorems.
• Relation between infinity and cardinality.
• Types of cardinalities, ergo continuum hypothesis. Ordinal numbers and their application; natural numbers.
• Most common methods to prove a statement.
• The structure of metric spaces and topology. 
• The basic real analysis concepts such as couchy sequences, continuity, dense Sets, compactness, connected sets, derivatives, chain Rule, measure spaces, Reimann sums and integrals. Extreme value theorem, and its importance for maximization problems. Lebesgue integral and the difference between Reimann and Lebesgue. 
• The probability theory tools such as random variables, probability distributions, law of large numbers.

Assumed prior knowledge and course material

The students who are participating should have passed a bachelor level Calculus I course. There is no book the course is following, also there is no shortage of explanations on the Internet for these topics. Moreover students should take notes at the meetings.

 Former occurrences of this course

• 4-15 March 2019