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.
Session times and outline in hours
The course consists only of theory and some exercises to have a deeper understanding of the concepts. The daily sessions involve 3-hour in the morning and 3-hour in the afternoon.
Requirements and ECTS
There will be two exams one right after chapter 4 and one after chapter 7. The mean of these exams will be the final grade of the students.
|WASS, PE&RC and WIMEK/SENSE PhDs with TSP
|a) All other PhD candidates b) Postdocs and staff of the above mentioned Graduate Schools
Fee includes coffee/tea, and course materials.
NB: for some courses, PhD candidates from other WUR graduate schools with a TSP are also entitled to a reduced fee. Please consult your Education/PhD Programme Coordinator for more information
The participants can cancel their registration free of charge 1 month before the course starts. A cancellation fee of 100% applies if a participant cancels his/her registration less than 1 month prior to the start of the course.
The organisers have the right to cancel the course no later than one month before the planned course start date in the case that the number of registrations does not reach the minimum.
The participants will be notified of any changes at their e-mail addresses.