Course detail

Welcome to Advanced Mathematics for PhD Candidates (2026)

Description: The aim of this course is to give the participants an idea of how the mathematical vocabulary is used and the strength of using it properly. This is needed by engineering PhD's when reading papers, which will often use the common language of mathematics, and in particular when writing papers. Moreover, it is crucial, that engineers understand when a given mathematical toolbox is applicable and when it is not. As an example: In favorable cases, differential equations have unique solutions, but this is not always true, and trying to approximate a solution in such cases may lead to results which are simply wrong. The topics covered are: metric spaces, convergence, continuity, compactness, completeness. Vector Spaces and linearity. Korovkins theorem on polynomial approximations via Bernstein polynomials. The Banach Fixed Point Theorem. Existence and uniqueness results for ordinary differential equations. The approach in the course is to stress the necessity of precise mathematical formulation, and, in particular, to give examples where the intuitive answer is not correct.

Prerequisites: A master's degree in engineering or similar.

Learning objectives: The approach in the course is to stress the necessity of precise mathematical formulation, and, in particular, to give examples where the intuitive answer is not correct.

Teaching methods: Lectures and exercises.

Organizer: Anton Evgrafov and Morten Nielsen

Lecturers: Anton Evgrafov and Morten Nielsen

ECTS: 4.0

Time: 2, 4, 7, 14, 16, 18 December 2026

Place: Aalborg University

City: Aalborg

Maximal number of participants: 30

Open for enrolment: 2. August 2026
Deadline: 11. November 2026

Important information concerning PhD courses: There is a no-show fee of DKK 3,000 for each course where the student does not show up. Cancellations are accepted no later than 2 weeks before the start of the course. Registered illness is of course an acceptable reason for not showing up on those days. Furthermore, all courses open for registration approximately four months before start of the course.

For external PhD students: This course is a general course and is prioritized for PhD Students enrolled at Aalborg University. If there are available seats, PhD students from other universities will be accepted. You will be notified shortly after the deadline if you have been accepted.

To attend courses at the Doctoral School in Medicine, Biomedical Science and Technology you must be enrolled as a PhD student.

We cannot ensure any seats before the deadline for enrolment, all participants will be informed after the deadline, approximately 3 weeks before the start of the course.

You may find more information in our FAQ: https://phd.moodle.aau.dk/local/page/faq 

For inquiries not described in the FAQ, please contact the PhD administration at phdcourses@adm.aau.dk. When contacting us please state the course title and course period. Thank you.