Advanced Mathematics for PhD Candidates 2025
Doctoral School of Engineering and Science at Aalborg University
Welcome to Advanced Mathematics for PhD Candidates
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 favourable 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.
Criteria for assessment: Research delivery
Key literature: Cooper, T. (Ed.). (2010). Longer lasting products: Alternatives to the throwaway society. Gower Publishing, Ltd.
Bakker, C., Wang, F., Huisman, J., & Den Hollander, M. (2014). Products that go round: exploring product life extension through design. Journal of cleaner Production, 69, 10-16.
Haase, L. M., & Laursen, L. N. (2022). Designing for longevity: expert strategies for creating long-lasting products. Routledge.
Organizer: Morten Nielsen
Lecturers: Morten Nielsen
ECTS: 4.0
Time: 3, 5, 8, 12, 15, 17 December 2025
Place: Aalborg University
Zip code: 9220
City: Aalborg
Maximal number of participants: 30
Deadline: 12 November 2025