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Since its establishment in 1974, Aalborg University has aimed to deliver cutting-edge research and innovative practices in engineering education. However, increasing complexity related to rapid developments in digitalization and emerging societal challenges offer new opportunities, requirements, and expectations across disciplines for educational institutions and staff to develop and adapt to an unpredictable and ever-changing future. This paper proposes a systemic approach to addressing these challenges in higher education and presents recent initiatives launched at AAU including a coming Institute of Advanced Study in PBL to support the digital transformation of problem- and project-based learning for the future. [ABSTRACT FROM AUTHOR]

In this paper, we consider roots of multivariate polynomials over a finite grid. When given information on the leading monomial with respect to a fixed monomial ordering, the footprint bound [Footprints or generalized Bezout's theorem, IEEE Trans. Inform. Theory46(2) (2000) 635–641, On (or in) Dick Blahut's 'footprint', Codes , Curves Signals (1998) 3–9] provides us with an upper bound on the number of roots, and this bound is sharp in that it can always be attained by trivial polynomials being a constant times a product of an appropriate combination of terms consisting of a variable minus a constant. In contrast to the one variable case, there are multivariate polynomials attaining the footprint bound being not of the above form. This even includes irreducible polynomials. The purpose of the paper is to determine a large class of polynomials for which only the mentioned trivial polynomials can attain the bound, implying that to search for other polynomials with the maximal number of roots one must look outside this class. [ABSTRACT FROM AUTHOR]