MEK2000 Mathematics 2000 Course description

This course, together with Mathematics 1000, will give the students an understanding of mathematical concepts, problems and solution methods with the focus on application, particularly in engineering subjects.

All examination support material is allowed as long as source reference and quotation technique requirements are applied.

No requirements over and above the admission requirements.

After completing the course, the student is expected to have achieved the following learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge

The student is capable of:

• explaining how functions can be approximated by taylor polynomials, power series and/or fourier series, explain what it means that a series converge, and differentiate and integrate powerseries.
• explaining what a frequency spectrum is, and explaining the principle of filtering signals in the frequency domain.
• describing and explaining how a sequence of numbers can originate by sampling, by using a formulae or as the solution of a difference equation.
• explaining how to interpolate sampled data.
• explaining partial differentiation and using different graphical ways to describe functions of two variables
• calculating eigenvalues and eigenvectors of matrixes and giving a geometrical interpretaions of these values

Skills

The student is capable of:

• discussing the connection between fourier series and fourier transforms
• discussing pro and cons using interpolating polynomials, splines and least squares method to interpolate sampled data
• discussing error barriers when using polynomials to approximate functions
• using simple tests of convergence of series, for example the ratio test
• giving a geometrical interpretation of gradient and directional derivative and using linear approximation and total differential of functions of two variables to calculate uncertainty
• using partial differentiation to calculate and classify critical points of functions of two variables
• using eigenvalues and eigenvectors to solve systems of differential equations with constant coeffisients

General competence

The student is capable of:

• identifying the connection between mathematics and their own field of engineering
• translating a practical problem from their own field into mathematical form, so that it can be solved analytically or numerically
• using mathematical methods and tools that are relevant to their field of engineering
• assessing the results of mathematical calculations and using basic numerical algorithms

This course provides an in-depth exploration of social science’s evolving role within society, alongside the potential influences of societal stakeholders on the social sciences. Closely related to the courses on the philosophy of science and science ethics, this course covers issues of new expectations and requirements of research to interact and engage with society, and how they may reflect more general societal transformations affecting the production and valuation of knowledge.

These expectations and requirements concern issues such as achieving societal impact, bringing onboard various groups of stakeholders, disseminating research findings to a wide range of and increasingly diverse set of audiences, reaching out to groups in vulnerable positions, and of incorporating non-researchers into the processes of planning, doing and publishing social science research. The course explores these trends against a backdrop of science integrity and academic freedom, which, in some European and wider international contexts, face challenges from political and societal pressures.

Theoretically, the course explores the transformation in knowledge production, moving from a traditional, discipline-centred approach to a more dynamic, context-driven and interdisciplinary one. It delves into, the ‘knowledge economy’ as a real and as an imagined phenomenon, and it considers the theoretical underpinnings of ‘evidence-based research’, including the realist approach. This course will allow candidates to critically reflect upon the drivers of recent trends that increasingly obliterate the borders between the field of science and surrounding fields of politics, practice, and the public sphere. Hereby candidates are prepared to utilize the many possibilities offered by these developments in terms of engaging with the wider society, while recognizing the pitfalls. Candidates will work with practical cases of how their own doctoral research can generate societal and practical impact, involve stakeholders and end-users in the science process, and integrate the principles and practices of ‘open science’.

No prerequisites.

Knowledge

After completing the course the PhD candidate:

• Has advanced knowledge about major trends in social science’s relations to the wider society
• Has extensive knowledge about specific topics that have come to dominate the academic field such as outreach, user-involvement, stakeholders in research and knowledge translation, citizen science, science skepticism and the politization of science
• Has advanced knowledge about theories explaining current trends in the relations between research, universities and society

Skills

After completion of the course, the PhD candidate:

• Can discuss his or her own research in terms of possible societal impact and is able to set up a concrete plan outlining the pathway to impact
• Can discuss his or her project in terms of strategies to involve ordinary citizens in fieldwork or end-users in the design, implementation and dissemination of the research

General competence

After completion of the course, the PhD candidate:

• Will have strengthened critical awareness when it comes to identifying trends in social science research’s engagement with society
• Will have improved understanding of their own role as researchers vis-à-vis diverse groups of stakeholders such as state agencies commissioning research, professional associations, user associations and the general public

Teaching will take the form of lectures and seminar discussions. Concrete examples, preferably from candidates’ own PhD projects, will be used as a basis for discussing different perspectives and aspects of the course’s content.

The course comprises three days of lectures (12 hours) and workshops (3 hours), amounting to 5 ECTS credits.

Active participation is necessary to adequately understand the course material and themes. Candidates will work with practical cases of how their own doctoral research relates to course themes, for example how their research outcomes may lead to impact (i.e. contribute to change in the field), how one may involve users or stakeholders in research activities or how to adopt an ‘open science’ approach. Participation is mandatory and expected in all days of teaching.

The assessment in this course shall be a written essay addressing one of the topics of the course and relating it the PhD student’s own dissertation. The scope of the essay shall be about 8-10 pages, and be delivered within two months after the course.Essays must be submitted within the given deadline, without extensions. Exceptions are made only in the case of illness (documented by sick leave). In these cases, an extension equaling the length of the sick leave can be granted (upon application).

The course has an overlap of 10 credits with MAPE2000, KJPE2000, EMPE2000 and DAPE2000, and an overlap of 5 credits with DAPE2000 and ELTS2000.