PENG9640 Avanserte emner i matematiske metoder: Anvendelser innen naturvitenskap Emneplan

Students who complete the course are expected to have the following learning outcomes, defined in terms of knowledge, skills and general competence:

Knowledge:

On successful completion of the course, the student:

• has a good understanding of the latest developments in the field.
• has a deep understanding of the fundamental scientific theories, standards and methods that are applied in the field.
• can evaluate the appropriateness and application of various scientific methods and approaches to research and development in the field.
• can contribute to the development of new knowledge, theories, methods, standards, interpretations and documentation in the field.

Skills:

On successful completion of the course, the student can:

• deal with complex technical questions and challenge established knowledge and practices within the field.
• formulate questions, and plan and carry out research development work at an international level in the field.

General competence:

On successful completion of the course, the student can:

• manage complex interdisciplinary tasks and projects
• pursue their research ethically and with professional integrity.
• participate in debates in international fora.
• communicate research and development though recognised national and international channels

Internal examination, with two examiners present. External examiner is used periodically.

Students who complete the course are expected to have the following learning outcomes, defined in terms of knowledge, skills and general competence:

Knowledge

On successful completion of the course, the student in depth knowledge:

• Identify contemporary issues and challenges in healthcare delivery in particular diagnostics.
• Identify unmet biomedical and/or healthcare needs and apply engineering and life science principles for designing appropriate solutions.
• Apply appropriate engineering and analytical principles to decipher, understand, and describe situations and problems in living systems.
• Describe the key design considerations relevant to the development of diagnostics.
• Describe the experimental tools and techniques used in diagnostic applications.

Skills

On successful completion of the course, the student can:

• Solve quantitative problems in living systems using appropriate engineering and analytical concepts and calculations.
• Collect, analyze, and critically evaluate experimental data.
• Define the technical and practical factors that influence the performance of diagnosis.
• Design solutions to current unmet biomedical and healthcare needs, taking into account key technical and practical considerations.

General competence

On successful completion of the course, the student can:

• Communicate technical information clearly and concisely in oral and written form.
• Demonstrate effective technical and scientific communication skills through the execution of various laboratory modules and projects.
• Read scientific journal papers with a cross-disciplinary approach.

Students who complete the course are expected to have the following learning outcomes, defined in terms of knowledge, skills and general competence:

Knowledge

On successful completion of the course, the student:

• knows how mathematical models can be derived from facts and first principles.
• has a repertoire of methods to solve and/or analyse both ordinary differential equation (ODE) systems and certain partial differential equations (PDEs).
• is able to apply analytical and/or numerical solution methods for PDEs to models of heat transfer, wave propagation and diffusion-convection and discuss the relevance of these models to real-world phenomena.
• is able to construct and develop relevant models and discuss the validity of the models.

Skills

On successful completion of the course, the student can:

• can determine steady states of ODE systems and use linear approximation to elucidate the stability properties of these states.
• can solve and/or analyse selected PDE models.
• is able to implement and use some numerical methods for solving relevant PDEs.
• can devise the solution of certain composite quantitative problems.
• can disseminate results and findings in an accessible manner – both orally and in writing.

General competence

• is aware of the usefulness and limitations of mathematical modelling as well as of pitfalls frequently encountered in modelling and simulation.
• is able to discuss properties of a system using the equations of the mathematical model that describes the system.
• can explain and use numerical methods, know their strengths and weaknesses and interpret results of numerical simulations.

Knowledge

On successful completion of the course, the student:

• has an overview of the different elements that comprise the architecture of today’s internet.
• has a good understanding about the approaches for conducting internet measurements and the latest advances in this field.
• be familiar of a broad set of tools that can help analyzing Internet measurments. Of a particular relevance here are tools that originate in other disciplines like Machine Learning and Statisitcal Physics. This will not only expand the available toolset but also increases the potential for interdisciplinory collaboration going forward.

Skills

On successful completion of the course, the student can:

• plan and carry out state-of-the-art measurement tasks
• can formulate research questions on the robustness and performance of operational networks, and design measurements for evaluating these questions.
• will have a general practical understanding of how different parts of the internet's architecture interplay to offer a performant end-to-end service.

General competence

On successful completion of the course, the student can:

• participate in debates and present aspects of his/her expertise in a way that promotes such discussions.
• drive innovation

Students will learn through a combination of interactive lectures, case studies, literature analyses, and guest lectures. Internal presenters in the course are from different departments. External presenters are from hospital, medical companies and interest organization with a cross-dissiplinary background.

The following required coursework must be approved before the student can take the exam:

• All planned seminars must be completed.
• The given exercises must be passed

Individual assignment (report) counts for 70% of the final grade, and oral presentation of selected material (30 minutes per candidate) that counts 30 % of the final grade. Review assignment of report on a chosen subject, maximum 10 pages. To be submitted no more than two weeks after the end of the course.

Both individual assignment (report) and oral presentation must be passed in order to pass the course. The oral presentation cannot be appealed.

None.