PENG9640 Advanced Topics in Mathematical Methods: Applications to Natural Sciences 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 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.

Two sensors, one from the teaching staff, the other may be internal or external. 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

Upon successful completion of the course, the student:

• Possesses comprehensive knowledge in specific advanced mathematical methods within the realm of the course, supplementing their existing specialization in applying mathematical methods in applied sciences.
• Demonstrates an advanced command of mathematical methods relevant to their doctoral research, positioning them at the forefront of knowledge in their chosen field.

Skills

Upon successful completion of the course, the student can:

• Apply advanced theoretical knowledge and mathematical techniques to solve intricate problems encountered in the application of mathematical methods.
• Strategically plan and execute scholarly endeavors within the scope of their doctoral research project, employing advanced mathematical methodologies.
• Critically analyze existing mathematical theories, methods, and solutions, both in theory and practical application, fostering a deeper understanding of complex mathematical problems.

General competence

Upon successful completion of the course, the student:

• Demonstrates competence in conducting extensive literature reviews, engaging in self-directed study, and employing research-based learning methodologies in advanced mathematical concepts.
• Applies acquired knowledge and skills to tackle sophisticated tasks and projects encountered in the domain of advanced mathematical methodologies.
• Effectively communicates intricate mathematical concepts, analyses, and solutions to audiences with varying levels of mathematical expertise, showcasing the ability to bridge specialist and non-specialist communication gaps.
• Exhibits the capacity to recognize the necessity for innovation within the realm of advanced mathematical methodologies and can initiate innovative approaches within their expertise.

The course is carried out by research-based learning and includes a major study (project) based on individual work and is supervised by one or more supervisors (internal/external). There are a number of minimum eight (8) lectures given by the course responsible teacher. The actual number of lectures depends on the number of students taking the course and their (research) interests. Culminating the course, each student presents a seminar on a specific topic based on the project report. Other students are expected to take an active role in these seminars as participants.

The course is part of a series of seminars in which the students actively participate together with members of relevant research groups. The students present papers and listen to paper presentations from other PhD students and staff. The students are also expected to actively critique and challenge fellow participants. The students are provided with a sound foundation in research skills and are naturally integrated into the local research community and its research discourse.

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

• Three individual oral presentations of assigned publications.
• Participate as prepared discussant for three presentations by other group members.
• Independently find and study publications relevant to the research discourse.
• 80% attendance at seminars.

Oral exam, 30 minutes per student.

The oral exam cannot be appealed.

None.

Pass or fail.