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

The course in Advanced Topics in Mathematical Methods: Applications to Natural Sciences covers carefully selected subjects chosen for their direct relevance to students' prospective doctoral research. The course material is curated in collaboration with the thesis supervisor, fostering a self-directed study experience under expert guidance. Each student needs to hand in a project report of about 5-7 pages within the course's comprehensive scope of study. 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. In addition to the project report and seminar, there is an oral examination. The number of lectures depends on the number of students taking the course and their (research) interests.

Recommended prerequisites include a Master’s degree in Mathematics/Applied Mathematics/Computer Science/Physics or a related field, accompanied by foundational knowledge in calculus, linear algebra, and basic programming.

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.

None.

The exam consists of two parts:

1. An individual written assignment (project report) of 5-7 pages (excluding references and appendices).
2. An oral seminar (other students present) and an oral examination (no other student present).

The student's project report and seminar are based on the same topic. Both 1 and 2 need to be passed in order to pass the course and are graded separately.

The student needs to pass the written assignment (project report) to be able to sit for the oral seminar/ oral examination.

The written report can be appealed, the oral part of the examination cannot be appealed.

Referring to the examination's two parts listed above:

1. All aids are allowed.

2. None, except that the students are allowed to bring their individual assignment (project report) to the seminar and oral examination.

Pass/fail.

Two internal examiners. An external examiner is used periodically.