PENG9640 Advanced Topics in Mathematical Methods: Applications to Natural Sciences Course description

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 language is normally English.

Technologies, from the stone axe to the computer, have been integral in shaping how we live, think, interact, and work. Advances in digitalization have made digital competences a significant factor in ensuring the employability of candidates in all professions vital to our society. Understanding the benefits, the limitations, and the transformative power of technologies on public and private life as well as professional practice is crucial.

In this course, students will acquire the basic knowledge needed to harness the potential of digital technologies and identify opportunities to use technology to foster inclusion, active participation, and sustainability in society and the workplace. Through individual reflection, shared exploration and group discussions, students will gain awareness of how technological developments might impact their future professions, and their role as citizens in an increasingly digitalized society.

This course will provide students with the foundational knowledge and means to become a responsible agent of change in their own profession and field of study. Students will learn to recognise limitations, strengths and potentially disruptive consequences of technological innovation and grapple with the social, ethical, and political issues that arise as technology becomes both increasingly complex and essential to the function of society.

No additional course-specific requirements.

After completing the course, the student should have the following overall learning outcomes defined in terms of knowledge, skills and general competence:

Knowledge 

Upion successful completion of this course the student understands: 

• basic concepts, mechanisms, and tools behind digitalization
• how digitalization shapes public and private life
• the role of technological innovation and development in equity and justice, sustainable development, and civic engagement
• how technological infrastructures shape and support society and the welfare state.

Skills 

Upon successful completion of this course the student can: 

• apply critical and analytical strategies to evaluate and critically discuss the possibilities and challenges of existing and potential technologies 
• reflect on social, ethical, and political consequences of technological change
• provide examples of local and global technological disparity, both in general terms, and in relation to their field of study
• analyse and interpret the processes by which information and disinformation is distinguished, disseminated and used in different contexts.
• identify and discuss central sustainability challenges with digital technologies

General Competence 

Upon successful completion of this course the student can: 

• discuss ethical, social, and political challenges arising at the intersection of technology and society
• understand how digitalisation and digital technologies facilitate and shape interdisciplinary collaboration
• examine contemporary, real-world cases from multiple perspectives 
• evaluate the potential impact of new technologies and digitalization processes on an individual and societal level
• understand the importance of user-oriented perspectives in the use and development of technology
• communicate concepts and models related to the use of technology in a structured manner.

The course uses a blended learning approach, with a combination of attendance-based seminars and digital learning materials. Students will explore real-world cases emerging at the intersection of society, technology and their future profession.

English will be the primary language of communication.