Current Topics in Mathematical Research

1. To deal with the concepts, methods and issues and classical mathematics contextualisation in current mathematical landscape.

2. To know some relevant lines of current research in mathematics.

3. To deal with the applications and usefulness of mathematics in different fields.

To explore the historical development and status of some mathematical concepts, with particular emphasis on the mathematical problems and lines of current research and relevant applications in various sciences (Art, Architecture, Biology, Social Sciences, Engineering, Physics, Computer Science, Music, Chemistry, Bioinformatics) and mathematics.

Organization of several conferences dealing with, among others, the following topics:

• Algebraic geometry

• Number theory

• Computational methods in algebra

• Differential geometry and its applications to physics

• Topology

• Continuous and discrete dynamic systems

• Qualitative theory of differential equations

• Functional analysis

Complementary bibliography.

V. ARNOLD, M. ATIYAH, P. LAX, B. MAZUR, (Eds.) Mathematics: Frontiers and perspectives, American Mathematical Society, 2000.

J. CARLSON, A. JAFFE, A.WILES (Eds.) The Millennium Prize Problems, Clay Institute/American Mathematical Society, 2006.

B. ENGQUIST, W. SCHMID, Mathematics Unlimited 2001 and Beyond: 2001, Springer, 2001.

G. TEMPLE, 100 years of mathematics, Duckworth, 1981. https://link.springer.com/book/10.1007/978-3-642-56478-9

R. WILSON, J. GRAY, Mathematical conversations, Selections from the Mathematical Intelligencer, Springer, 2001. https://link.springer.com/book/10.1007/978-1-4613-0195-0



Database of Zentralblatt für Mathematics: https://zbmath.org/

Database of Mathematical Reviews: http://www.ams.org/mathscinet/search.html

(Access outside the university via SIR: http://sp.bugalicia.org/san/subjects/guide.php?subject=gsir )



Database of Arxiv: https://arxiv.org

Database of Mathoverflow: https://mathoverflow.net

In addition to contribute to achieve the general and transverse competences taken up in the memory of the master, http://www.usc.es/export9/sites/webinstitucional/gl/servizos/sxopra/mem…, this subject will allow the student to get the following specific competences:



CE03 - To develop the necessary skills for the transmission of mathematics, oral and written, both regarding formal correction, and in terms of communicative effectiveness, emphasizing the use of appropriate ICT.

Attendance (or viewing) to scheduled talks and conferences, both face-to-face and telematic is mandatory. The talks can be face-to-face or telematic, and not necessarily carried out expressly for this subject. For example, conferences may be available on the internet. Discussions with lecturers and teachers, when possible, personal reflection, the preparation of summaries and proposed work are activities that facilitate the passing of the subject.

The evaluation will consist of attendance (or viewing) of the scheduled talks and conferences (40%). Completion of works, summaries, and conclusions (60%).

In those cases of fraudulent behavior regarding assessments the precepts gathered in the “Normativa de avaliación do rendemento académico dos estudantes e de revisión de cualificacións” will be applied.

Classes / computer lab: 5 hours

Tutorials Group: 5 hours

Attendance at lectures, exhibitions and other activities recommended: 25 hours

Individual or self-study group: 20 hours

Writing exercises, and other findings: 20 hours

Total working hours in the classroom attendance: 35 hours

Total working hours of student: 40 hours

Knowledge of mathematics at degree level.