Please note! Course description is confirmed for two academic years (1.8.2018-31.7.2020), which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.


Students will learn to recognize and analyze symmetric patterns and structures observed in our environment and in their own professional surroundings. Mathematically rigorous treatment is used to illuminate elegant structures and shapes from an intuitive perspective and to provide the students with a widened scope of possibilities especially within practices involving modular repetition. By the end of the course, the students will be able to detect aspects of their own profession that can be presented, investigated, and developed using the language of modern mathematics.

Credits: 5

Schedule: 08.09.2020 - 16.10.2020

Teacher in charge (valid 01.08.2020-31.07.2022): Kirsi Peltonen

Teacher in charge (applies in this implementation):

Contact information for the course (applies in this implementation):

CEFR level (applies in this implementation):

Language of instruction and studies (valid 01.08.2020-31.07.2022):

Teaching language: English

Languages of study attainment: English


  • Valid 01.08.2020-31.07.2022:

    Topics discussed include planar, spherical and hyperbolic 2D symmetries, Kleinian groups, conformal dynamics, 3D geometries, manifolds, orbifolds and fractals. This course provides views on research level differential geometry to a broad audience. During the course, we will consider methods offered by various fields of mathematics that meet needs in art and architecture. Through concrete projects, we will encounter different kinds of phenomena and interpretations of these phenomena provided by both classical and modern mathematics.

Assessment Methods and Criteria
  • Valid 01.08.2020-31.07.2022:

    Students must participate in 80% of the contact teaching. Exercises, workshops, learning diary.

  • Valid 01.08.2020-31.07.2022:

    Contact teaching: 6h/week x 6 weeks=36h

    Individual/group work: 87h


Study Material
  • Valid 01.08.2020-31.07.2022:

    To be determined at the beginning of the course.

  • Valid 01.08.2020-31.07.2022:

    There are no prerequisites from mathematics or art.



Registration and further information