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## Course description

Learning outcomes

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.

Content

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.