Computer Science 39, Section 1

Symmetry and Topology (2 units, P/NP)

Professor Carlo Sequin
Monday 4:00-6:00, 606 Soda Hall, Class number: 46527

Symmetry plays an important role in art, fashion, architecture, engineering, computer modeling, biology, and in all the sciences in general; as well as in music, poetry, and psychology. We will explore its use in several of these domains. We will enumerate all possible types of symmetry and establish a rigorous understanding of them. We will start with simple mirror images, proceed through wallpaper patterns and hyperbolic tilings, finishing up with the symmetry of 4-dimensional "Platonic" solids.

Topology focuses on the connectivity of objects or of abstract constructions; it is important in the design and analysis of complicated shapes. It also allows us to extend the notion of symmetry to the interconnectivity of networks and to "regular maps" on surfaces of arbitrary genus (smooth donuts with one or more holes). We will get familiar with all surfaces of low genus, including Moebius bands, cross-caps, and Klein bottles.

The goal of this course is to give the participants a good enough understanding of the basic principles of symmetry and topology, so they can put this knowledge to good use in their future studies. This course, even though offered by the CS Division, will involve no computer programming, but will occasionally ask participants to construct models from paper, clay, or pipe-cleaners.

Instructor Bio

Carlo H. Sequin has been a Professor in the EECS Computer Science Division since 1977. He has taught courses concerning the design of integrated circuits, micro processors, and campus buildings. He has also taught courses on geometric modeling with hands-on assignments in the design and fabrication of mechanical puzzles, artistic maquettes, and mathematical visualization models. Outside of the classroom he has made use of symmetry and topology in the layout of solid-state image sensors at Bell Labs, in the design of the first RISC (reduced instruction set computer) chips with Professor Dave Patterson (CS), in the conception and construction of Soda Hall (the current home of the CS Division), and in the generation of various large-scale geometrical sculptures with artist Brent Collins from Gower, MO.

Faculty web site:


Students are welcome from many departments. In the past I have had students from EECS, ME, CE, IEOR, BioE, Math, Physics, Architecture, Art Practice, ... <br><br>Students should have some love for geometry and abstract mathematical thinking.