OFFICE HOURS: see my homepage; -- LOCATION: 639
Students should have an interest in geometry and its many
applications in art, architecture, engineering, and most
domains of design.
They should not be adverse to seeing some mathematical
notation, and to using precise formulations to clarify some
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,
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,
to the symmetry of 4-dimensional "Platonic" solids.
Topology focuses on the connectivity of objects or of abstract
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 understanding 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.
"The Symmetries of Things" by John H. Conway, Heidi Burgiel
and Chaim Goodman-Strauss (A.K.Peters, Wellesley, MA, 2008)
"Symmetry" by Hermann Weyl (Princeton University Press, NJ,
1952, new issue: Jan 1, 1983)
"Shapes, Space, and Symmetry" by Alan Holden, (Dover,
Columbia University Press, 1971)
"Symmetry -- A Unifying Concept" by Istvan & Magdolna
Hargittai, (Shelter Publications, Bolinas, CA, 1994)
To probe further:
"Symmetry and the Beautiful Universe" by Leon M. Lederman
and Christopher T. Hill (Prometheus Books, Amherst, NY, 2004)
"Symmetry-- An Introduction to Group Theory and its
Applications" by Roy McWeeny (Dover, Mineola, NY, 2002)
About the Instructor:
Carlo H. Séquin has been a
professor in the EECS Computer Science Division since 1977.
He has taught courses concerning the design of integrated
circuits, micro processors, 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
Outside of the class room 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.