CS 39R:
SYMMETRY & TOPOLOGY

## Catalog Entry and Schedule

### CS 39R: SYMMETRY & TOPOLOGY

• FULL COURSE TITLE:  Symmetry and Topology
• COURSE NUMBER:  CS 39R
• COURSE CONTROL NUMBER:  25892
• UNIT VALUE:  2 units  P/F
• SEMESTER:  Spring 2016
• CLASS TIME:  Monday: 4:10pm - 6:00pm; -- LOCATION: 606 Soda Hall
• INSTRUCTOR:  Carlo H. Séquin
• OFFICE HOURS:  see my homepage; -- LOCATION: 639 Soda Hall

### PREREQUISITES:

• 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 "fuzzy" concepts.

### CONDITIONS FOR PASSING THIS COURSE:

• Good class attendance (not missing more than 1 or 2 classes).
• Active participation in class discussions.
• Making an honest effort on the homework problems.
• Giving an oral class project presentation.
• Writing a brief report on your class project.

## Course Description

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,
to 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 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.

## Inspirational Books:

"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)

"The Knot Book" by Colin C. Adams, (W. H. Freeman and Co., New York, 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)

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 visualization models.
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.