Instructors:    Araceli M. Bonifant   Office: Math Tower 4-107 Phone: 632-8275 Email: bonifant@math.sunysb.edu

Susana Core   Office: Math Tower 4-116 Phone: Email: susana@math.sunysb.edu

Office Hours: Tuesday, Thursday.

About the course: In this course we will introduce the students to some of the basic notions of topology. Our main goal will be to gain an intuitive acquaintance with some of the fundamental notions of topology and the way they differ from one another. Curves are relatively simple examples of topological spaces however they give rise to extremely complicated phenomena. We are also interested in looking at those closed, non-self-intersecting curves embedded in three dimensions, called knots. 

The plan is the following:

Dates	Topics	Assignments
Jan. 28	Graphs Euler's formula Planar graphs
Jan 30	Dual graphs Coloring graphs The six-color theorem
Feb. 4	Surfaces The flat torus, graphs on the torus Euler's formula Regular graphs
Feb. 6	More surfaces: holes, connected sums One sided surfaces, two sided surfaces
Feb. 11	Knots Alternating knots
Feb. 13	Unknotting number Linking number Coloring knots and links
Feb. 14	Presentation of projects

Project:  In the second week of classes we will distribute a list of projects to the students. The students are required to hand in a written report of this project. The project should be done in groups of 2 or 3 students.

Bibliography

Knots and Surfaces, A guide to discovering mathematics

by David W. Farmer and Theodore B. Stanford.
American Mathematical Society, 1995.

The Shape of Space, How to visualize surfaces and three dimensional manifolds

by Jeffrey R. Weeks
Marcel Dekker 1985.

The Classification of Knots and 3-dimensional spaces

by Geoffrey Hemion
Oxford Science Publications 1992.

Geometry from Euclid to Knots

by Saul Stahl
Prentice Hall 2003.