## Math 430 |

In Algebra, once one understands what groups, rings, etc., are, one
then asks: given two groups, are they the same, i.e., are they
**isomorphic**? In Topology, once continuity is understood, we classify
sets (really topological spaces) by asking if there is a continuous
bijection with continuous inverse between them. If so, we say they are
**homeomorphic**. We will only touch on this. Much more will be said
in Math 530.

Almost all phenomena studied in modern Mathematics is either discrete (algebraic) or continuous (topological). So, Algebra and Topology might be said to span most of Mathematics.

The branch of topology that has been most widly used in other areas of mathematics and in applications is the theory of manifolds. Most beginning level topology textbooks just touch on manifolds. Lee's text gives the basics of point set topology then applies it to manifolds throughout. You may wish to read the reviews on Amazon.

- Textbook: Introduction to Topological Manifolds by John Lee

- Syllabus: We will cover what we can.

- Grades will be based on a midterm (30%), a final (50%), and homework (20%). You can expect to be assigned about 5 problems a week. Students may be asked to give short presentations of homework in class.