MATH 324T Topology (Not offered 2006-2007; to be offered 2007-2008)
Topology is the study of when one geometric object can be continuously deformed and twisted into another object. Determining when two objects are topologically the same is incredibly difficult and is still the subject of a tremendous
amount of research, including current work on the Poincare Conjecture, one of
the million-dollar millennium-prize problems. The first part of the course on "Point-set Topology" establishes a framework based on "open sets" for studying
continuity and compactness in very general spaces. The second part on "Homotopy Theory" develops refined methods for determining when objects are the
same. We will prove for example that you cannot twist a basketball into a
doughnut.
Format: lecture/discussion. Evaluation will be based on homework, classwork,
and exams. Prerequisites: Mathematics 301, or permission of instructor and
Mathematics 305 or 312. Not open to students who have taken Mathematics
323. Enrollment limit: 10 (expected 10).