Two geometric objects are topologically the same when one object can be bent and twisted, but not ripped, into another one. Determining when two objects are topologically the same is incredibly difficult and is still the subject of a tremendous amount of research. The creative process of mathematics may be described as postulating conjectures and then either proving them, or constructing counter examples that disprove them. In this course students will study topology through the creative search for counterexamples. This process is as lively and creative an activity as can be found in mathematics research. Students will develop their critical reasoning and analytical skills by working in teams on construction and revision of counterexamples. Format: lecture. Evaluation will be based on homework assignments, oral and written presentations, and exams. Prerequisites: Mathematics 301, or Mathematics 305 with permission of the instructor, or Mathematics 312 with permission of the instructor. Not open to students who have taken Mathematics 323 or 324. No enrollment limit (expected: 25). (This course is part of the Critical Reasoning and Analytical Skills initiative. ) This is a quantitative/formal reasoning course.