Oral test 2 on material up through and including Problem Set 4. Review definitions, examples, and reasons why statements are true or false from the problem sets and solutions, the WebCT quizzes, and class notes.

This test will be closed to notes and help and comments can only come from Dr. Sarah.

Review especially the definitions and examples that I listed for the material from Oral test 1 as it is likely that some of these problems will reappear on this test. In addition, make sure that you also know

  • Definition of Zariski Topology
  • Definition of Hausdorff
  • Definition of T1
  • Definition of the Cantor Set
  • Numerous examples and of spaces for each of the following (or an explanation of why numerous examples are not possible) that are
    T1 and Hausdorff,
    T1 but not Hausdorff,
    Hausdorff but not T1,
    neither T1 nor Hausdorff.
    For each example, you need to demonstrate why it satisfies the criterion.

    In each case, I will be looking for clarity and depth, and a clear demonstration that you understand "why". Don't be afraid of repetition - when you get up to the board, restate your question, explain the relevant background material, answer your question, and then review what you did and explain again how it relates to the original question. Make some connections, and relate it to big picture ideas or metaphors too. For the following Thursday, I will ask you to reflect on your oral presentations via a self-evaluation that reflects on
    Your demonstration of an understanding of relevant definitions and the problem and its correct solution without help from others
    Eye Contact
    Included enough repetition
    Included connections and big picture ideas or metaphors