Topology Course Project

If I have seen further it is only by standing on ye shoulders of giants.
[Isaac Newton in a Letter to Robert Hooke, dated 5 February 1675]

Einstein and Leisureguy's (Michael Han) grandson. Posted March 23, 2007.

You may work alone or in a group of 2 people. Topics are first-come-first served with a maximum of 2 people per topic and they are approved as a Message to me on ASULearn.
  • Closed Sets, Open Sets, and Limit Points
  • Compactness
  • Connectedness and Disconnectedness
  • Continuous Functions and Homeomorphisms
  • Metric Spaces and Topological Spaces
  • Product Spaces and Quotient Spaces

    Create the following components, which you will bring with you and present in a research session on the final exam day:

    1. Maximum 4-Page Review
      Include the relevant definitions, mathematical symbols and notation, theorems, important proofs, and examples in order to review the major concepts from class and homework.
    2. 2-Page or 3-Page Timeline of Historical and Modern Importance and Applications
      Create an attractive and professional timeline. Be sure to include the important contributions as well as interesting pictures that relate to your topic, such as pictures of some of the mathematicians. Approximate dates can be noted as ~1762 or by a range of dates, such as 1700-1800.
      Here is a sample timeline from linear algebra and from first year seminar
    3. Annotated Bibliography
      Use many different types of sources, including scholarly references and library sources. Submit a separate annotated bibliography of all of the sources you used in your project, with annotations explaining what content in the reference relates to your topic, how you used each reference, where the pictures came from, etc. Use as many pages as you need for the bibliography and annotations.
    All components must be typed products that you create yourself in your own words, and that look professional and flow well. Mathematics symbols and notation should be typed in a program like Latex (I will prove some sample documents with topology notation in them and I will discuss Latex).

    Research Session Presentations on final exam day Bring a printed version of your all of your work to class to post on the wall [I will bring tape]. We will divide up the class into two sessions (half the class will stand next to their work as the other half examines the projects, and then we will switch roles). During your session, you must stand by your work to discuss your topic and answer questions. If you work with another person, they will be in the other session so you should be prepared to present the entire project. The presentation sessions are similar to research day at Appalachian, poster presentations at research conferences, or science fairs. In addition, when you are viewing other projects, you will conduct peer review:
    1) Name of the person and the topic.
    2) List a few strengths of the project.
    3) Provide suggestions for improvement, including any aspects you would have added to the review.
    4) Invent a question about the project. List the question and the person's answer.
    5) What you learned about the mathematical connections

    For Graduate Students In addition, write a paper in your own words that summarizes the following research and be sure to give proper reference where it is due.

    1. Research in Munkres the information we did not cover in class that relates to your topic.
    2. Research graduate texts in my office, the library, and on Google scholar, and on the web in order to find out whether the topic has a role in Algebraic Topology, Differential Topology, Geometric Topology, Combinatorial Topology, and low dimensional topology.
    3. Research at least one problem that was open in 1990 that relates to your topic, for example, from a source such as Open Problems In Topology II.