Term paper for Math 436

You will write a paper in lieu of a final examination. This assignment reflects several of the university's Undergraduate Learning Outcomes, including the following:

  • Evaluate, analyze, and integrate information from a variety of sources.
  • Demonstrate effective writing skills.
  • Exhibit the skills necessary to acquire, organize, reorganize, and interpret new knowledge.

The goal of the project is to research some topic related to topology and to write an exposition of that topic at a level suitable for other students in Math 436. Below is a non-exclusive list of possible topics. If you have an idea for a topic not on the list, great! But please get the approval of the instructor for your topic.

While researching and writing your paper, you should consult multiple sources. Remember that in the academic world, plagiarism is a major offense, so document your sources carefully.

The length of the paper should be about 2,000 words. (The number of pages is somewhat indefinite, of course, being dependent on the margins and the font size.) You may use your favorite software to type the paper. (If you want to write like a professional mathematician, then use the free and powerful LaTeX; one convenient place to get started with LaTeX is Overleaf.)

List of some possible topics for the term paper

  • Alexander horned sphere
  • Banach–Tarski paradox
  • Borromean rings
  • Brouwer fixed-point theorem
  • Cantor set
  • Compact–open topology
  • Covering spaces
  • Euler's formula for polyhedra
  • Hairy-ball theorem
  • Ham-sandwich theorem
  • Hausdorff distance
  • Homology
  • Hopf fibration
  • Jordan curve theorem
  • Klein bottle
  • Knots
  • Königsberg bridge problem
  • Lakes of Wada
  • Lens spaces
  • Long line
  • Map coloring
  • Möbius band
  • Moore plane
  • Order topology
  • Orientability
  • Partitions of unity
  • Simplicial complexes
  • Sorgenfrey plane
  • Space-filling curves
  • Stone-Čech compactification
  • Topological dimension
  • Topological manifolds
  • Topology in chemistry
  • Totally disconnected spaces
  • Ultrametric spaces
  • Uniform spaces
  • Weak topology
  • Zariski topology
  • None of the above: please discuss your idea with the instructor