Mathematics Capstone Course Project

The course project will investigate some aspect of mathematics in significant depth through an exploration of recent research. This project will build upon previous research experiences, independent studies on advanced mathematics, foreign exchange program experiences, or advanced topics from 3000 or 4000 level classes in which the student has developed an interest. Participation in the final project is mandatory to pass the class.

Part 1 Choose a topic for the course project. Print and turn in your LaTeX code and the LaTeX'ed document for the following:

  1. Your topic
  2. Your name and prior experience with the topic
  3. Search and report back on one interesting item related to prior progress in the area of your course project (it could be someone who laid groundwork on the topic, or peripheral but connected research or history). Include the date and the name of the person and their contribution.
  4. Search MathSciNet or other Library Databases for recent scholarly journal articles related to your course project topic and write down one item that you find, including the date and the journal, as well as the title.
A LaTeX template: LaTeX code for Part 1 of the course project and the pdf version. [Due Feb 9]

Part 2

  • Beamer: Create an introductory slide in Beamer with your title, a second slide that includes your prior experience, and a third slide related to prior progress in the area of your course project (it could be someone who laid groundwork on the topic, or peripheral but connected research or history), including the date and the name of the person and their contribution. Include an image on at least one slide.
  • A preliminary bibliography list in LaTeX that is added to Part 1 of the course project.
  • Print and turn in your PDFs. LaTeX templates:
    Beamer slides template: LaTex code and Figure 1, Figure 2 must be in the same directory to LaTeX (or you can comment out the \includegraphics code with a % until you are ready to add your own picture). pdf version. Beamer theme gallery
    Part 1 + Preliminary bibliography template: LaTex code and pdf version
    [Due Feb 23]

    Parts 3 and 4 The majority of the course project will occur when you create a work of your own in your own words that is a 7-10 page long written paper using LaTeX and a 9-11 minutes long LaTeX Beamer presentation. Include the following components:

  • Information about your prior experience with the topic before the capstone, including how and in what context you covered the topic in classes and other experiences as above, including definitions and a summary of examples, important results, proofs, etc, from your experiences prior to this capstone. This may form the majority of your paper and presentation.
  • Investigate and include historical and recent progress in the area [into at least the 20th century] via a literature review in your own words that includes at least five sources.
  • In addition, find at least two scholarly research articles from journals aimed at experts from the last 10 years that relate to the topic, to show that related research continues, and include them in your bibliography.
  • 7-10 page paper: Paper template LaTex code and pdf version.
    Here are two prior student papers: The Euclidean Algorithm by Deniz Gurel and The Beauty of Analytic Hierarchy Process by Huy Q. Tu
    [first draft due Mar 23, final draft due May 8]

  • 9-11 minutes Beamer presentation: Beamer presentation LaTex code, Figure 1, Figure 2, Figure 3, and Figure 4 must all be in the same directory and pdf version
    [presentations on Apr 13, 20, 27 and May 8]

  • The course project will be graded using this rubric

  • LaTeX Mathematical Symbols [for anything not on this, I google "LaTeX code" and the name of the symbol]
  • LaTeX is on the campus computers. Free installations are also available for your computer, such as MiKTex or MacTeX [can take a long time to download]
  • How to Talk Mathematics by Paul Hamos, Notices of the AMS (v. 21, 1974, pp. 155-158)

    A first draft of the paper will be due before the presentation and you should strive to improve the final version of the paper using feedback from us, peer review comments from the class during your presentation and your own experiences during the presentation.

    Your grade will be based on the depth of the mathematics, and the clarity, quality and creativity of your work. You should strive to turn in work of publication quality in your course project: neat and easy to read, complete sentences, proper grammar and spelling, correct units, well-organized, and a demonstration of your mastery of the subject matter. Future employers and teachers will expect this quality of work. Moreover, although submitting work that is publication quality requires "extra" effort, studies have shown that the effort you expend in clearly explaining your ideas solidifies your learning. In particular, research has shown that writing and speaking trigger different areas of your brain. By communicating your ideas to others - even when you think you already understand them - your learning is reinforced by involving other areas of your brain.

    The writing center in the library is available to help improve the quality of your writing.

    See library and other searches

    One example of a possible course topic would be the idea of transformations [of a space/object]. In MAT 2240: Introduction to Linear Algebra you explored matrix transformations in 2-D and 3-D. If you took MAT 3610: Introduction to Geometry or MAT 3110: Modern Algebra, you would have explored symmetries or groups, like the dihedral group, the group S4 or the symmetries of a cube or tetrahedron. Research on Felix Klein and his Erlangen Program as well as this application of transformations in modern algebra to physics and chemistry would provide some examples of 20th century perspectives. In addition, recent research on transformations is also easy to find via a MathSciNet search from the library.