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
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:
A LaTeX template:
LaTeX code for Part 1 of the course project
and the pdf version.
[Due Feb 9]
- Your topic
- Your name and prior experience with the topic
- 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.
- 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.
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
Beamer slides template:
and Figure 1,
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).
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
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
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
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