Each student will carry out a research project during the semester. These will be done in teams of two or individually. Ideally this project will allow you to explore an area where numerical computing overlaps another area of interest that you have. These projects should involve programming and numerical experiments as well as have a significant writing component. You will need to locate and utilize references beyond our text, carry out your experimentation and then write a report that explains your work in a coherent manner.

It is not sufficient to merely research a particular numerical method or topic and report on it. You must engage the topic in a substantial way, addressing and solving a particular problem. For example, if you chose to work with finding eigenvalues of matrices you should learn about the various ways this can be done for different types of matrices, implement numerical procedures (using Python or some other programming system) to carry some of them out, demonstrate your code works properly by finding eigenvalues, and summarize your results.

Your projects will probably include multiple figures and perhaps data. Most likely the will also include a significant number of mathematical formulas and equations. Because figures and formulas can take up a lot of space, it's probable that the papers will be somewhat longer than a typical paper for your other, non-science subjects.

Finally, although the learning curve is steep, you may want to learn how to use LaTeX to write-up your project; LaTeX and the underlying TeX system are the undisputed standards of text-processors for mathematical papers. Overleaf provides web-based LaTeX document preparation systems. If you want to work off-line, try TeXstudio; packages are available for Windows, Linux, and Mac. There is a lot of good documentation on writing LaTeX documents; Google around to find some you like. A good reference is The Not So Short Introduction to LaTeX 2e. Another nifty LaTeX helper is the Detexify LaTeX handwritten symbol recognition page, where you can draw a symbol and the site will tell you the LeTeX code for the symbol. We have a copy of Learning LaTeX 2nd Edition, by David Griffiths and Desmond Higham, SIAM, 2016 in the Mathematics Library.

Project Components

Initial Topic Idea

You should submit a tentative topic from the list of suggestions that appeals to you or another topic that you think would be appropriate. In either case, please include a paragraph explaining your interest in the topic, how you think it helps to meet the objectives of this course, and a short list of places that you will look for references. You will need to schedule a meeting with me to discuss your topic idea.

Final Topic Idea

You have selected a topic and discussed it with the me. As part of this process you should have begun to identify the resources that you will use in carrying out your project. Also you should have an idea of the type of computation you will need to do.

Tentative Project Outline

You should submit an outline of your paper and any other output necessary to demonstrate substantial progress in your numerical work. At this point much of the programming or mathematical modeling should be completed and you should have begun to piece your presentation together in to a coherent whole (hence the requirement of an outline).

Project

This should be not be treated as a first draft but as a complete, final project. I will grade the projects and return them to you with comments so that you may make changes and resubmit for an improved grade.

Revised Project

The final version of your project is due. You only need to turn your project in again if you've made changes since I returned them to you. If you do resubmit, please turn in both the version with my comments on it as well as the new version.

Class Presentations

You should plan on a ten-to-fifteen minute presentation followed by a time for questions. You may use a computer in your presentation (Beamer, PowerPoint, etc.), document camera, or the board.

Advice

Start early. Find a topic that truly interests you. Consider the computer and programs like Python, Octave, Mathematica, and other software as exploratory tools that allow you to try things—even if it's just because (especially if it's just because) you are curious!