MATH 588, GEOPH 605, CE 697

Spring 2011

PROJECTS

**Introduction**

After an introduction to inverse problems, you will be required to define a realistic inverse problem which you will solve three different ways in three different projects: statistical methods, Kalman filtering and optimization methods. The goal of the projects is different than that of homework problems because it is a research assignment that has a general goal, but may not have a clear direction or answer. You are supposed to use the knowledge acquired in class to think about the problem for several days, to ask new questions and to try to answer them, to stir your imagination, and to search for suitable references. Start as soon as possible, and let your subconscious work for you.

**Project proposal**

In your proposal motivate the problem, give sufficient background and formulate the appropriate inverse problem(s).

**Oral presentation**

Presentations should be 20 minutes long. The presentation should follow this outline- Problem description. This should take 1-2 slides and your goal should be to motivate why one would want to study this problem. For example, justify the equations, describe what type of phenomena they describe and outline the questions you intend to answer or explore in your project.
- Approach. Do not spend a lot of time going through the math but outline the approaches or methods you used from class (or outside of class) to study your problem. This should take 1-2 slides.
- Results. You may want to show graphs or tables at this point but make sure there is a summary slide which lists your conclusions about the graphs or tables. Do not show a table or graph unless it explains a point you want to make or one of your conclusions.
- Some general suggestions:
- Make the presentation simple, and do not include too many details. If someone is interested in your work, they can read the full project.
- Realize that your audience is the other members of the class.
- Do not put up a slide with very complicated drawings or millions of numbers. Less is more.
- Begin with a slide containing the title of the project, and anyone who contributed to it e.g. your advisor.
- Use a large font, or write large enough so people can see in the back of the room. I would use no more than 12 lines per slide.

**Written report**

Each project should demonstrate that you have a good understanding of the problem, its importance, limitations and complexity in addition to demonstrating your knowledge of the methods used to solve it and their limitations. The background understanding of the problem will evolve with each project, and results from previous projects should be included and compared in subsequent projects.

- Each project should include an introduction, methods, results, and discussion section accompanied by tables and graphs illustrating your results. Follow the basic instructions I gave above for the oral presentation. In addition, use complete sentences, good grammar and correct punctuation in your mix of equations, formulas and prose. Your report should be written in such a way that it can be read and understood by anyone who knows the material in this course. You will be graded on your written presentation as well as the mathematical content.

A one-page executive summary or abstract should also be included at the beginning of each project. Write this in non-technical language for the reader who has an interest in the research question but does not have any technical training. It must state briefly: (1) the research question and why it is important; (2) the methods used to study the question; (3) the findings and what they mean; and (4) what action you recommend on the basis of your findings.