This must be written as a formal document, and you should extend your style; for example, consult Strunk and White (op cit). Your report must be done with LaTex, and a clinic style file will be provided for you to use. Carefully proofread your report for spelling, grammar, etc. You are encouraged to read at least one other team's report (before the final due date) in order to help each other with final proofreading. It is imperative you s t r e t c h your communication skills!
The style file will take care of this, but you should be aware of what is needed.
The table of contents describes the organization of your report. Here are some details about each section.
The purpose of an abstract is to communicate what the paper is about. State the problem, or problem area, and highlight your main results. Avoid special symbols, replacing mathematical notation with words, and do not give any citations. It should appear on a separate page (after the cover) and have about 75-100 words.
The purpose of an introduction is to tell the reader what you are going to say. This is a succinct description that not only gives guidance to prepare the reader for what follows, but also offers motivation for the reader to want to read the rest of the report. It begins on a separate page (following the abstract), which is page number 1.
This can be viewed as a technical introduction with citations that give a review of the relevant literature. Each citation has a reference (see below). In addition, this section contains basic terms and notation that are used in presenting the main results.
To elaborate, the Background section gives technical terms and concepts that are basic and serve to inform the reader who might not know such things. (It could just as well be titled Terms and Concepts; it's a matter of taste, as long as you choose a title that accurately describes the section's contents.) For example, the paper might be about certain graphs. The Background section introduces graphs, giving their formal definition, and whatever special graphs are appropriate for the particular project. The Background is also where many of the citations appear, describing some of the seminal works that are pertinent. For example, this can include a basic reference to graph theory for the reader to learn more general background, as well some reference(s) to a special graph that is the subject of the paper (eg, bipartite graphs).
Compared to the Introduction, both the purpose and the form are different. As a rule, the Introduction is short and is designed to give a succinct description of what follows, including the organization of the report. It is appropriate to see a paragraph that begins with: "The rest of this report is divided into n sections. Section 2 gives the background..." Also, the Introduction should motivate the reader, maybe offer some excitement about the subject. There is thus no chance to give background that might be necessary for the reader's comprehension. That's what the Background section does, including examples, figures, etc.—none of which have any place in the introduction.
Note: Some authors combine the functions of an introduction and background, in which case the section title reflects this. That decision is made by each clinic teacher.
3. Main Results
Divide this into subsections as appropriate. The last subsection should be a summary and/or conclusions (this could also be a separate section; it's a matter of taste).
4. Avenues for Further Study
Give avenues that include things you wish you had time to explore.
Use this for extended background or lengthy proofs that would interfere with the flow of text.
References and Bibliography
Use any acceptable format (as you learned in high school), but be consistent. References are associated with the citations in the text (mainly in the Background section). Additional bibliography may include references you explored but deemed irrelevant to your work. You are urged to include this, perhaps with some annotation. You may separate References from Additional Bibliography, the former being cited in the text and the latter annotated (say why each entry is included but not cited—for example, it might have seemed relevant from the title, but it turned out otherwise).