Components of your report

Your research report should have the following particular sections. Depending on your project, you may have additional sections. You can always do more than is required.

  • An abstract: this is where you give a very brief synopsis of what your research project studied and what you found out. Think of the abstract as an advertisement. A researcher looking for some result to help them with what they are interested in isn’t going to have time to read through your entire paper. Instead, they will look at the abstract to see if it might have something useful or relevant. If they don’t see that, then they are not going to read the rest of the paper for sure! Your abstract should help researchers who should read your paper to be interested and read on while helping researchers who aren’t thinking about your topic to quickly realize that they need to look elsewhere.
  • An introduction: this repeats the information in the abstract but more verbosely, with greater detail. Here, we will make sure to define any undefined terms in the abstract. We may also introduce any information we might know about the history of the problem, or any connections it might have to other parts of mathematics that we know of. A researcher who has read your introduction should be hyped about your work and should also have a good idea of exactly what you did and what the results were. The rest of the paper is explaining the details.
  • A methods section: this talks about the scientific or mathematical methods that you happened to use for your results. Did you use experimentation? Random trials? A computer code or algorithm? A mathematical theorem? Describe that in detail here!
  • A results section: this is where you describe exactly what the results were of your research. If you were conducting random trials, what were the results of the trials. What was the output of your code or algorithm? When you applied the mathematical theorem to your situation, what popped out? Using figures or graphs can also be very nice here! Be sure that any figure has appropriate labels (legend, labelled axes, and units!!)
  • a conclusions section: much like the introduction, you will summarize your paper here. You will talk about the problem and what your progress toward a solution was. You can also discuss future research directions or maybe why what you tried failed if that was the case.
  • an acknowlegements section: this is where you thank anyone not listed as an author who helped you with your project. If you consulted another student or a professor, you have an opportunity to say thanks here!
  • a bibliography section: this is where you cite any external sources or papers that you used to help you with your research. Did you borrow an image from somewhere? Put that here! Did you look at a solution of a similar problem online on some website? Did you use an academic paper for its results or methods or inspiration? Did you borrow someones computer code? Make sure to say so here!

Here is an explicit example of what your report might look like in the end. Feel free to use this document as a template, where you replace the content with your own work.

Grading the report

Your report will be graded based on the following criteria.

  • Readability (1-4): was the paper well-written? Were there lots of spelling or grammar mistakes? Was it well-formatted, or are things just thrown in willy-nilly?
  • Mathematical accuracy (1-4): does the math, computation, or code check out. Are there mistakes?
  • Depth (1-4): did we dive into and explore the problem in detail. Is there obvious effort or is it clear that there is only a superficial investigation.
  • Completeness (1-4): are the required sections in the report? Is the content of each section what it should be, or is it lacking or missing entirely?