Math 3MB3 Final Project Report - Instructions
This part of the project is worth 25% of your final course grade and is due by 11:59pm on Friday, Dec 13th, 2024.
You should submit your final report in .pdf format and named the file as “Group XX-Topic X-Final Report” . Each group should have only ONE submission by email to instructor (zhaos126@mcmaster.ca). The title of your email should be “MATH3MB3 Final Report-Group XX” and you should copy (cc) every group member in the email. Make sure that you add your final report (as a .pdf file) as an attachment of the email, links to shared cloud files will not be accepted even if it is downloadable. You should also submit all supplementary files (R other programming code, picture or figures, etc.) by compressing all of them in
a .zip/.rar/.7z file and submit it together with the final report.
There is no strict page/word limit, but suggestions are given below for approx- imate lengths of each section. Any reference style is fine for citations; so long as all the information is there, I’m not picky about what style you use. Please note that your submission will automatically be passed through Turnitin after it is submitted.
Your final report should read as one cohesive document and should be written using complete sentences/paragraphs. It should be structured into the following sections:
1 Introduction (approx. 3-5 paragraphs)
This section should outline the real-world background and context of your model. Discuss the motivation one might have to study this model. You may want to research the relevant literature and include some citations to support your framing of the real-world context (depending on the project). Be sure to include only background information and context that is directly related to your research project. Really focus on what the reader needs to know to understand your work, and be interested and excited by it.
The final paragraph of your Introduction should frame. your research question and de- scribe what you will be studying in your paper. Briefly mention, in words, what you will be doing and showing in the rest of the paper. It is often good to lay out your main find- ing/result here, too. A good Introduction section for an applied mathematics paper ideally has no mathematical symbols or jargon; instead, it should be focused on the real-world con- text and what you are trying to study. The math is a tool you will introduce later, not the main focus of the paper.
2 Model (this should be as long/short as it needs to be,
it’s hard to give a length estimate for this section)
This section is where you will lay out your base model, any analyses you performed on it, and the extended version of your model. It should be structured into three subsections, as follows:
2.1 Base Model
Start by explaining the real-world mechanisms you’re modelling, and any you’re omitting. Discuss the assumptions you’re making in reducing the real-world system to a mathematical model. Define the state variables you’ll be working with. Don’t forget to clearly state the units of the variables.
Define parameters (and their units) and cite any sources for the values you’re using to parameterize your model. If you cannot find specific parameter values in the literature, make educated guesses for values and explain why you’reusing these particular values (in this case, you may want to consider a range of parameters instead of just one specific value to ensure your modelling results are robust to some uncertainty in parameter values).
You may want to to include a model diagram (e.g., if it’s a compartmental model). Write out the model equation(s) and explain any modelling choices you’ve made in them (e.g., discrete- vs. continuous-time).
2.2 Analysis of Base Model
This subsection should describe the various analyses you’ve performed on your base model and the results you’ve obtained from them. You should be using a mix of analytical tools (e.g., finding equilibria, determining stability) and numerical tools (e.g., model simulations in R). When discussing analytical calculations, you don’t need to list out every single step of your calculation; just present the important/key steps. When discussing numerical simula- tions, you should describe what your R code is doing and present some plots to supplement your written descriptions; all R code should be presented in an appendix at the end of the paper (see below). Be sure to describe what these analyses tell you about your base model and what predictions they make (this should be in the context of the real-world scenario framing your project).
2.3 Model Extension
Here, you should describe the extension you’ve chosen to study for your model. Start by discussing what the extension is and how you plan to change your base model to account for it. Similar to the base model subsection, be sure to talk about any assumptions in your modelling, define state variables and parameters (including units), and describe any modelling choices made. In particular, you should highlight how your extended model differs from your base model. If appropriate, it would be good to include a model diagram. You should also write out the model equations. Do not discuss any analyses of the extended model here. That will go in the next section.
3 Results (again, it is hard to give a length estimate for this section; it should be as long as it needs to be to convey all of your results)
In this section, you should describe the analyses you performed on your extended model. Be sure to motivate your analyses in the context of your research question (i.e., why do you want to perform. each analysis, what are you hoping it will tell you). These analyses can be purely simulation-based: you are not required to perform. any mathematical analyses of your extended models, but if you can, you should! Mathematical analyses generally tell you more about model behaviour than simulations (when both are possible). You should be including plots here, as well, to go along with any simulations you did. Unlike with the draft, this section of the paper should now be complete and all results should be discussed in the paper.
4 Discussion (approx. 4-5 paragraphs)
This is the final section of the main body of your paper. Start by briefly summarizing the main results you presented in the last section and relating them back to your research question. This is also where you should be providing answers, based on your results, to your research question(s). Be sure to interpret your results in the context of the real-world scenario framing your project. What are the implications of your results?
You should also discuss limitations of your work. This is usually related to the modelling assumptions you made before. When are your results applicable and when are they not applicable? What factors have you omitted from your model that may affect the predictions? This is important to discuss, otherwise the reader may come away from your paper with the impression that your results are universal which is rarely the case.
Finally, you should discuss possible directions for future research. Did your results open up any other questions? Where else could you go with this work? Are there other things you’ve read about in the literature that could be interesting to look at? You should also use this as a way to conclude your whole paper.
5 References
This section should be a list of any references cited throughout your paper. Again, as long as all the information is present, you can use whichever citation style. you prefer.
6 Appendix: R Code
This appendix should list all of the R code used in your project.
7 Appendix: Individual Contributions
This should be a list of each group member and what they contributed to the project (in- cluding the presentation). If it is clear from this list that a group member did not contribute equally to the whole project, their individual grade on the final report and/or presentation will be lowered below what everyone else in the group receives.