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How to present calculations in a report

I recently spent a decent amount of hours trying a answer a question my advisor had asked. As a result, I ended up with a pile of papers, some printed out graphs and pieces of Matlab and MathCad code, and random sheets with hand calculations – and only an indication of the answer. As I thought this topic deserved some additional attention, I combined the chaos on my desk into a 44-page report (in less than 20 hours of time, while still running additional calculations).

Here’s how I organized the material:

1. How did it start?
Why did I decided to spend some time on this topic? What are the limitations of the previously used techniques and what will I try to solve in this document?
I used the answers to these questions to try and keep the bigger picture in mind.

2. What does the literature say?
What useful information and descriptions are available in the literature?
Not all of the papers I had read were useful. I did end up citing most of them, but some of them I discussed in larger detail. I distilled the methods which I ended up trying out myself, and clearly wrote how they should be applied for the question at hand.

3. Structure the calculations
Even though this is work-in-progress, I wanted to bring the different pieces of code and calculations together. I went through the print-outs of code, my own hand calculations, the tables and graphs I had accumulated while working on this problem, and decided to copy and paste the relevant parts right into the document. Although this would not lead to a neat final report, I decided I wanted to show the train of thought which I followed to my advisors, to show clearly the process and be able to discuss the steps I took.

4. The assumptions
I made a separate section which focused on the limitations and assumptions I had used in the calculations. I also discussed some advantages and disadvantages of some of the assumptions i had made – to facilitate the discussion on the calculations. Likewise, I added a list of questions and uncertainties which need to be discussed.

5. Give up on perfectionism
Even though I aimed at fully answering the question my advisor had asked me, I contented myself with the idea that I had found interesting material on my way, had played around with several methods, and learned from it – but I did not find a conclusive answer yet. A few years ago, I would have never the problem rest before having a full solution. However, that is not even possible in research – assumptions need to be discussed , and sometimes some advice along the way is more than welcome.

6. What did we learn?
After all the calculations, which directions are open to be chosen? What can we conclude up to now?

Do you have a clear way to present calculations? Please let me know in the comments section

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