MSc Mathematical Modelling and Scientific Computing

BIG EDIT (02/2022):
After speaking with the course director, Kathryn Gillow, which has a strong influence on the selection for the program, I learned that they mostly care about a student's grade and reference letters. Therefore, the personal statement is not really crucial, and in fact, most people who eventually ended up in my course didn't spend too much time on it. With that being said, I am leaving the original post intact as the guidelines on the SoP helped me land offers at other top unis, so I believe them to be relevant.

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I had my interview today. It went pretty well: it took me some time to answer the questions and I did some very stupid mistakes along the way (like errors in summing stuff, plenty of those, or wrong parenthesis placing) but I eventually got to the correct solution for each answer and I proved my background knowledge.
This very night, right after the interview, I got the email with my offer(!). Now that my journey to get into Oxford is over, I would like to share what I learned along the way. Of course, there are super thorough guides all over the internet (youtube was incredibly helpful for me) but I'll just hive my 2 cents. If anything that I say here goes against the rules let me know and I will edit the post asap.

Application and Personal Statement:
All you really need to get into this course, as far as I learned, are 4 things:
- Good scores on courses corresponding to the prerequisite materials (and obviously a 1st or strong upper 2nd degree)
- Some academic extracurricular experience (personal projects etc)
- A strong statement of purpose
- Study the prerequisites for the interview

For the statement of purpose you will need:
- a good reason to apply, possibly somehow bonded to something deeply personal that characterizes your personality and character;
- to show that you looked through the course structure and courses thoroughly and state what you like about it;
- to prove that you push yourself beyond what's normally needed on a regular basis (again, projects etc. You might want to exploit those to also show how you are able to autonomously overcome difficulties);
- to prove that you have a good handle of the prerequisites (if that is not absolutely obvious from your transcript, this mostly applies if you are non-UK).
I also suggest searching for examples of letters on youtube as they help understand how to give the proper assertive tone to yours.

Once you do that, and you ask for feedback from people who got into a top uni, you should have a high chance of getting to the interview.


Interview:

Do obviously study the prerequisites. They mostly want you to be able to do exercises or calculations/manipulations of formulas in general, so don't focus too much on theorems.

In order of importance, they mostly care about:

0. (linear algebra, they just want to check if you have the basics and they will go very quickly on this if you have them)
1. Solutions of PDEs via separation of variables (as they listed in the prerequisites, and as other people already mentioned here) just do the chapter on PDEs on the book they mention (I personally liked Kriesigz)
2. Taylor expansions (as for limits or finite differences formulas)
3. ODEs
4. Complex analysis

They might of course ask you else so don't slack off on the other material, as previously suggested.

Do say out loud what you're doing. Say clearly what you intend to do on each step and if you're not sure about whether that's the right idea, just wait for the examiners' reaction. Mine were extremely sympathetic and engaging and would guide me through.

I hope this all will be of some help to random people surfing the internet for advice like I was. Do not be afraid to apply, just give yourself the proper amount of time to do it well. I myself would have never ever believed that I would have been accepted, I thought the extracurricular stuff I did was not enough, or that my motivations were not sufficiently strong, and so on.. Just work on the application and do seek advice and feedback from people who got into a top uni and therefore know how to write a personal statement (for the interview, all you need is in the thread).


Best wishes!