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LSE MSc Applicable Mathematics vs UCL MSc Mathematical Modelling

Hello! I have two MSc offers, one for LSE Applicable Mathematics and one for UCL Mathematical Modelling and I am undecided about which one I should go to. My career aim is to do a PhD in Financial Mathematics/ Discrete Mathematics and do research in Quantitative Finance or Algorithmic Mathematics within academia or for a company.

So far my pros and cons for each are:

UCL is ranked much higher (no.9 in QS is quite impressive to me) and the university is much bigger so I am thinking there may be more freedom for me in terms of finding someone to work with for a PhD. On the other hand, the course is kind of physics-oriented, which I am not a huge fan of. There are a lot of PDE modules and things not related to what I want to do, but there are some okay ones too, but not as many as in LSE.

On the other hand, the LSE course goes much better with what I want to do, they have a lot of Discrete Maths, Machine Learning and Financial Maths modules. So, in my head, LSE is great, but my only concern is how good their Maths department is. Also, they are ranked much lower and I am not sure how much the ranking really matters in real life, considering how well known LSE is. I am expecting to do my PhD in the same place where I did my Masters and as LSE is more of a Social Science school, how would my PhD in Maths from LSE stand against the PhDs of people from other universities when applying for positions? In the long term which choice do you think is more advantageous for the plans that I described?

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