Help a fellow STEMfag /sci/

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So...I have a bachelors in computer engineering and I'm content with it right now..
..but I've always been fascinated by pure maths and wanted to pursue it as my major before I eventually went for the normie option. I chose computer engineering as my major solely due to the prevalent consensus in the industry, but an insatiable urge to learn more maths has pushed me towards a compromise......that is to get a PhD in theoretical computer science(as I'd have to get a separate bachelors degree in maths to really pursue purely mathematical fields). Here's the question: Do I need to take any pure maths courses before applying to a university for theoretical CS?