Fresh grad from a non-CS background

Hi all,

I'm about to complete my PhD in mathematics (my research is in probability theory, not directly related to ML).

My goal is to find a job at a tech company, though I'm not sure what roles are really "open" to me. Are there any particular advice/thoughts anyone has for someone with my background?

I've been (and will be continuing) to do (and redo) leetcode problems and learn more DS and algo. Apart from this how does one go about getting (and preparing for) an interview?

Are there other technical skills I should work on (i.e. not leetcode style algo problems)? I've been doing everything in python, should I pick up some better SQL skills too?

The only real coding experience I can put on my resume is an internship I did in 2013 as an undergrad (and I'm not sure I should put this since it was so long ago). I'm working on making my resume show I am a capable self learner, I learned some basic DS and algo on my own following some textbooks/online problem sets.

Location: USA (open to any area really, with preferences for LA/SF/NYC).
Citizenship: USA ( I assume this can make a difference)
Education: BS in math,physics PhD in applied mathematics. PhD from R1 school, reasonably big name overall.

Thanks for the read/thoughts! good luck everyone!

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