Changing streams in PhD I've a masters degree from a reputed Indian university in pure mathematics, with a specialization in Algebraic Number Theory. However, I'd like to apply for a PhD in computational math/theoretical computer science in US universities next year. How should I go about it? Considering that I've little or no formal background in the applied branches or computer science, do I stand a chance of getting accepted in a good PhD program? 
Also, what should I tell them when I write SOPs? How should I make myself appear to be a good candidate for a CS PhD without having any formal background in the area?
 A: You're way ahead of most U. S.-born college students. One time I asked a chemical engineering student what $\sqrt{-25}$ is. Wanna know what his answer was? 5. Let's just hope he doesn't decide to switch to electrical engineering.
So if I was you, I'd be more worried about having too many programs to choose from. If you've got some family already in America, you'll probably be able to choose a program that is prestigious and close to your family.
A: Speaking as someone who has a masters degree in Mathematics from India and is now doing a Ph.D. in CS in Europe:
I would expect you to just be honest in SOPs about: 


*

*Why do you want to do a Ph.D.? Maybe because you read about some topic and became interested, you tried a machine learning model and realized that you would like to study more on this

*Why should the university choose you? Because you have already shown the grit to understand highly rigorous and technical mathematical texts. A lot of theoretical computer science is based on pure mathematics. 
Regarding the showcase of your commitment, you could do online courses to have a deeper understanding of which field to explore and which sub-field to specialize in. This would even help your CV.
