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?
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.
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.