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Applying to CS grad school as Math undergrad


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I graduated from a top liberal arts college with a math degree two years ago (mostly focusing on Abstract Algebra). During this time, I published two papers.

After working for two years, and taking an online course from Harvard on Deep Learning and Natural Language Processing, I decided I wanted to switch my career and do research in Machine Learning. However, the problem is that I've only had one single CS course during undergrad -- intro programming. I'm taking an online Data Structures and Algorithms course to compensate, but that still leaves me without any fundamentals and CS basics.

I'm wondering if I have any realistic chance at breaking into a top CS grad program: relatively good undergrad math background, but not a big CS background.

I'm thinking of applying to Masters Programs since perhaps I'm underqualified for PhD programs. However, if I have some realistic chance of getting into a PhD program, certainly I don't want to waste two years.

As not all schools let you apply to the PhD and MS programs concurrently, this is a struggle for me, since I have no idea how well I scale up to others.  

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