Pursue a Masters in Comp Sci immediately after BS Math?

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I'm finishing my BS in math this spring. I know a little c++ but not much to say I have mastered it. Is it smart to start a MS in comp sci so soon?
Should I wait and do some self study and then apply?
 
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I'm almost certain that most grad schools, if not all, require courses in data structures, algorithms, databases, operating systems, computer architectures, (although it's might not be necessary to include all of these core courses) and additionally senior-level specialized courses.
 
I was just talking about this with a friend who is in the program I intend to attend. He told me that there are several people in the program who have degrees in other fields, like math, physics, chemistry, and engineering. Apparently this program offers graduate leveling courses. That's why ask however; would it be worth it to go ahead and jump into leveling courses and go from there, or should I self study for a semester or two and then go from there. Also, the community college in town offers several computer science classes, like c++, java, networking, etc., would that be a better choice? Forego graduate studies and get a community college degree/certification? Completely or just in the meantime? I've read a lot that for jobs in industry, a degree in computer science isn't always necessary which muddles the waters even more for me. Any hints?
 
What topics are good to self study and with what books/resources? Which are best to wait and learn in a class setting with more guidance?
 
There really isn't a best way. If the school has a hard requirement that you have course x, y, and z as an undergraduate, then you'll have to take said courses. If the school is flexible and allows you to take course x, y, z within a year of starting your program, then I would focus on improving my programming skills while at the same time learning about the material that will be covered in said courses.

Computer science can be fairly theoretical and abstract, but at the same time, each class generally has something you can take and apply to a project. When I'm learning something new relating to CS, I generally think about a project that can use it and see if I can implement the concept. In doing this, I'm forced to check my understanding, and dive deeper than simply reading the words.