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Disclaimer: I'm a CS PhD student that did pure math in undergrad, so I probably have a different perspective on these things than someone who did CS only.

CS, at a graduate level, is a much more varied field than most people, even CS undergrads, realize. In fact, a lot of the main research groups in my department (graphics, vision, image analysis, robotics, VR, visualization) are things most CS undergrads don't even get exposed to.

In math or physics, a lot of the undergrad courses are kind of basic, entry-level things that give you a feel for some of the different fields of research without going too far in depth. This isn't really the case with CS, because CS departments have to cater to several different audiences who tend to fall into one degree. They have to come up with a curriculum that balances programming/development concepts for people who want to be developers, networking/administration stuff for people who want to be IT (although this is more and more being moved into a separate program), and theory for people who actually want to be computer scientists. Even then, this theory is mostly relegated to computation theory, which is only a small part of what research computer scientists do.

Personally, I'm in medical image analysis, which is a field which is a collision between a ton of different areas, including physics, statistics, operations research[1], numerical analysis, image processing, differential geometry, and medicine. I don't know that I would consider any of those fields to be the "easiest branch of mathematics" (what does that even mean, anyway?)

This post has kind of gotten off the rails a little bit, so I'll end with this: I think, if you just look at a CS undergrad program and try to project that to what actual CS research is like, you end up getting a much narrower and incomplete picture than if you do the same thing to a math or physics department, partly because CS research tends to be much more interdisciplinary than others (I have many more collaborators in many more areas than some friends of mine in math/physics/biology do).

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[1] http://en.wikipedia.org/wiki/Operations_research



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