Does Nikon D3100 have with sync connection?

I want to take a photography class but it is required that I bring a DSLR with a hot shoe or sync connection. I have a basic D3100 and I know it doesn't have hot shoe but I'm not sure about possibility for sync connection?

And if not, what Nikon do you recommend that has these features?

The Nikon D3100 has a hot shoe.

See pages 2, 172 and 198 in your user manual

The D3100 has a standard hot shoe, as does just about every SLR camera since at least the 1980s. Most photography classes require you to have a hot shoe on your camera so they can teach you how to properly use a flash gun, which mounts to the hot shoe in order to "sync" with your camera. Any flash mounted to a hot shoe should sync with your camera, in that they will fire as soon as you press the shutter. And that's any flash, even very old ones.
But if your camera doesn't have a hotshoe, then you can use a flash sync cable and a remote to trigger it. That's what I understand "sync connection" to mean anyway. However, you don't need to worry about that.
Enjoy your course.

All DSLRs have hot shoes - they just differ between manufacturers.

The old PC socket is long gone, but there are a plethora of cables on the market which plug into the hot shoe and allow off-camera flash.