When most people think of the core muscles, they think of the abs and lower back, but any muscle that attaches to the pelvis could be considered a core muscle.
 
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Overtraining is a common Ab Workout Mistake.
The abdominals are just like other muscles, which means that you can work them too much.  There's no need to slave away doing 30 minutes of ab work.
You can strengthen your abs in 1-3 sets of 2-3 exercises.
Don't kill yourself in the gym doing 1000's of reps.  Just do a few good and productive exercises and that's all you'll need for a strong core.