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I'm not sure how the switching process works in Engineering, but if you want to try take the lower div requirements for it (which overlap with math and pretty much all the engineering classes) and visit the department or email them about impacted admissions. Worse comes to worse, take another engineering, or math, and get a minor in it.
Nothing about getting into it if you're not already on the MAE site. Though, the Engineering Sciences major looks like it's a pretty similar major, you should check it out.
Best.
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