I requested input from our ECE Head Advisor, Dr. Molly Shor, who received the A.B. degree in applied mathematics from Harvard University, Cambridge, MA, and then the M.S. and Ph.D. degrees in electrical engineering from University of Illinois. (so I thought she would also have good input)
Professional degrees in engineering are at the undergraduate level, unlike the fields of medicine and law. A graduate degree in engineering does not give you the same background to make you work-ready for industry and to be able to apply your engineering knowledge. It does not give you the breadth, either, in your field of study.
There are many universities that restrict entrance to the professional engineering programs at the upper division (junior and senior) level, based on academic performance in the first two years of study. Selecting such a university with a selective professional program may appeal to you.
You may also wish to minor in mathematics or pursue a double major. Since engineering programs typically require a year of math and basic sciences, your preparatory math courses will likely prepare you for the upper division mathematics coursework. As you decide on your programs of study, ask to speak to an advisor for the math programs as well as consulting with an engineering advisor.
Dr. Annette von Jouanne, Ph.D., P.E.