Majoring in economics while aiming for a PhD in math is feasible, provided the individual has a solid foundation in mathematics through self-study or coursework. Admission to reputable graduate programs will depend on the extent of mathematical knowledge acquired and the specific area of math pursued. Similarly, transitioning from an Electrical Engineering background to a PhD in physics is possible, but success hinges on the undergraduate coursework completed and the desired physics specialization. While switching from engineering to physics is less common, it is more typical for students to move from physics to engineering. For those in engineering fields like materials or aerospace, the same principles apply; the relevance of undergraduate studies to the intended graduate field is crucial for admission prospects.