I'm a high school student who is considering doing an undergraduate in engineering. However my the long term plan is to pursue math at a higher level. I want to do engineering at undergrad because I think studying it will help me find real world applications for the math I learn later on.
However, I'm worried that if go through with the engineering option it will be difficult to get into a math masters program because I'll be unprepared for the rigor. The most math intensive engineering is called Engineering Physics. The 3rd and 4th year math courses taken are PDEs, complex analysis, intro to real analysis, and groups and symmetries.
Are my worries necessary or is this sufficient preparation for a masters program in math? If it is not, is the only way to prepare for a masters in math through a math undergrad or can I somehow supplement my knowledge in order to prepare gain the required knowledge for higher level math?
Thanks in advance.