Is an undergraduate in engineering sufficient preparation for a masters in mathematics? 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.
 A: My answer is probably no, speaking as someone who did both undergraduate and graduate studies as an engineer, and works in industry as an engineer.
Engineering has very little emphasis on mathematics as a science and far more as a toolkit for solving engineering problems.  For example, there were virtually no proofs in class, but a very strong emphasis on application.
This is necessary. In electronics engineering, you need Fourier analysis and Laplace transforms by the second semester in order to perform AC and transient circuit analysis.  At sometime in the second year, you'll need ODEs and PDEs to analyse control systems and electromagnetics.  You'll need probability theory to tackle communications problems by the third year (e.g. matched filtering).
The immediacy of the engineering problems at hand does not really allow for in-depth mathematics training.  I hate to admit it, but many of the questions on MathOverflow are gobbledygook to me :(
Nevertheless, many graduate problems in engineering are highly mathematical, particularly in information theory, signal processing, control theory and robotics.  Many papers that I read actually come from mathematics departments rather than engineering departments.  Those with engineering training (like me) just have to catch up :)
