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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.

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  • $\begingroup$ You are probably in US, so I do not know the system very well, but if you plan to do "math at higher level", I suggest you to do maths and not engineering. I know many people which have done this successfully (going to banks, industry, ... after a PhD in pure maths or a master) and I know nobody which suceedded the other way (although I'm sure that it exists). This is of course just an opinion and maybe other people could have other experiences. $\endgroup$ – Jérémy Blanc Apr 7 '14 at 12:46
  • $\begingroup$ Both the math program and the engineering program I have received admission from are both in Canada. $\endgroup$ – imu96 Apr 7 '14 at 12:50
  • $\begingroup$ Ah OK, sorry. Anyway, I do not know the system there. My comment was just general. $\endgroup$ – Jérémy Blanc Apr 7 '14 at 12:57
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    $\begingroup$ Without knowing precisely the syllabus, I'm pretty confident that an undergraduate in engineering (any engineering) is way too little for graduate studies in mathematics in general, though perhaps it could be enough, or close to, for applied mathematics. OTOH, you could ask some graduate schools about this, perhaps providing the syllabus of the undergraduate progam you intend to take. $\endgroup$ – DonAntonio Apr 7 '14 at 13:25
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    $\begingroup$ Depends what kind of maths you will do in the Masters. If you will do applied maths, then maybe yes. If you intend to focus on pure maths, then definitely no. $\endgroup$ – Frank Apr 7 '14 at 13:58
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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 :)

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  • $\begingroup$ Well, it's a good thing that I chose maths as my major then. :D $\endgroup$ – imu96 Oct 5 '14 at 1:41
  • $\begingroup$ So if most of the engineering research you read is from maths departments, does that mean that you can go into an engineering graduate program from maths, or would you be lacking too much background knowledge in terms of other sciences? $\endgroup$ – imu96 Oct 5 '14 at 1:45
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    $\begingroup$ Indeed. As it turns out, it's not terribly unusual for mathematicians and/or physicists to be eventually employed as engineers - particularly in software with a mathematical emphasis. So there are plenty of options for you. Good luck! $\endgroup$ – Damien Oct 5 '14 at 1:46
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    $\begingroup$ It will depend on the school and/or professor, but I can't see too many issues with a math graduate doing engineering research. This is particularly true of the more mathematically inclined disciplines where you're more likely to use a supercomputer than a soldering iron... $\endgroup$ – Damien Oct 5 '14 at 1:49

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