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I'm currently studying electrical engineering and considering on getting both a physics and math minor. I'm wondering though, is it possible to get a Ph.D. or a Master's degree in Physics or Math when I only have the minor and not a real degree?

Is it likely at all to be admitted into a graduate study with only a minor? I'm wondering because I don't know whether or not the minor is actually worth it if I won't be able to pursue a graduate degree later on with my credentials.

For reference, a math minor at my school typically means 3 extra upper-level math courses (300-400 level), and only 2 more physics courses (one in waves + light + thermodynamics; the other which samples different fields of modern physics, all required for the degree program)

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    It is indeed possible with the right alignment of the stars. – aparente001 Apr 28 '17 at 5:25
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    In the UK, as long as you can demonstrate that you have the necessary interest and skills, you can. – 101010111100 Apr 28 '17 at 6:36
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    Why not just major in physics or math? – Azor Ahai Apr 28 '17 at 6:40
  • @Azor-Ahai at this point, I'm more interested and likely to do eecs, but I just want to know if it's possible, just in case I get interested some time soon. – A_Happy_Student Apr 28 '17 at 18:33
  • @101010111100 I'm just wondering in that case, if a minor demonstrates the skills? – A_Happy_Student Apr 28 '17 at 18:35
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In the U.S., for graduate work in mathematics, even a minimal major in mathematics is not really adequate preparation for a good graduate program in mathematics. Not enough coursework, which means insufficient exposure to higher-level ideas (assuming, as is apparently mostly the case, there's not much interaction with mathematics outside coursework). Even though various engineering programs require quite a bit of mathematics, in my observation the topics exactly do not get to fourth-year mathematics, so that exactly rigorous analysis, abstract algebra, point-set topology are not seen. The latter are a very minimal preparation for graduate work in mathematics of almost any sort. Still, if there's room for those courses in a "minor", then some minimum thresh-hold would be reached for appearing to be prepared for math grad school.

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    Are 2-3 extra courses reaching the threshold? – A_Happy_Student Apr 28 '17 at 18:36
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    If those "extra" courses are rigorous analysis (not just "advanced calculus", at most places), abstract algebra, and maybe a semester of point-set topology, then at least you won't be immediately disqualified. That does not mean that your application will be competitive, though, since math grad programs would prefer (all other things the same), not to have students spend too long acquiring or mastering undergrad material. – paul garrett Apr 28 '17 at 19:29
  • What is your definition of "advanced calculus"? The class for analysis at my school is called "advanced calculus"math.lsa.umich.edu/courses/undergrad.html#451 – A_Happy_Student Apr 28 '17 at 20:56
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    @A_Happy_Student: Yeah, terminology does vary. I think you would want 451, 490 (but better 590), and 412, and hopefully 452 also. Again this is a bare minimum to not have your application thrown in the garbage and most of your competition would have much more preparation. By "advanced calculus" Paul means something like 351, which would not be suitable. – Nate Eldredge Apr 28 '17 at 22:23
  • @A_Happy_Student: But you will get much better and more specific advice by talking to someone in your own math department. They will have a clear sense of what's in their courses, and how it fits into a course of study to prepare one for grad school. – Nate Eldredge Apr 28 '17 at 22:24
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You should talk to the student advisor of the corresponding graduate program. In general it should be possible to change your major, but there might be some rules to that, e.g. you not only need to take the 3 courses you already take but a few more to fulfill the prerequisites for the program.

I don't think that only undergraduate students from the same university and the same major are admitted to the graduate program, there surely are also externals, internationals,... and yes, also people changing their major might happen. Thus, just talk to people and find out, the rules might be different at each university.

Also, depending on how far you already are into your studies, you might consider changing your major already now. If you are only just a few months in, that might be easier than to do it later. Switching major and minor, you might even be able to keep all the courses you already did in your record. Once again: Talk to the responsible persons at your university, the rules are different everywhere.

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