<p>I'm in a bit of a bind. As a high school junior, I'm looking at majors and colleges that offer them. Unfortunately, my interests don't correspond exactly to any one major...</p>
<p>I am passionate about math. I've always been reasonably good at it, but last year I began to self-study more rigorous math on my own. I absolutely love the induction used in mathematical proof. The moment when everything falls into place and the answer becomes clear is magical. I also enjoy chemistry (though I haven't taken a serious class yet - AP Chem will be senior year) and physics (self-study - starting AP this year), but not in the same way.</p>
<p>Engineering has always seemed like the obvious career field for me, but now I'm not so sure. Most of the engineers in my family are mechanical types, and after talking to them I'm a bit worried. While I enjoyed my experiences with LEGO Robotics and my own Erector set, that sort of design never evoked much passion and I was never very talented at it. I just don't have that sixth sense some engineers I know of have (the ability to visualize how to design a mechanical contraption).</p>
<p>I haven't given up all hope for engineering. Out of interest, I took a look at some of the electrical engineering coursework on MIT OpenCourseWare. It seemed much more to my liking, though almost everything was too far over my head to be sure. </p>
<p>I've also had some doubts about a degree in math. Most of the careers outside academia aren't much more appealing than engineering, and I'm not sure if I want to become an academic. While I have an aptitude for induction, I'm definitely not brilliant and I don't know if I could conduct meaningful research.</p>
<p>So, I have the following questions:</p>
<ol>
<li><p>Is it possible to go from an engineering program with proof-heavy math classes (such as engineering science at the University of Toronto) into grad school for mathematics?</p></li>
<li><p>Is it possible to go from a bachelor's in math (maybe with some engineering electives) to a masters or PhD in engineering of some kind?</p></li>
<li><p>What kind of math do you do in your job as an engineer? Please list your specialization as well.</p></li>
<li><p>When did you find out that the degree you chose was a good fit for you? Was there still ample time to transfer?</p></li>
<li><p>Any other advice for me?</p></li>
</ol>
<p>1) I had a math professor who did his undergrad in Mechanical Engineering, and did his graduate school in Applied Mathematics, so yes, you can go from engineering to math.</p>
<p>2) I had a coworker who did math in his undergrad, and then moved to Mechanical Engineering for his graduate school to work on CFD, so yes, it is possible to go from engineering to math.</p>
<p>3) The type of math you do as an engineer in your job relies heavily on what your position is. I have friends who used almost no math at work, and others who regularly solved differential equations at work, so it is quite a large range.</p>
<p>4) I knew in High School that I wanted engineering, and went into mechanical, and I knew as soon as I hit Thermodynamics, and especially Fluids, that mechanical was right for me. I also would have been happy with aerospace. However, most people change degrees at least once, and most technical majors are roughly the same for the first 3 semesters or so, so you have a bit of time to decide.</p>
<p>If you’re trying to choose between a math degree and an engineering degree, personally I think the choice is simple: choose engineering.</p>
<p>An engineering degree will prepare you for actual and specific types of jobs, especially those that carry the title “engineer”. There are much fewer (if any) jobs that carry the title “mathematician”. So the utility of an engineering degree is more obvious.</p>
<p>Moreover, you will take many math courses throughout your engineering degree and thus, not only will you be qualified for engineering jobs, but you will also be qualified, indirectly, to perform many jobs that math majors take on. </p>
<p>The engineering degree, although more difficult, and 1 year longer, will open more doors than a pure math degree, IMO.</p>
<p>How is an engineering degree any more difficult or longer than a math degree? They are both 4 year degrees, and both far from easy. In fact, for me, engineering would be (was) easier given that I cannot stand proof-based math, which is a huge part of math degrees. Moreover, math majors and engineering majors only have a slight amount of overlap in the potential careers. Math is a much more fundamental science than any engineering, and so it will definitely be much more abstract, while engineering will require a better physical intuition.</p>
<p>However, I suggested looking into applied math, as it sort of blurs the line between math and the more practical engineering disciplines.</p>
<p>I think you’re probably right. Plus, from what I hear EngSci grads often get their PhDs in physics or math, so the option is still open. Now all I have to do is get in (and find some similar programs as backups)…</p>
<p>EDIT: Re applied math, the jury’s still out. Most of what I enjoy most about math is anchored in derivation and proof, so a very rigorous engineering course with lots of math might be just as valuable as an applied math major.</p>
<p>Well just as a caveat, most engineering degrees have a good amount of math, but stop short of any sort of in-depth class that requires induction or heavy proofs and derivations. EE is probably the most math intensive engineering major that I know of.</p>
<p>^ Yeah, from what I understand it’s mostly application. However, I doubt if I’d do all that much better with most professions applied math leads to (operations research, actuarial, etc.)</p>
<p>I’m going to do an internship at some point over the next year, probably in engineering. Most engineers up in this neck of the woods are petroleum types, but it’s still something.</p>
<p>EDIT: Besides, the Engineering Science program @ UofT is known for sadistic math and physics classes emphasizing theory and proof. Sounds like fun :). Do you know of any similar programs at other schools?</p>
<p>I almost forgot: your passion is also really important when deciding on a major. Both degrees are good, overall. But you’ll be much happier, and much better able to get through the tough study times if you are passionate about the subject matter.</p>
<p>In the other advice category…
It seems like I only have one song and dance, but you’re really setting me up here.</p>
<p>Computer science / software engineering has good job prospects and includes proof-heavy courses (mathematical induction being one of the most important techniques). It’s like a math degree in that it’s proof-centric (to varying degrees) and it’s often possible to double in CS and math (because they’re so similar).</p>
<p>Something to think about…</p>
<p>(Also, industrial engineering you might like. It’s probability and statistics based.)</p>
<p>@AuburnMathTutor: I have done some programming for fun, and while it is mathematical I don’t really see myself doing that for a living.</p>
<p>@chuy: That’s what I’m thinking too…</p>
<p>If anyone here could recommend programs similar to EngSci @ UofT, that would be great. I’m thinking of an extremely rigorous grounding in math, science, and engineering principles for the first year or two, then specialization. I know that many schools offer a general first-year program, but most of them don’t have this much rigor.</p>
<p>Harvey Mudd, Caltech, and MIT all have the sort of 1-2 year rigorous introductory “core” that you are looking for. Granted they are all extremely selective institutions.</p>
<p>Maybe I’m mistaken as to what an EE degree entails, but I thought it was more physics-heavy than math-heavy. What kinds of things do EE majors have to prove?</p>
<p>If you choose the right area of EE, you can almost avoid physics entirely. Digital signal processing, communications, & control systems theory attacks engineering problems at a much higher level of abstraction than at the physical level. </p>
<p>These subjects are important and necessary in the practice of EE. Being able to mathematically describe and model complicated electrical systems at a high level is p. useful. If you were to attempt design of these systems starting at the device or circuit level (actually, design at these levels is divorced from the physics as well!), you’d quickly get overwhelmed in the details.</p>
<p>I definitely don’t need to “avoid” physics (I enjoy it). I just prefer the pure logic of mathematical induction, some of which filters down to physics anyway.</p>