<p>i am currently a first year mechanical engineering major but im not sure i like it very much. ive always liked math so i thought maybe i’d change to a math major, but I don’t know if i can handle it. I’ve done pretty well on all math i’ve done up to this point, I got a 5/5 on the calculus AB/BC test and got an A in the multivariable calculus class i took this year but i’ve heard that higher level mathematics is completely different from calculus and to do well you really have to be brilliant.</p>
<p>because the engineering school is really hard to get into if i change my major to math and then i decide i dont like it i wont be able to get back into the engineering school. so how do you know if you’re smart enough to be a math major?</p>
<p>I am confident that you are “smart enough” to major in math. The real question is if you are interested and motivated enough to major in math. </p>
<p>Are you comfortable reading and writing proofs? Upper-level math classes are taught in a definition-theorem-proof(-example) style. Your linear algebra class may or may not be taught this way. Most students find proofs dead boring or not very insightful. If you like proofs, there is a very good chance that you would enjoy a math major.</p>
<p>Here’s another way to approach your question: do you like logic puzzles? A math major is all about problem solving. You might encounter weekly problems sets with only 5 problems that take 10+ hours to complete. That can be very frustrating and requires dedication more than anything else, though a bit of creativity and cleverness definitely help.</p>
<p>That being said, the best way to make your decision is to try what a math major would be like. You probably don’t even need to drop the engineering major for the time being since so many lower-level math classes are required or useful for an engineering major anyway (multivariable calculus, linear algebra, differential equations). I would wait at least through linear algebra before I would change my major to math. If your linear algebra class is more computational than proof-based, you might try to squeeze a proof-based class into your engineering schedule as well (e.g. transitions to higher math, discrete math, number theory, probability or set theory if not analysis or abstract algebra). Once you have taken - and enjoyed - your first proof-based math class, it should be relatively safe to switch your major to math.</p>
<p>Well, in some ways all the problems one solves in math are logic puzzles, because they’re about determining under what situations something is true or false, though the unspoken additional aspect is that it’s about using this logic to put a puzzle piece inside the grand portrait of some theory. If you think the principle of abstracting exactly what characterizes various structures that may appear natural (the integers, polynomials, various spaces with a notion of convergence – all things you’ve seen somewhere), and developing the means to adequately think about them, math works for you. Keep in mind that asking things about these objects can lead to huge digressions into entire theories developed to account for certain behaviors, so some innate attraction to this philosophy of study must be there in combination to a love for the logical thinking. Obviously ba@r!um knows all this, but you as an aspiring math student may not so well. </p>
<p>As for safety, yes I think you should touch the first class or so where you write proofs. If you like them, you may survive a math major, but a little extra is necessary to know what to do with the major.</p>
<p>To echo b@r!um, it’s certainly less about smarts and more about how hard you’re willing to work to comprehend difficult concepts. I remember when I first made the jump from concrete mathematics to abstract mathematics (i.e. calc. to real analysis, modern alg., etc…), I was completely taken aback. I couldn’t understand how to write proofs, how to be ‘mathematically clever’, and I was debating switching my major. But I stayed motivated and kept w/ it. And by the time I graduated I actually enjoyed writing proofs and higher level math courses. Like the previous poster said, it’s a lot like solving puzzles/riddles, which I have always enjoyed since I was young. But at some point you WILL get stuck and hit a crossroads. And the point I’m trying to make is that you need to stay motivated to make it through to the end.</p>
<p>^ I would say that (esp. at the undergraduate level) how smart you are is irrelevant. If you enjoy a subject and apply yourself you will do well. You may have to work more or less at it, but in my experience usually not by more than a factor of 2 or 3 times. The real question, then, is whether you like math or not.</p>
<p>Despite the fact that upper-level mathematics is qualitatively different from Calculus, how well you do in Calculus is usually a good indicator of how easily you’ll get more complicated stuff. Some people are just better at things like symbolic manipulation and formal logic than others. I remember way back thinking that math courses were so easy, since I did so well in them, and that they must get hard eventually. The thing is that this isn’t really true. Granted, if I were reading some of my current books as a freshman, I wouldn’t know what was going on at all. But that’s just because I hadn’t seen it before.</p>
<p>There are some hard courses in math, but there are hard courses in any discipline. If you can figure out what the hard courses at your program are, and look into what those courses entail, you can see whether or not you can get over the “hump”, so to speak.</p>
<p>Finally, there are other majors the more mathematically inclined may consider. Some that come to mind…
Statistics
Physics
Computer Science</p>
<p>These fields are all based in mathematics, to varying degrees, and lean to varying degrees on the “applied” side of mathematics, which means fewer proofs than a straight mathematics degree. Physics, esp., you may enjoy as it’s a halfway house between engineering and math.</p>
<p>One last thing: a semester’s exposure to any major isn’t long enough to know you don’t like it yet, especially engineering. Mid and upper level engineering courses are nothing like the introductory versions, either. They become much more mathematical in the sense that they rely on applications of calculus, differential equations, linear algebra, and the like. Mechanical engineering especially. I’m guessing you initially picked MechE for a decent reason, and it would be well to consider that reason when switching to other majors which you may not initially (or worse, in the long run) like any better.</p>
<p>Math is easy. Whenever you get stuck in a proof, use one of the following to finish:</p>
<p>“The rest is trivial.”
“The rest is left to the grader as an exercise.”
“And as this can be verified at once, the proof is done.”
“The rest can be seen even by the most casual observer.”
etc. </p>
<p>In all seriousness, just do it. Pick up a nice intro. to proofs book and see if you like the content. If you are feeling bold, pick up “Calculus” by Michael Spivak and see if you like that.</p>
<p>At UCLA, that class is Math 115A (Linear Algebra). I would suggest taking 33B first, even though it’s not a prerequisite. And I’m not sure it’s that difficult to transfer back to Engineering, as long as your GPA is fine, but you may want to consult a SEAS counselor about that first.</p>