Any thoughts on math major?

College Majors
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phuriku, you should have pointed out that some college math entails trivial exercises and concepts that are not rigorous at all. I'd say that only beyond a certain course level (Multivariable Calculus, Linear Algebra, etc.) will you see proofs being practiced in an open, free-response style essay and answers being formulated upon hours and hours of critical problem solving and just all-around hardcore thinking.

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<p>Don't most math majors start college with Real Analysis though? Nowadays, MVC and LA have become high school topics.</p>

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<p>Oh how much I wish my high school was that fancy enough to have MVC and LA.</p>

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As you can see from this link, there are a lot of "applied mathematics" research interests among the MIT faculty, and combinatorics is often listed.

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<p>That has nothing at all to do with it. Just because some applied mathematicians study combinatorics doesn't mean that's it not a branch of pure math - that's exactly what it is. There's a ton of math literature out there that falls exclusively in a pure combinatorics section.</p>

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<p>Fred, long time no see! How's Michigan treating you?</p>

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That has nothing at all to do with it. Just because some applied mathematicians study combinatorics doesn't mean that's it not a branch of pure math - that's exactly what it is. There's a ton of math literature out there that falls exclusively in a pure combinatorics section.

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<p>I know. I talked with arkleseizure about this via AIM and he convinced me that combinatorics was indeed pure math, although I still believe that it is still less pure than most other topics of mathematics that would be labeled pure.</p>

<p>My links were primarily to show the fallacy of his argument (I tried to emphasize this by using the words "If you want to go that way") -- that just because Wikipedia says it's pure math doesn't make it pure math, just as my links aren't credible in proving that combinatorics falls under the applied mathematics category.</p>

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<p>yea arkleseizure your pretty much a moron, that made no sense, and not because I don't understand it cause I absolute do, it was just a REALLY bad example, and you didn't post a question in that entire statement, it was just you talking, basically you were story telling, ever considers a switch in major to creative writing?</p>

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<p>^no it was actually a great example for someone who hasn't taken any college level math. he showed how a pure math major thinks without using convoluted, symbolic language that the op couldn't interprate. </p>

<p>i think math majors, as a group, just have a really bad superiority complex and like to brag by flashing these advanced problems that no one would understand unless they took the class. then they label these problems as 'easy' or 'elementary' to assert their overwhelming intelligence that's so many standard deviations away from the typical student that no non-math major could possibly comprehend the god-like cognitive abilities it takes to get through it. just give people a chance!...and stop pretending to be this elite group of geniuses that requires a permission slip from God to get in.</p>

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<p>Some high schools offer Real Analysis. Some are lucky to offer Calc AB. A friend of our always cites the kid he knew at Penn who got into the engineering school with only pre-calc (the highest level his school offered). He struggled the first semester, but once he caught up with the math, he was unstoppable, and in fact, incredibly strong in math.</p>

<p>There are plenty of extraordinarily bright kids who don't have the opportunities that others do in terms of access to classes, resources, etc.</p>

<p>Phuriku, my guess is that many math majors come in at MV these days, and even then, they may re-take depending on the quality of their preparation.</p>

<p>It is darned tough to come in as a math major starting in Real Analysis unless one applies to a fairly limited list of schools. There just aren't that many (esp. four year programs w/o grad courses available) that can support four years of math <em>starting</em> at RA. RA is typically a junior level course.</p>

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<p>el duque, I haven't seen that among many mathematicians at all -- and I have seen it in some, so I know what it looks like. There is a world of difference, however, between most high school math and most college math. Most college math beyond calculus (and I count analysis as above calculus) tends to scare people off, though. That's most of how that sort of thing originates: most people get scared off by math above a certain level.</p>

<p>Phuriku, I haven't yet seen much in the way of what I'd call pure analysis. Show me some sometime. I've always thought of combinatorics as the most elegant and pure type of mathematics, but, then, I haven't been exposed to as much analysis or topology as I'd like.</p>

<p>Hostile, I'm not sure what your problem is, and that's how most proofs are written.</p>

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<p>If you are interested in engineering, there are probably many universities that have a "Math for engineers" class that isn't as proof based as the regular course. This usually ends after the fourth semester of the Calculus sequence because that is usually all the Math engineers have to take. I just got back from "Linear Algebra and Diff. Eq. for Engineers" and someone asked if we would prove Cramer's rule and the Prof. laughed a little and told him that we won't really prove much of anything in that class. Let alone we don't really even talk about the general case all that much. It's just a lot of number crunching. Just something to chew on.</p>

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<p>Yeah, don't major in math if you don't like math. And avoid English, History, and Poultry Science if you dislike writing, reading, or chickens, respectively.</p>

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Phuriku, I haven't yet seen much in the way of what I'd call pure analysis. Show me some sometime. I've always thought of combinatorics as the most elegant and pure type of mathematics, but, then, I haven't been exposed to as much analysis or topology as I'd like.

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<p>Of course, the penultimate example is Harvard 55 problem sets, although if you just look through Rudin, you can see the essentials of analysis.</p>

<p>Here is the first problem set of Harvard 55a:</p>

<p>Problems: <a href="http://www.math.harvard.edu/%7Eelkies/M55a.02/p1.pdf%5B/url%5D"&gt;http://www.math.harvard.edu/~elkies/M55a.02/p1.pdf&lt;/a>
Solutions: <a href="http://www.math.harvard.edu/%7Eelkies/M55a.02/sol1.pdf%5B/url%5D"&gt;http://www.math.harvard.edu/~elkies/M55a.02/sol1.pdf&lt;/a&gt;&lt;/p>

<p>One thing that I have against combinatorics in terms of purity is that I haven't seen it start from axioms and spread out from there. Instead, it kind of assumes that the reader just knows how to deal with integers, what integers are, what rationals are, what the reals are. In analysis, we start from the very basics such that you cannot start much earlier (well, you could go back to the Peano Axioms, but this is really unnecessary).</p>

<p>We define the naturals to create the integers, use the integers to create the rationals, and from there, use Cauchy Sequences or Dedekind Cuts to create the reals. Following courses such as topology don't need to do this because it has already been cleared up in analysis, but combinatorics requires no analysis prerequisite.</p>

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<p>I don't want to highjack the tread, but I have a quick question that you guys would seem to have some expertise in. I am a sophomore econ major at a state school, where the math requirements for the program aren't strenuous. The math requirements are introductory statistics, which I took AP in high school, and applied calculus. The calculus class is intended for students who are not going to pursue higher level mathematics (econ, pharm, finance, bio majors, etc). Anyways, I finished in the top 15% or so of the class. I put forth a moderate effort to succeed, but I could have tried harder. </p>

<p>My problem is that grad econ programs all require more math than what I have taken and I am not sure I can cut it in higher lever classes. The real analysis material looks very intimidating. I am planning on sitting in on a calc I course this semester just to see how it goes. Are the schools you guys are familiar with have applied calc courses like mine? If so, how much more difficult are the regular calc classes? Thank you for the help.</p>

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<p>all i'm saying is that it's incredibly unreasonable to post a real analysis problem set and say "see, math is just too hard for you. now go away." of course it's hard! it's a 400 level class in most schools and you're talking to a guy with <em>maybe</em> 1 or 2 calc classes under his belt. it's like telling a prospective foreign language major to write you a 15-page paper on french literature in french with only a HS background in the subject.</p>

<p>point is, if you take the most advanced classes of any major whatsoever, the material is going to look intimidating. but instead of using it as a 'keep out' sign, the responsible thing to do is to bring it down several notches and use it as a welcome mat. just let the guy try it out for himself, that's what all the other majors suggest to interested students. math majors seem to be the only ones that actually discourage people.</p>

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math majors seem to be the only ones that actually discourage people.

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<p>Yeah, and Caltech's pretty much the only school where you'll visit and students will tell you "Don't go here. It's too hard!" (I actually got this at Chicago, too.) Why do these comments only happen at very difficult institutions? Because they want to give you a little warning before you come in and think you can do it, and then notice that you're nowhere near the level of the other students at the institution and have to drop out/transfer. This is exactly why students in quantitative fields discourage students from joining this field -- we're just giving a huge warning... and considering that the student doesn't think he's any good at math, it was intended to be a humongous warning sign. The simple fact is that math is hard, and many don't realize this until they get into college, even if they did do really well in their calculus classes in high school. If you do not have a natural ability for mathematics (something that the OP apparently lacks), you won't go very far in this field. Period.</p>

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all i'm saying is that it's incredibly unreasonable to post a real analysis problem set and say "see, math is just too hard for you. now go away." of course it's hard! it's a 400 level class in most schools and you're talking to a guy with <em>maybe</em> 1 or 2 calc classes under his belt. it's like telling a prospective foreign language major to write you a 15-page paper on french literature in french with only a HS background in the subject.

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<p>All of the math majors that I know have taken real analysis in their first or second year. Thus, it's not that far advanced if you're a math major. The reason I'm specifically choosing analysis is that it's a required course for any kind of math major -- at my school, real analysis is a prerequisite for many applied mathematics courses. Any institution without such a policy is clearly not a very good institution, as without real analysis, you really can't do anything in mathematics.</p>

<p>High schoolers looking to go into mathematics should see this stuff as soon as possible. Mathematics in high school is pretty much all calculation -- mathematics in college is pretty much all theory. If you have trouble doing calculation in AP classes (which are very easy), you're going to have trouble in college. And if you have trouble dealing with variables, then you're not going to be able to do anything involving delta-epsilon, which is what most calculus and analysis courses revolve around. See my logic? Usually if a student looks at it and it seems hard (not in the sense that the student doesn't know how to DO the material, but in the sense that the student looks at it and says something to himself such as "Oh... I couldn't really comprehend delta-epsilon in Calculus" or "I'm not very good in dealing with variables or arbitrary numbers"), then in most cases, it will be hard for the student.</p>

<p>Even as a math major, I've never had any experience with stuff such as algebraic topology, but having seen the material, I know that it's something that is definitely feasible for me, even if I don't know how to solve the problems or do the proofs. If someone showed me a course that looked heavily dependent upon graph theory or combinatorics, which, unfortunately, my experiences have shown me I am not skilled in, I would immediately see that that class was not appropriate for me.</p>

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<p>For my Physics major, the math courses I have to take are Cal I-III, Linear Algebra, Differential Equations, Intro to Partial Differential Equations, and Vector Analysis.</p>

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<p>Phuriku,
Do you like Rudin better than Spivak for analysis?</p>

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<p>bump. Any help would be appreciated.</p>

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<p>Phuriku,
Mathematicians in my experience have been humble and excited to introduce math to others. You do not fit that role one bit.</p>

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<li><p>I assume you're an early learner and that's great, but the majority of math majors take real analysis in their junior or senior years.</p></li>
<li><p>I agree with your warning but you may be taking it too far. If the OP is intellgient and interested in a math major, then he can pass a math major.</p></li>
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<p>The only thing the OP should worry about is that success in math requires pure interest in math. It's something you dedicate yourself to 100% it can't JUST be a stepping stone to something else, i.e. finance jobs.</p>

<p>for the record I came into college knowing only a little (basic) calculus but after alot of time/interest/dedication I'm now doing reasonably well. - if you're like me though expect to rent books from the library and self-study to compete.</p>

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<p>If the OP really thinks they're bad at math, that betrays a deeper psychological aversion to studying it at all. Maybe they're smart enough, and maybe they'd do fine, but for the lack of confidence. Unless the OP was being overly modest when they said they weren't good at math, majoring in math would be torturous. Don't believe me?</p>

<p>I suck at history. Had I been a history major, I would have probably ended up psychotic. Life would suck. Why would I do that to myself?</p>

<p>I can't play an instrument, and I've never liked art. Thus, a fine arts major would have essentially been 4 wasted years and endless boredom / frustration.</p>

<p>If the OP isn't good at math - can't solve equations, doesn't understand geometry, never wants to touch proofs, can't remember trigonometric identities / notable angles, etc. - they should really consider the fact that <em>that's what they will be doing for the next four years, and once you're far enough down a math major, classes start not transferring to other backup majors</em>. What do I mean by that? Well, as far as I know, real analysis is only required of math majors here. So taking that class and then switching majors would be wasted time. Etc. etc.</p>

<p>Ultimately it's the OP's decision, but... well, he did ask for our opinions.</p>

<p>On a side note, the OP might be really good at proofs, and just not so good at the algebra. So he might do fine in a math major... there's no way of knowing. OP, if you want some proof problems look at, let me know... it'll give you some idea of what you might end up doing in a math major.</p>