Just how smart / good at math do you have to be to major in math?

College Majors
1

<p>I'm a HS senior thinking of majoring in pure/theoretical mathematics (as well as economics), and so I was just wondering about the question in the title.</p>

<p>Actually, I'm not really worried about me personally---I got a 710 on the SAT math section and a 33 on the ACT math section, and I've always gotten near-100s in HS math classes, so I'm assuming that with enough effort I'd be able to do well as a math major. (Right?) So mostly I'm just curious about the question in general. Most people regard math as the hardest thing to major in, so I'm wondering exactly how demanding it really is.</p>

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<p>Chances are the math you are doing in high school is nothing like the math math majors do. Math majors are not about getting answers, thats an engineers job, rather, they are about proving concepts, with rigorous logic. It is difficult to tell if one can handle this type of class based only on test scores. My advice is to take as much math as you can, until you can't "get it" and then move on to a subject that you can excell, such as economics.</p>

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<p>mikenthemaddog66: Right, I understand that upper-level math is more about proof than computation (which is precisely why I'm interested in it---proving things in geometry class was perhaps the only thing I enjoyed in HS math), but are you sure there's no good prediction of success?</p>

<p>Edit: Oh, and do you happen to be a math major yourself?</p>

4

<p>Go for it. If it doesn't work out for you, you can always change your major. People do it all the time, and with plenty of math classes under your belt, it won't be too difficult to switch majors (unless you go to English which I doubt you'll do :))</p>

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<p>Well, Mike pretty much hit the nail on the head. And while it does depend on what classes you've taken, as he said, chances are, you've not taken anything like what you'll encounter. I'd even venture a guess that the calc I class is much harder than what you've had.</p>

<p>No offense to you, but your 710, 33, and HS scores -while quite good - are virtually worthless in predicting success. In all honesty, you don't even know what math really is. The level of conceptual difficulty as you hit analysis-level classes jumps quite sharply.</p>

<p>As a math major in undergrad, I saw and knew plenty of kids that had similar, and even better scores than yours, and who even did well in their first class or two, and changed majors by the time they hit analysis. At that point, it becomes much, much less about putting in another hour or so, and cranking through problems, etc.. You've simply got to be smart enough and have a brain that works in such a way to get the material. </p>

<p>All of this being said, you've got an option for choosing some of your upper divisions, so you can probably work around some of the more difficult classes. But one way or the other, you'll have to take analysis, the class that gives math majors everywhere (and I mean everywhere) nightmares.</p>

<p>"*unless you go to English which I doubt you'll do *"
Never know....one of the best math majors I ever knew was a math and english double.</p>

6

<p>The best recommendation I can give you is to go through the process yourself. Different people have different opinions, which also include what they claim to be difficult or not. If you don't like it, go head and switch, which is not a big deal at all. You have other great options such as computer science, physics, and engineering that will very well suit the math courses you have taken.</p>

7

<p>Or statistics. Don't forget statistics. People who are good at math but really don't enjoy upper level math classes might like upper level statistics classes. And I think everyone who liked high school math is likely to enjoy most statistics classses.</p>

<p>To me, what you learn even in the least applied stat classes like stat theory and probability theory make more sense than (the following from MIT) Topics in Several Complex Variables: Harmonic theory on complex manifolds, Hodge decomposition theorem, Hard Lefschetz theorem. Vanishing theorems. As time permits students also study holomorphic vector bundles on Kahler manifolds. </p>

<p>Vector bundles are not for me, but I think it just depends on how your brain works. </p>

<p>Think about how much you enjoy classes like this and what you will do with a math major. Would a computer science, engineering, or statistics major be a better fit for what you plan to do next? I'm biased - my opinion is that math majors are best for folks going into graduate school in mathematical areas - or for math lovers with double majors.</p>

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<p>
[quote]
To me, what you learn even in the least applied stat classes like stat theory and probability theory make more sense than (the following from MIT) Topics in Several Complex Variables: Harmonic theory on complex manifolds, Hodge decomposition theorem, Hard Lefschetz theorem. Vanishing theorems. As time permits students also study holomorphic vector bundles on Kahler manifolds.

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<p>Come again, JJG? I thought a manifold was something in a car... :confused: </p>

<p>That's it. There goes another major off the list. ;)</p>

9

<p>ill first say that i am a first-year graduate student in mathematics with interests similar to yours: logic, set theory, proof theory, et cetera. incidentally, i also double majored in math and economics as an undergraduate.</p>

<p>yours is a difficult question to answer... for a two main reasons.</p>

<p>one, the difficulty of math curricula varies WIDELY from school to school. i suppose this is true of many disciplines, but it is especially apparent in mathematics given the transparent nature of the subject. what is expected from a math major at harvard is simply in a completely different league than what is expected from someone at a third tier school. </p>

<p>two, as has been mentioned, not all math majors at the same school are created equal. substitute enough probability and elementary number theory for differential topology and advanced analysis and the major becomes significantly less challenging. depending on what you want to do with your degree, this kind of substitution may or may not matter significantly.</p>

<p>that said, i will say with some conviction that your scores probably are on the low end for 'successful' math majors at top 50 schools and are nearly unheard of at top departments. that doesnt mean you wont be successful--and you will only gain highly marketable skills in trying--but many of your peers will enter with flawless scores and still find themselves in over their heads within the first couple of semesters.</p>

<p>just as there is a big intellectual jump from trig to calculus, there is a similar jump from intro courses to discrete math and real analysis and yet another jump to graduate-level work... a long, long way from high school geometry class... unless, of course, your geometry teacher only spoke 28 distinct english words the entire semester (true story, and the class was great).</p>

<p>with that, my recommendation is to seriously consider your goals and how they mesh with your prospective schools. harvard is not a good place to major in economics and 'dabble' in math. yet if you are sold on being a top-notch academic (or bust), there is nowhere better to be. the best place to find information? search for lectures and homework assignments for the first math class you will take as a freshman. is it completely over your head? just incredibly difficult? does it look about right? could you do some of it now? no better way to find a good match. </p>

<p>hope that helps. and good luck! we need more pure math majors!</p>

10

<p>OK, some questions for the math majors here:</p>

<p>1) At what point does "analysis" begin? Calc BC? Multivariate? DiffEq?<br>
2) How much math did you come in with from high school?
3) What are good things to look for in a math program or when sitting in on a math class as an observer?
4) Did you start at the next class after your high school sequence or did you backtrack one semester to accommodate whatever you might not have been exposed to? </p>

<p>Feel free to PM me.</p>

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<p>
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1) At what point does "analysis" begin? Calc BC? Multivariate? DiffEq?

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<p>With Analysis That other stuff is just fancy arithmetic. ;) The first analysis course that you'll encounter would be Real Analysis or Advanced calculus. These are your first "real" pure math courses. </p>

<p>After that there's Analysis II, Measure Theory, Functional Analysis, Complex Analysis, and sometimes Matrix Analysis. Numerical Analysis does not count. </p>

<p>This is standard material from Real Analysis. This is the easy stuff:</p>

<p><a href="http://www.math.louisville.edu/%7Elee/RealAnalysis/ra_sect06.pdf%5B/url%5D"&gt;http://www.math.louisville.edu/~lee/RealAnalysis/ra_sect06.pdf&lt;/a&gt;&lt;/p>

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2) How much math did you come in with from high school?

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<p>I'm a bad example, but I think the highest level was Precalc. I think I earned a B in my best marking period. My first shot at college I took it twice, earning a D followed by an F.</p>

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3) What are good things to look for in a math program or when sitting in on a math class as an observer?

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<p>For most people it wont matter. Go to a good school. That's about it. Access to grad courses is a good thing if you're thinking about grad work in math.</p>

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4) Did you start at the next class after your high school sequence or did you backtrack one semester to accommodate whatever you might not have been exposed to?

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<p>See 2. When I came back after dropping out, I started at algebra. I finished with measure theory.</p>

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<p>SAT/ACT scores are poor predictors, AP Calc BC scores are better......and better than that are AMC/AIME scores. Success at math, at the highest levels, can simply be reduced to a single item. IQ. Much more engineering, statistics, economics or lesser majors is success in math due to IQ.</p>

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<p>Thanks for all the info and advice, everyone. I notice there's a bit of a disagreement here, though: RHSstudent07, for example, says to just go ahead and try math in college and see where that takes me; if I don't do so well, then I can always switch to something else. ericatbucknell, on the other hand, says that at a top school (and I may or may not end up attending a top school), it's hard to "dabble" in math like this. What RHS said makes sense to me, so ericatbucknell, do you think you could elaborate?</p>

<p>Mr Payne, yeah, I bet you're right about IQ. What IQ would you (or anyone else) say college-level math demands? 120? 140? 160?</p>

<p>theghostofsnappy, I'm assuming your early bad grades had nothing to do with actually finding the stuff difficult?</p>

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<p>ill put it this way. every year a good 10-15% of matriculants at princeton intend to major in mathematics. four years later those 150 will have turned into 20.... obviously its not because anyone there is stupid; rather, math classes at princeton are simply very, very hard. thats a great thing for the highly gifted, determined math major with every intention to study at the graduate level, as he will recieve an education matched by few universities in the world. its not so great for pretty much everyone else, as taking math on the side, simply for the fun of it, becomes a not-so-terribly-viable option.</p>

<p>that doesnt mean you or anyone else shouldnt try, regardless of where you end up. i hoped i had implied as much in my original post as, in fact, i encourage EVERYONE to take as much math as he or she can (our society is hopelessly innumerate). what i did mean, however, is that at a harvard or mit or princeton you are probably going to hit your 'wall' pretty quickly. and thats something you should keep in mind when choosing a school if taking advanced classes in logic/foundations/whatever is important to you. in other words, i simply wanted to point out that the 'best' may not be the best for you, a classic case of finding the best possible academic fit.</p>

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<p>@ericatbucknell: Okay, that makes sense.</p>

<p>Not to get off onto a tangent (bad pun intended), but I find it surprising that so many Princeton freshmen come in hoping to major in math (even when considering the excellent department)... That's gotta be the highest in the nation, right?</p>

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<p>To show you how different advanced college math is from HS math (and even much of the math used for engineering and physics), my first wife was a mathophobe in HS, and took the bare minimum allowed for graduation. In freshman year of college, she took a required math survey course. It was taught by a higher-level math professor whose specialty was topology. He recognized her innate talent and tried and tried (unsuccessfully) to make her change her major from Speech to Math.</p>

<p>Later, when I was in grad school, I had a KILLER graduate-level logic course. It was so hard that we had a take-home final exam(!). I was working on it all night. She woke up at about 2 AM and came in and asked me what I was doing. I told her, and she pulled up a chair. "You know I love logic puzzles," she said. I grimaced and said "It's not that kind of logic." She pressed on, so I thought I'd snow her with one of the problems I couldn't even get started on. The terminology was beyond her, but she asked me to explain in simple terms what the problem was asking. After I explained it, she said, "Well, that's obvious!" and went on to explain to ME how she arrived at an answer!!! And she helped me on all the other problems as well. She had not taken the class, she had not taken much math in HS, and she only had the one survey class as a freshman. Unbelievable, but that was the way her mind worked. </p>

<p>Which was not necessarily a positive thing. The movie "A Beautiful Mind" hit home.</p>

<p>BTW, Of 50 grad students, I was one of only two who received an A in the class.</p>

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<p>Ooops - sounds like I was guilty of cheating. But it didn't seem like cheating to get help from someone with no math background at all. Plus, once she explained it to me (or we worked out problems together), I then DID understand. SHE should have been teaching that grad-level course.</p>

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<p>
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Mr Payne, yeah, I bet you're right about IQ. What IQ would you (or anyone else) say college-level math demands? 120? 140? 160?

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Well, for undergraduate I'm sure it depends very much on your institution. MIT/Princeton/Harvard/CalTech/Berkeley will absolutely maul their freshman class in order to seperate the talent. At one of those institutions I'd assume a 130-140 IQ (98th-99th percentile) simply to complete the major. However, if those Princeton statistics are right, it could very well be a lot higher than that. To do well in the major (ie: go to a major grad school), you'd probably need to be measureably higher than 140. I'd assume 150 is probably the average IQ of most math departments of top universities. Again, this is might be a underestimation, but it's certainly not overestimation. This is purely speculation though, as someone in my IQ range would probably fail out and do something where the highest math is PDE stuff.</p>

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<p>I agree with Mr Payne, "maul" is the correct description for what they try to do to prospective math majors. I am currently a math major at Princeton, and I would highly discourage anyone, regardless of determination, skill, and IQ, from pursuing math there. I have been very interested in math for a long time, in fact my favorite stuff so far is logic/foundations. I am extremely determined to major in math, and I think I am pretty good at it--not a genius or prodigy, but the makings of an academic mathematician. My IQ is above 164 (professionally tested, not one of those online things or anything). Yet I am transferring out of Princeton because that is the only way I can see for me to major in math. </p>

<p>I am now of the opinion that the most important thing in choosing where to study math is the responsiveness of the professors. All professors have Ph.D.s in math, which means that they are better mathematicians than many of us math majors will ever be. But not all professors are willing or able to explain mathematics to you, and the WORST thing that can happen to an undergraduate who wants to pursue math beyond college is to have gaps in knowledge caused by inadequate teaching, unnecessarily fast courses, etc. So it is most important to go someplace where professors will pay attention to what you need to learn, and make sure that you are not missing anything. If you are, it will come back to bite you, guaranteed. </p>

<p>That attention is not happening to anyone I know at Princeton. Don't go here. A reputation for harshness is bad for more reasons than that it is "mean"--it is academically detrimental in the worst possible way. (Anyone here is welcome to PM me about math and Princeton in particular.)</p>

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<p>Interesting take on Princeton. One of the strikes against Harvard for my S was hearing from a math prof elsewhere that, more than other colleges, Harvard is known for a "star system" in math, giving attention to the very best of the best.</p>

<p>I think it's great to head to college with the intention of majoring in math. I'd suggest you take a proof-based class as soon as possible to see whether or not you like pure math. If you don't, there are still many useful math electives and combined math majors, as well as science majors that require math. My S is a typical "good at math" but turned off by proofs. He's ended up as an economics-math major, also doing a concentration in physics, and thinks he might go on in applied math. (He will take analysis senior year. Although, as the math advisor for econ-math majors said -- and imagine a French accent here -- "you do not take analysis, analysis takes you.")</p>