<p>I don’t want to throw cold water on Inpersonal’s plans–just to indicate that it is right to think that majoring in math or physics will be a challenge.</p>
<p>A friend of mine had not intended to go to college, but then decided to go to the college his girlfriend was attending–a college that is rarely (ok, never) endorsed on CC. He wound up majoring in a hard science, and after moving up consistently in the field, he is now a member of the National Academy of Sciences.</p>
<p>A couple of additional questions that might help Inpersonal decide:</p>
<p>You mentioned that your high-school grades were “good, but not great.” How were your grades in math and science? If they were also “good, but not great,” was this because you didn’t do the homework routinely, but did well on the tests? In that case, you aren’t likely to have a problem, as long as you are willing to do the homework consistently in college. On the other hand, did you find the material conceptually challenging? In that case, you may run into difficulties in college, unless you take extra time to come up to speed.</p>
<p>When you approached problems in math, did you look for set patterns of “this is how you do this type of problem” (not so good) or did you understand the logical structure of the subject (much better), so that you didn’t have to learn how to work problems in various categories? </p>
<p>I assume that you took high school physics. Was your course equation based? If so, did you tend to look up the equations in the book and plug in the variables, or did you tend to derive the equations for yourself, based on the underlying principles? Do you enjoy abstraction?</p>
<p>I had a student a while ago who did not do very well on timed exams in undergraduate courses, because he was not willing to memorize anything. Instead, he derived everything he could from scratch (and just a few known results), right during the exams. Usually he ran out of time on the exams. But in grad school, he did really well, because he had an unusually strong grasp of the concepts, and could apply them with no trouble.</p>
<p>@Quant:
I always got good grades in the Humanities and languages. Not so much on the Quant subjects. I think that one of the reasons is that when I was left to my own devices, I found much more interesting to study, say, History or Drama than Chemistry and Physics.</p>
<p>It is only recently that I learned the power of some of these more dry subjects. For instance, when I initially learned about matrices, it was something I could not understand why people would come up with something just for the sake of doing. Only later I understood that matrices are very useful when one needs to deal with a lot of data at the same time. I can now see that you can effectively use matrices to more efficiently deal with, for instance, graphics processing. It was the same for some other concepts in the natural sciences. My eyes were not open enough to understand why they were useful. Why would anyone care about angular speed, for instance. Now I can see better.</p>
<p>Those are very hopeful signs in your post #63, Inpersonal. More than anything else, they indicate some of the problems with science and math education in the US–basic ideas without context.</p>
<p>Practically everything that is taught in high school math, chemistry, and physics actually is useful–even important–for multiple applications. For example, matrices are needed for quantum mechanics as it is practiced at present (even though Schrodinger got along without them, at least initially), and not just to deal with a lot of data, but to find the energy levels of quantum systems.</p>
<p>Incidentally, have to add this: One of the most interesting applications of matrices in quantum mechanics is connected with the uncertainty principle.</p>
<p>This starts from the observation that matrix multiplication is not commutative. That is, if you take ordinary real or complex numbers a and b, then a times b = b times a. The order doesn’t matter–they commute. However, if A and B are matrices, then often A times B is not equal to B times A.</p>
<p>Here is the interesting part: In quantum mechanics, each of the matrices A and B represents a property that can be observed (measured). But can the values of these properties be known <em>at the same time</em> ? If the matrices A and B don’t commute, the answer is no. If the matrices don’t commute, there is an uncertainty relation between the properties represented by A and B, like the uncertainty relation that governs position and momentum.</p>
<p>To tie in with the concept of angular speed, another uncertainty relation governs the x and z components of the angular momentum. In general, you cannot know both at once, for a quantum system. As you improve your measurement of the z component, you lose knowledge of the x component.</p>
I, of course – based on my previous posts – am fuming a little about this piece of gratuitous snobbery from QuantMech, although I am grateful that she later acknowledged a friend who originally didn’t intend to go to college and who wound up in the National Academy of Sciences. I also endorse (with some reservations) her questions in #61. In the end, it’s not enough to say that the OP could major in a STEM field at a reach college; the OP still has to look in the mirror and determine that his or her interests and abilities would support that.</p>
<p>But the OP does NOT have to catch up with more advanced classmates to make a degree useful. Sure, if the OP wants to continue to a PhD program, the OP may have to do supplemental coursework and research to catch up. Many, many students find themselves in that position, and there are lots of ways to skin that cat; it’s no reason to decide at 17 or 18 that you are frozen out of the career you want to pursue. </p>
<p>Furthermore, it is absolutely not the case that all degree recipients have to be on the same level to find a good job or otherwise advance professionally. I know for a fact that there is a wide range of abilities and experience represented by Harvard math or economics majors, and somehow few if any of them are flipping burgers. If, for example, the OP ultimately wants to go to medical school and to become a physician, it will not matter a whit that he or she has not reached the most advanced level possible in math or physics. And I would be stunned if he or she had trouble finding an advisor for an honors thesis (unless it was on the basis of unpleasant personal characteristics that would hold back a truly advanced student, too).</p>
<p>Here’s a story out of my experience. My best friend growing up went to an Ivy League university intending to major in History. He never took physics in high school at all, and took the equivalent of AP Calculus AB. He took no science or math courses in his first two years of college. As a first-semester junior, wanting to dispense with a hard-science distributional requirement, he took “Rocks For Jocks” (an introductory geology course for non-majors not known for its rigor). It changed his life. By the end of the course, all he wanted to study was geology. However, he had not completed a single course that counted towards the major requirements in the Geology Department.</p>
<p>The department worked with him to create a path by which he could complete a Geology major in three semesters. Some requirements were waived; he was permitted to take other courses out of sequence. He got a lot of advice in crafting a senior project he could handle. Did he have departmental honors when he graduated? No. Did he know less than perhaps every other Geology major our year? Probably. Did he go on to become a great academic geologist, or to do exploration for a major oil company? No, again.</p>
<p>He went to law school. He became an environmental litigator, and then a Senate staffer, and ultimately a senior staff person at a respected national science-oriented environmental nonprofit. His imperfect Geology major was a key to most of what he did in the next 25 years or so, and the passion he discovered as a late-to-the-party science major was the engine that produced an extremely satisfying career.</p>
<p>He was helped enormously, by the way, by being at an elite private university rather than a large public university. At most publics, doing what he did would have taken him an extra two years at least, maybe more if he had difficulty registering for the classes he needed. Few departments would have been as flexible as his was in helping him meet requirements. (It also helped, I’m sure, that Geology was a relatively small department at his college, with only about a dozen majors per class, and that he was an engaging, positive, energetic person – although not an academic star – who was good at recruiting allies.)</p>
<p>Anyway, my point is that you can get a lot out of doing what you want to do, if you do it intelligently and stay within yourself, even if you aren’t the Number One (or Two, or Three) student in your field.</p>
<p>JHS, my remark that you quoted wasn’t intended to be gratuitous snobbery–sorry if it came off that way. It is the same thing that I would tell anyone I cared about. They’d need to know what they are getting into.</p>
<p>Of course, it is possible to do useful things with a math/science degree, while remaining on math track a) at Harvard, or doing the equivalent elsewhere. I think this would be great preparation for a lawyer or a physician. I suspect that a person who did well on track a) could go into finance or a related field very successfully. It could also work for someone who wants to be a mathematician, and has a plan to make up the difference between tracks a) and c) at a later point.</p>
<p>Life is long and the undergrad period is short, so a lot can happen post-BA. I know an eminent molecular biologist who did undergrad work in literature at an Ivy and “converted” to science post-BA.</p>
<p>On the other hand, a student who wants to be a mathematician and takes track a) at Harvard might have a difficult time getting into a top-ranked grad program, directly out of the BA degree. I am not certain about this, but I suspect that it is generally true. I can say that a student who completed only the courses listed in the track a) BA degree would wind up taking “remedial” courses as an entering grad student in mathematics programs at some of the better large state universities. I am not saying this to be snobbish–I am reasonably certain that it is true, from conversations with a few math department chairmen.</p>
<p>Addendum: If I had written a bit longer posts (readers, in chorus, "Nooooooo . . . "), I would definitely have mentioned earlier on that considerations are different for someone who does not plan to do day-to-day work in math or physics, but wants to major in one of those fields as an undergrad, and then do work of another type, but drawing on the experience gained in the college program. Then the progress made during the undergrad program is paramount, and the level reached at the end of 4 years is much less important.</p>
<p>The person who would like to do math, or physics (or geology) on a day-to-day basis does need to catch up, though.</p>
<p>JHS–What advice would you give an aspiring cellist, who had played only the flute up to age 18? The OP’s situation is far from being that extreme, but the comparison is not totally off base.</p>
<p>Agreed, mini, and I am among them. I think that if the OP went to a less selective university and majored in math, the level reached after 4 years would probably wind up being somewhere between track a) and track c) at Harvard. So the OP would need to weigh the personal desirability of the various outcomes. I don’t want to actively advocate for the less prestigious choice, because it might not be the preferable one for the OP–but it might be. And if the OP could spend longer at the less prestigious place, that could really help in catching up, if that matters.</p>
<p>Obviously, I would say if you want to learn the cello, it’s a good time to start. Like you, I would also say don’t count on joining the Berlin Philharmonic as a cellist anytime soon. But, honestly, the same probably applies to your hypothetical student as a flautist. If the only reason to study an instrument is to perform professionally at the highest level, there are maybe 50-60 people/year, max, worldwide, who would even think of bothering with it.</p>
<p>Luckily, the math/science world can accommodate many more new entrants than the cello world, and hardly any of them are going to be the international creme de la creme.</p>
<p>By the way, I think you are being unintentionally snobby again with your comment about how someone who did well on the easy math track “could go into finance or a related field very successfully”. At some levels, of course that’s true. But the real math jocks in finance are real math jocks, not benchwarmers. I have a friend who has a math PhD from a top-10 program, and who had no interest whatsoever in finance until he decided he couldn’t stand being an academic any longer. He was hired by a financial firm that does almost all of its hiring among math PhDs and ABDs, and he was stunned at how interesting and challenging the work he was involved in after he was hired. (What he said was, “I’m really glad they are paying me, but I would probably do this for free if they asked. It’s that interesting.”)</p>
<p>What do you want to tell the OP? “You won’t be a good candidate for the math PhD program at MIT when you graduate, so you should go major in Graphic Novels now”? “You will never be first chair of the cello section in Berlin, so keep playing the flute even though you won’t succeed with that instrument, either”? That’s a really counterproductive message. Why not, “You are 17, so if there’s something you want to do, now is a great time to start. And don’t get bummed out because some other kids started when they were 13.”? If that “something” was Olympic swimming, he or she would be SOL. Luckily for the OP, though, what he or she wants to do CAN be started at 17, and without superhuman genius and stamina.</p>
<p>If someone who had not played the cello before age 18 wanted to major in cello performance, I don’t actually think that’s possible at any college I can think of, without taking some time off in the interim to gain the skill level that’s required. Of course, the person could start cello lessons at 18. The person might even become an extremely skilled cellist–possibly even a professional member of an orchestra. There are no outcomes that are closed off, but some of the routes to getting to the outcomes are closed off (i.e., go straight to college as a cello-performance major).</p>
<p>From other threads, I know that you, JHS, know a great deal more about mathematicians in finance than I do. I am not trying to downplay the intellectual firepower of some of the mathematicians in finance! On the other hand, I am guessing that some people are very successful in finance without being the best-prepared mathematicians in that field. Is this incorrect? If not, then finance would presumably be another field where the OP would need to catch up mathematically.</p>
<p>I started my contributions to the thread up front with an implicit suggestion for the OP: Namely, to think about a 5-year (or even 6-year) undergrad degree. This can put the OP on par with other strong bachelor’s-level mathematicians/physicists–of whom there are many more than 50 or 60 a year. I see advantages in this, if the OP is thinking of mathematics or physics as a career, for the long term. On the other hand, I also see advantages of “top” colleges, where 5 or 6 years is hard or impossible, not to mention financially draining (in the general case).</p>
<p>I don’t think we really disagree at all. I am certain you are right when you say that the path to a good-quality PhD program in math or physics probably isn’t a four-year path for the OP. I didn’t read the OP’s first post as saying “I want to get a math PhD from a top program,” however. What I read was “I have slotted myself as a humanities person through high school, and I haven’t taken calculus, but now I want to change direction. If I care about my GPA, is it a big mistake to go to a ‘reach’ college where I will be far behind some of the students, or should I go to a public university where there will be more students as underprepared as I?”</p>
<p>The OP isn’t thinking very clearly, but I didn’t think that we parents were thinking very clearly, either, in the responses we gave. There was a whole lot of explicit and implicit “Oooooh, you are far, far behind my advanced S or D.” There was a lot of “Use the academic support services provided when you take courses that are over your head.” There was a certain amount of “You aren’t worthy of a major research center,” and “How can you think of a STEM major if you didn’t even take AP Physics?” Also, people tended to support, or not to challenge, the wrongheaded notion that somehow the OP would be less far behind at a generic state school. </p>
<p>Now, far be it from me to tell people not to be humanities majors. I was a humanities major, and I did fine. I think being a humanities major is great. But I hate the thought of a 17 year-old thinking he or she is so far behind in math or science that a STEM major is forever barred – that’s just wrong, and terribly self-defeating. (My sister apparently felt that way, and then had a midlife crisis at 34, whereupon it emerged that she had spent the past 15 years regretting her failure to study science after 10th grade. Now she’s a 48-year-old ER physician. But that was a long, tough haul that would have been a lot easier if she hadn’t stereotyped herself out of her dreams at 17.)</p>
<p>I also hate the notion that if you are not at the front of the pack, you are a piece of crap who will never get a job or any happiness in life. That isn’t true either, although it may be true that some jobs ARE reserved for front-of-the-packers. There are fields where it is true, but they aren’t STEM. (Theater leaps to mind. And management consulting.) </p>
<p>Finally, I think the OP is probably wrong in thinking he or she will have an easier time in a STEM field at a large public vs. an elite private. From what I can tell, many public universities accept the idea that there will be unqualified kids in the classroom, and they will sink or swim, and if they sink they can drop out or become general studies majors and that’s OK. A gifted, advanced student at a public university can find myriad opportunities to learn and to shine, but a run-of-the-mill, behind student may experience triage. Meanwhile, at elite privates, they think it is their job to help students succeed in whatever field they want, and they have the resources to make that happen.</p>
<p>But you are certainly right that the OP needs to look inside and to figure out if he or she really wants to study math and science, or whether this is just a case of the grass looking greener on the other side of the fence.</p>
<p>I hope that my posts haven’t conveyed the idea that someone has to be at the front of the pack to have any happiness in life! I couldn’t claim to be there myself–at least, I couldn’t claim to be there with a straight face, or uncrossed fingers. </p>
<p>On the other hand, I think it is best for a math/science student to try to be as capable and knowledgeable as possible. Lately, I have encountered a few students who’ve had a hard time getting into the type of grad schools they’d like. For people who are closer to the math/physics hiring scene currently–outside of academia–what do the job prospects look like? In academia, they don’t look too good at the moment: typically there are 200+ applications for each beginning faculty position at Not-That-Great-State.</p>
<p>There are too many individual variables to say whether a prospective math/science major would be better off at an elite private or somewhere else, without more particulars. One of my friends was a top-flight science student coming out of high school (Westinghouse finalist, etc.), went to Harvard, and learned that scientists mainly come from the lower middle class; and while they tend not to stay there, it would be unusual to wind up much above upper middle class. She converted to a major in humanities pre-law. She is a partner in a major law firm, and must surely make at least 10 times my salary. If she had gone to a large state university, she might have stayed in science. There are pluses and minuses to either outcome. I personally am happier doing what I’m doing (ok, twinges of jealousy about the income, but I really do like my work), and I suspect she’s happier doing what she’s doing.</p>
<p>Some of the faculty at large public universities are as unconcerned as JHS indicates, about students leaving STEM fields. Others will work pretty hard to keep any serious student in the field. I’ve known a successful math major at my university recently, who started in pre-calculus mathematics as a freshman, and just kept going (took 5 or 6 years, though).</p>
<p>Oh, error: Make that at least 20 times my salary</p>
<p>Very good coments here, although I have to say that after reading everything now I am much more informed than before… But also much more undecided than before.</p>
<p>On the interest of better disclosure, let me say that the reach school I was mentioning is WUSTL.</p>
<p>Inpersonal: support support support! That is the key. Mom son is considering turning down some top-tier schools in chemical engineering to attend UMBC as a Meyerhoff Scholar – why? Support. Students who attend UMBC as a Meyerhoff are 5.3 times more likely to get their MD/PhD then those who turned down the program. Why? Support. As questions like what tutoring programs they have? Do they have mentorship? Can you get a personal advisor regarding your academic schedule? Do they offer free tutoring? Will they help you get research opportunitties/internships as an undergraduate? Ask for examples of students just like you and where are they? What are they doing. So many kids drop out of STEM/Hard science because they think it is too hard because they don’t have the support. Ask about class size? How many freshman do they retain? Is there support for a 5th year (Meyerhoff provides this if needed). Do you research before you pick a school.</p>
<p>I will give you first hand advice since I have a child at WUSTL who is finishing junior year double majoring in STEM and a social science. This was a valedictorian, national merit and a winner of one of WUSTL full tuition merit scholarship. The academic, especially in the math/science course are extremely tough (and I know because my husband is a physics professor). There were a couple kids with similar gpa/ranking that graduated the same year as my child and went to our state school and found the classes there challenging but manageable. Of course, it all depends on how hard you want to work and the finances should play a large role.</p>