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Is the Math/Science Taught at MIT, Caltech, etc. Harder?

  1. Dec 19, 2014 #1
    I'm currently in community college and will be transferring to a 4-year university hopefully in 2016. I'm wondering if the math and sciences taught at "big name" or "elite" colleges, such as MIT, Caltech, Princeton, Harvard, etc., are harder or more advanced than those same subjects taught at non-elite schools?

    I'm not at all suggesting that I will be transferring to one of these elite schools (I don't know where I'll be going yet). But I'm simply wondering about this topic, as someone who attends a community college and has heard it said before that our classes are "inferior" to those of "real" colleges. I'm wondering about whether there is this gap in expectations generally and, if so, how big that gap is between various academic institutions.

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  3. Dec 19, 2014 #2


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    Well not only is the material harder, the quality of students is an incredibly high. I'm currently a first year grad student (one of my best friends at another) at one of the schools you mentioned and a lot of my classmates went to two of the others. The students from these schools are incredibly intelligent, hardworking, and also very advanced course wise. For example, many grad students come in having taken a ton of grad courses. I came from another Ivy (top 20 in physics) and placed out of 4 of my required courses based on my precious grad coursework.

    MIT and Caltech are particularly grueling and require a very distinct personality type in order for a student to be happy and successful.
  4. Dec 19, 2014 #3
    Would you say it's the way the material is tested that is harder? ...The volume of the material? ...The content of the material itself? All of the above? o0) Just trying to get a better sense of what this difference entails.

    I do occasionally watch lectures on YouTube of MIT courses through the Open CourseWare channel. But since I haven't taken most of those subjects yet, I wouldn't even know whether they were harder than what I'd done at community college.
  5. Dec 19, 2014 #4
    All. People are smarter, more serious, work harder, teachers are better, more facilities, higher pace, more depth, more advanced courses, more research opportunities, etc.

    Education in the US isn't standardized. What is a college BSc in the US spreads from vocational education that isn't even worth a BSc degree to the very best education of the world.

    If you are at a truly lower level community college then the degree you are taking isn't even comparable to a physics degree from a top 50 world university. Two different worlds.
  6. Dec 19, 2014 #5
    Don't listen to the elitists harp about how much better they think their school is than yours. I've studied at top 5 universities and I've studied at an unranked university no one outside my state has ever heard of. As long as you do your homework and take what a professor says in class seriously, and you put in an appropriate time towards studying you will pass at whatever university you study at. For a given degree, you get the same education no matter where you go, as long as it's accredited. You will likely subjectively find the experience to be "harder" at a school like MIT because your classmates are all essentially valedictorians from whatever high school they came from. This tends to cause anxiety issues and self-doubt, but everyone goes through that. A person who graduates with a given set of knowledge from Princeton is no different than a person who graduates with that same set of knowledge from hillbilly state.

    One of the main reason these universities are lauded as "prestigious" is because of the insane amount of donations and funding that is given to their endowment by rich alumni, which tends to translate into better research facilities and more attractive salaries and benefits to attract superstar researchers. The actual teaching abilities of some of these people can be abysmal. I'm beginning to develop the philosophy at this stage in my life that there is no such thing as a "difficult" class - only classes which are not taught well enough. The most passionate mathematics teacher I have ever met is actually at my undergrad. He takes time out of his nights and weekends to individually teach advanced real analysis courses to aspiring graduate students, and has successfully gotten his students into programs like Cambridge's PhD in Mathematics. Try getting that level of input and teaching effort from your MIT professors.
  7. Dec 19, 2014 #6
    OP, from your post it seems like at some point you would love to be a part of a top tier school and that certainly can be done. Not all community colleges are created equal. Some are known for their academic rigor and some academically, are like taking a walk in the park. Assuming that in your case it is the former here is what I would do...
    1) Choose good but challenging professors who push you beyond your limits. ( our limits are preconceived anyways )
    2) Do much more than the allotted homework. Try to work through many more problems including the tough challenging problems. Meet your professors on a weekly basis in this regard. They would be more than willing to help you out.
    3) Go beyond the scope of the class, like solving challenging problems. learning new things related to that subject. For example when a thermodynamics course is taught to most premeds in general chemistry class, how many really think of thermodynamics from a biological perspective and relate it to the human body ,instead most try to memorize the equations and concepts with the hopes of getting a good grade.
    4) Use websites like MIT opencourseware to your advantage by attempting to solve homework problems and assignments allotted by them. You can also do online courses from top universities through websites like Coursera which is fantastic, plus it is free.
    5) Have this insatiable appetite to learn new things. Be like a sponge.
    Now, granted that the courses conducted at MIT, Caltech etc are going to be much harder because the average student body in these universities is going to be way different than that found in CC but a smart, ambitious student can definitely go to such a university and be successful. I have seen numerous people from my community college going to several ivy league schools and doing well. Good luck to you.
  8. Dec 19, 2014 #7
    I've always been of the opinion that someone who would be remarkably successful will be remarkably successful regardless of what school they go to. That said, schools like the ones you mentioned DO have the ability to increase the pacing of their courses because of the abilities of the students. As far as the essentials of any major go, I don't imagine those schools will provide any information another decent college would. The exceptions might be the research areas of the professors, the "name value" of the professors, and perhaps accessibility of graduate courses.
  9. Dec 19, 2014 #8


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    I completely disagree Hercuflea. As I remember, you are currently applying to grad school. It's not that there aren't many smart students at other schools, it's just that there is an incredibly high concentration of brilliant students at the schools mentioned which cannot be found at many places. In fact, I have spoken to a lot of students who have gone to top grad schools from less known undergrads, it's a major adjustment in the beginning even though most do go on to be very successful.

    It's also untrue that the professors at top schools only care about research and not teaching. Having been at two Ivy league institutions, most of my professors have been absolutely excellent and at the same time top in their respective fields.
  10. Dec 19, 2014 #9


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    the short answer is yes, courses are harder at elite schools, but the answer is more complicated than that. When I was there, there were non honors routine math courses at Harvard that were somewhat comparable to those at average universities, but there were also super advanced honors courses at Harvard that were light years ahead of anything at an average school. So the range at Harvard is greater. they do have a routine calculus class for pre med students or people who don't want the hardest math course in the country, but they also have math 55, and there is nothing like this at most schools, even good ones. If you only have a handful of super top students, as is the case at most schools, you cannot offer a whole course aimed just at them,

    From my experience as a student at Harvard and a professor at a good average state university, Harvard, MIT, .... are blessed with more well prepared, more motivated, and harder working students than we have at most places. Not necessarily smarter, as I have seen some of the smartest students at state school I have ever met. But they are not challenged as they would be at Harvard.

    There are exceptions. When I was a professor at Central Washington state college, I wanted to provide the best opportunity to my top students, so I taught an extra calculus class from Mike Spivak's book to the few who could handle it. I taught it free so my department did not mind that it only had three or four students. We went from that into Spivak's Differential Geometry as a seminar, and those students, and several faculty who attended, learned a lot.

    I also taught advanced calc once there from Spivak's Calculus on Manifolds, and although I blew away most of the class, one student who had enrolled during a hiatus from Notre Dame, liked it fine and went back to Notre Dame the next semester. But they never let me teach it at that level again, because for the other students it was inappropriate in the extreme. I once offered a class there, complex analysis, that only enrolled one student, as no others were up for it.

    So in any school you may find exceptional classes that some students will benefit from, almost as if they were at a top school, maybe moreso since they will be treated very personally.

    Many state schools have outstanding professors, e.g. my friend Ted Shifrin at UGA, who previously taught at MIT and Berkeley, and has offered advanced math classes at UGA to top students for years. But they may have to stop offering those classes soon, partly due to lack of demand.

    The one thing you may find at Harvard, MIT, etc... that you will probably not find at most other schools, is a super advanced class in which the professor who is a world expert in a topic teaches new material he/she actually created, and it just isn't known in that form to the rest of of us.

    E.g once in a graduate course on differential topology Raoul Bott wanted to present the proof of the Kodaira vanishing theorem, but he found the proof in Kodaira's book too tedious. I myself had slogged through that proof once in a seminar and I agree. But Bott simply made up another nicer proof. I recall his saying "to read that proof you have to have real stamina!"..pause..."I didn't have that"...great laughter..." so I used the principal bundle". There were Fields medalists sitting in that class with us to hear his lecture that day. This does not frequently happen everywhere I suspect, although even average state schools also have world experts on some topics.

    But most of those classes are not for most of us.
    Last edited: Dec 19, 2014
  11. Dec 19, 2014 #10


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    I will agree with most others that not all schools are created equal. Here is my anecdotal evidence: as a high schooler I took the full year intro chemistry sequence at the local state university (Central Washington University - where Mathwonk apparently taught for awhile!); this was taken by chem majors and was one of the major weed-out courses for pre-med students. When I went to college at a "lower" Ivy I knew I was underprepared in most subjects so re-took chemistry my first semester. I was an engineer so took the easier "chemistry for engineers" class; it covered more material in more depth in one semester than the full year-long sequence I had taken at Central. The chem for engineers class was NOT a weed-out course for anyone; it was not even "good enough" for pre-meds to take; it was just a typical class.

    Likewise in graduate school one of my advisors younger grad students did his undergrad at a small, relatively unknown university. He was drowning in graduate courses so I tried to help him out. It turned out that his electromagnetic theory background was awful (a problem if you are studying plasma physics!) - his full year upper division undergrad sequence covered less material than the first semester of the sequence I had taken. He had similar problems in other subjects. He simply was not prepared for grad school at that level. Hard work payed off and he eventually made up the deficiencies, but it was a long, hard slog.

    HOwever, I think both of these examples are a little extreme - both the "lesser" schools were pretty far down the ladder. I am convinced that most students can get a very good education in a large number of universities in the US if they work hard and take advantage of the available opportunities. For example, I would have had no use for Harvard's math 55 (I wouldn't have understood or passed the class!), but there are a few brilliant students around that may almost require that opportunity to thrive and make the most of their talents.

    Last edited: Dec 19, 2014
  12. Dec 20, 2014 #11


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    Not all community colleges are equal. I'm in a community college currently, and I don't feel that I lack a good physics professor. He has a bachelors from Northwestern and a PhD from the University of Chicago. He's been employed at Fermilab, Brookhaven, and several other big name private research facilities. He has a ton of published work on black holes and quantum cosmology. He was teaching at a top fifty 4 year university for about 4 years prior to coming here. I'm from a fairly small town in Northern Illinois, and he's originally from this area. He came back here because he missed the area and the small town life.

    There are some perks. I had some friends in my physics classes last year that have since transferred to UIUC. This last semester they were in the same course as me, but I was at my CC and they were at UIUC. They were in a giant lecture hall with 300+ people while I was in a classroom with only 12 students. I've talked to them several times since they transferred, and we've discussed some of the relevant material. There have been times that I had to explain things to them.

    Point being, you get out what you put in. No, a community college isn't going to compare to MIT or Caltech regardless. But they are not the dismal, 3rd world education that some people make them out to be. At least not in any universal sense. I feel lucky to have my current physics professor, and I know that I'll be prepared to move into the upper level course work at UIUC in the fall. I do a lot of extra work though. I have supplemental books that I study alongside the primary text, I do honors projects every semester, and I always work to really -understand- the material.
  13. Dec 20, 2014 #12


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    I think this is probably the main advantage at a top school if one is lucky, to see material that is not in any textbook, and a point of view that is only sketched in papers that one may miss if one doesn't know what one is looking for.
  14. Dec 20, 2014 #13


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    That is often one of the bigger differences.

    Another very large distinction between the two is that community colleges are obviously not research environments. Undergrads at 4 year universities typically have a lot of research opportunities available, many of which can even be taken for college credit. That's a big shortcoming of community colleges. It simply is not within the scope of the community college philosophy.

    However, I've managed to make up for it as much as I can. I've done some pretty extensive honors projects and I'm applying for a bunch of internships this summer. Either way, I'm ready to be transferring on to UIUC in the fall. It'll be nice to be in a bigger atmosphere.
  15. Dec 20, 2014 #14


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    Not a single thing you said is even remotely true. There are several (huge) advantages to doing undergrad at a top university for reasons that have already been stated multiple times in this thread and can be attested anecdotally by many people, myself included. You're just making blanket statements without any evidence to back them up.
  16. Dec 20, 2014 #15
    Like I said, in other countries they amount to completely different degrees and completely different job descriptions. People who do the lower level of education are a completely different type of person, and not just intellectually. You still get a BSc for that degree in international terms, but we still use their old names to differentiate them as they are not at all the same.

    Low level high school -> low level community college, then learning only really starts at the community college. That means that compared to other western countries, you are 2 years behind. Your real education only starts in the third year and your MSc.
    In the US for most children high school is more of an experience than a real education program. Much more emphasis on growing up, doing sports and all that.
    In other countries everyone who goes to a proper research university will have done the equivalent of AP Calculus/International Baccalaureate.

    At a lower level you can't do a physics oriented degree. You will be doing some engineering degree because the math is too hard and you will be working as a professional and not as a scientist/academic. Same in the US were many community colleges don't offer physics BSc programs. If they do, maybe they are an above the average CC? I guess this is also why every once in a while "Only a physics BSc" thing pops up. I guess that's not really a terminal degree and you neither learned a profession or learned to do cutting edge science.

    Do note that there is a lot in between the top schools and the local community college. US is really polarized in terms of quality of education, but there is still a middle ground.
    And MIT/Caltech are getting really extreme were only those that are both very gifted and very motivated(think obsessed) can make it.

    As for 'that you can make of it what you want it to be' by studying harder, sure. But you don't need to earn a degree to learn something. In the end a degree is also a guarantee you can give your employer that you have the skills you claim you have. And in the US the name and reputation of the school tells them what level they can expect the degree to be. In other countries, different children go into different levels of education. I think that in the US many people still don't complete any college degree but instead learn their skills in apprenticeship. In many other countries you always (try) to get a degree, no matter what job you want to do.

    This is why I am also often confused when people mention an engineer here. Do they mean a car mechanic or an electrician or some other tradesperson? Do they mean someone from a polytechnic or institute of technology? Or do they mean an academic engineering degree that prepares you for PhD work and publishing in scientific literature.

    Also note that all these ranking lists of top universities often ignore or undervalue the experience of (undergraduate) students.
    Last edited: Dec 20, 2014
  17. Dec 20, 2014 #16


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    In the US, community colleges are 2-year institutions that don't offer bachelor's degrees at all, only "associates degrees". However, classes taken at a community college can usually be used as "transfer credit" in a bachelor's degree program elsewhere, subject to whatever restrictions the second school imposes.

    Students often start at at a community college, take 2 years' worth of classes there, and then transfer to a 4-year college or university to finish a bachelor's degree, ideally in 2 more years. This probably doesn't happen very often with places like Harvard and MIT, though.
  18. Dec 20, 2014 #17
    Yeah, I've finished my BS and I'm working on an MS while applying to PhD programs. The question the OP has asked is difficult to answer in any quantifiable way. The best responses he will get are going to be anecdotal like all the previous comments. He asked if the material at these elite schools is "harder and more advanced." Well, with regards to "more advanced," like mathwonk and others said it's definitely possible to take advanced courses at these schools because they likely have the world expert in some advanced topic in-house who is willing to teach a course on it, in addition to the fact that there is significant undergraduate demand for advanced topics. So, the answer to the question about "more advanced" would be yes. At other state schools and CC's, many times there simply isn't enough demand for advanced special topics courses, but it is still possible for any individual student to pursue independent study under the supervision of a professor.

    However, a given difficulty level of material is just that - a constant. Can you really say that freshmen taking calculus out of, say, Spivak at Harvard are actually getting any more knowledge or are experiencing a "harder" class than someone learning out of Spivak at any other school? It really depends on the professor at the individual class level at that point. Some are hard-bleeps and some aren't. Granted, there may be a higher percentage of hard-bleeps at the elite schools because of the haughty mentality they tend to promote, but does this facilitate learning or does it only discourage would-be scientists and engineers from pursuing their dreams? If you know a topic then you know it, it doesn't matter where the knowledge came from.

    I'm not denying that there are greater "opportunities" at these elite schools, nor that is generally a higher quality pool of students there, nor am I denying that they are fantastic schools where one can get a fantastic education. I'm just saying that it's equally possible to get a fantastic education at an unknown school if you play your cards right. I went to a university that mostly only offered 4-year bachelor's degrees. It did not even have a physics department or major. However, by bugging the crap out of the few physics professors who were there, I was able to convince them to let me study advanced courses in a supervised fashion with them and I ended up getting a wonderful education out of it which led to knowing exactly what I wanted to do for my graduate research. When I was a transient student at Georgia Tech, the main lesson I learned was the institutional pressure on the professors to essentially sabotage the students' "raw" scores on exams by giving them exams that are impossible for a reasonable person to complete in the alotted time, only to "curve" the class back up to a pretty bell curve that looks nice on departmental reports. Call me crazy, but this method of "teaching" is the antithesis of education. It's institutionalized fraud and does nothing to help students learn and develop useful skills, which is ultimately the point of university. I learned next to nothing while I was there. The material I learned in my one-on-one directed study courses with professors and in my own independent study vastly outweighs anything I learned in an standardized classroom.

    I think that this is one of the main advantages of attending an elite university. But, I don't know if this answers the OP's question, which I interpreted as at a given level are the courses at Harvard, etc. necessarily more difficult than at a state school?

    My thoughts on this matter are summarized by QuantumCurt's words:

  19. Dec 20, 2014 #18


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    I still disagree. Even courses at the same level cover more material at elite schools. Just because they use the same textbooks sometimes doesn't mean they don't cover more material, including stuff that is not in the textbook. I've known people who transferred, it is definitely an adjustment. One guy who went from U Florida (a top state school) noticed a large difference in the curriculum when he transferred to an Ivy. Places like Harvard, MIT, and Chicago are at a whole other level, even including most state schools (probably in physics with the exception of schools with top grad programs like UCSB, Berkeley, Illinois, Michigan, and Texas.
  20. Dec 20, 2014 #19


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    @Hercuflea: thank you for a well reasoned and balanced post.
  21. Dec 20, 2014 #20


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    A lot of people talk about how transfer students coming from community colleges often struggle initially with the material after moving into a 4 year university. There's a lot of truth to this statement, but I don't think it can be stated in terms resembling a universal fact. What a lot of people neglect to consider is the fact that there's a lot more at work here than simply a transition from a CC to a university. There is also a transition from lower level courses to upper level courses. By the very nature of how the material progresses, the upper level material is more difficult. It is studied in greater depth, with more concepts, more difficult problems, and a higher level of abstraction. Many university students experience these same difficulties transitioning from the lower level courses to the upper level courses. This is why so many students end up ultimately switching their major in their junior year.

    I think arguments can be made both ways on this subject. Universities may have more specialized instructors, but they also have some drawbacks. An introductory physics class at most 4 year universities is going to have a few hundred students in it. As I mentioned previously, my physics class this last semester (Physics II - E&M) had 12 people in it. I'll have Modern Physics next semester, and the class will have 3 people in it. Yes. 3 people. While students at a university are typically a random face within the crowd in these introductory classes, community college students in the same classes are often known on both a first and last name basis by ALL of their professors. Individualized attention is a very big thing here.

    It's no mystery that a lot of community college students are less than stellar academically. These students often do transfer and perform horribly. There are a lot of reasons for students to attend a community college aside from poor academics. Financial situations sometimes necessitate it. I'm completing my first two years of college with zero student loan debt, and that's a big deal to me. Some community college students are incredibly academically gifted, and they're the ones that will move on and succeed. One of the transfer schools I was considering was UC Berkeley. It's ultimately going to be cost prohibitive for me since I live in Illinois (out of state rates are crazy), but I gained some very valuable information from considering it. I spoke with an admissions adviser there a couple of times, and one thing she said really stuck out. She said that they love their community college transfer students because they've found that they are often MORE prepared for upper level courses than the students that have attended UC Berkeley or other universities for all 4 years. She said that the CC transfer students are often a lot more motivated and ambitious. Clearly this is anecdotal, but hearing an adviser from one of the top schools in the world say this struck me as quite fascinating.
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