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<p>It’s not like an accounting or physical therapy or tourism management major would never get to take a single English class or read another book ever again.</p>
<p>Besides, I would argue that most students are not actually passionate about academics anyway. They might find women’s studies less painful than vocational subjects, but they could go on and live perfectly happy and fulfilled lives if they chose another major.</p>
<p>You’re comparing taking a few advanced math courses at university to having a pHD, owning Apple and Microsoft, and being 10 feet tall? lol.</p>
<p>I’ve asserted since page 6 that I’ve taken advanced math courses. Diff EQ, multivariable calculus, and number theory. I’d already taken BC Calc, linear algebra/ geometry and all that junk in high school. Hardly comparable to a math major, but I’ve aced them all. Don’t believe me, I don’t care. it’s honestly not that impressive, but you apparently disagree. Well, thanks, I’m flattered lol.</p>
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<p>Perceptions of advanced vary widely.</p>
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<p>After taking these, you believe that every problem comes down to one
answer? Did you take any math courses where every class starts out with
doing a proof, homeworks were doing proofs, and tests were doing a few
proofs? Where the answer to problems were proofs and where there are
multiple correct answers?</p>
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<p>I guess I can understand why you think that advanced math is formulaic.
But there are a lot of other kinds of math out there that are not so
formulaic.</p>
<p>Honestly…nothing new of any value has been added to this thread in the last 10 or so pages. It’s time to just let it die…</p>
<p>“I have life experience.”
<p>“And I know the life experiences of a lot of people.”
<p>“Kids say things when they are children.”
<p>“Most do grow up at some point.”
<p>“If you are one of the few that plans to never grow up, then I guess you could be part of that small exception.”
<p>“But I don’t think so.”
<p>b@rium:
I agree most students aren’t interested in academics. So why have a system that forces them into universities? Give them trade schools where they can spend all day learning about stuff to make them better at doing jobs. If they need some theory, let them contract a course or two at a university, or have professors give visiting lectures. Professors love doing that kind of stuff. Why mix the two groups?</p>
<p>I understand what you’re saying — but only one math course I’ve taken focused on proofs - and that was high school geometry. The others used proofs as background, but no, you didn’t have to “create” the proofs yourself - how could you be expected to innovate and “prove” essential and innovative theories in mathematics out of thin air?</p>
<p>As a better test ---- I know it might be difficult to scour sources, but could you find a math problem in the fields I’ve mentioned, that DOES have multiple or separate complete answers? There are infinite problems that have a SET of answers, yes ---- but there is only one full answer that describes the full set of solutions — although many times, the answer is not even a set but only one expression.</p>
<p>EDIT: nevermind … I’ll try to let this thread die</p>
<p>The bottom line is that a certain degree only limits you if you allow it to. </p>
<p>And for the record, if everyone became engineers we would live in one really boring world. Think of your favorite TV shows, favorite movies, favorite books, the newspapers you might read. Think of the people who are going to teach your children in the future. For many, many of these people who create that world you have liberal arts degrees to thank.</p>
<p>Number theory is anything but formulaic. In a lot of ways number theory is the hardest kind of math there is.</p>
<p>You didn’t actually take Linear Algebra if the only class with proofs you’ve taken is Geometry. Linear Algebra is at least 50% proofs, and depending on the professor, it may be nearly entirely proof-based.</p>
<p>“how could you be expected to innovate and “prove” essential and innovative theories in mathematics out of thin air?”
<p>In all fairness, the proofs in LA tend to be on the formulaic side.</p>
<p>Is V a vector space? Oh God.</p>
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<p>You seemed to think that philosophy was dependent on logic, and I wanted to let you know that major schools of thought don’t center on logic. What’s the issue here? Can I not provide information without you getting all huffy about it?</p>
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<p>Depends on the level of the class. Whether something is a vector space is first week type stuff.</p>
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<p>Also first week</p>
<p>Here’s a more advanced example:
Let T be a normal operator on a fi nite-dimensional real inner product
space V such that the characteristic polynomial splits. Prove that V has
an orthonormal basis of eigenvectors of T, hence that T is self-adjoint.</p>
<p>“The liberal arts is historically a program of study exclusively for the very wealthy. It was a mark of wealth to not have to be concerned with accruing marketable skills.”</p>
<p>Not really accurate…</p>
<p>Does a solution exist ?
Must a solution exist ?
Is the solution set finite ?
OR
Why was it so damned hard to see that the fundamental theorem of calculus existed ?</p>
<p>Applied and theoretical math are very different; the latter feels like thought experiments – to me at least. Number theory is a completely different animal that demands intuition from the applicant to be fun. – thoughts from a decidedly non-mathematician.</p>
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Aren’t those trade schools called community colleges?</p>
<p>Currently the system forces students into a university that offers technical majors as well as liberal arts. Students are not forced into the liberal arts. In theory at least. In practice students are required to apply to technical/vocational/professional programs at the time of admission while liberal arts majors can apply undeclared. That might encourage too many students to go into the liberal arts. Why not just require everyone to declare a major upon admission? That might actually get students to reflect on why they are going to college before they spend $100,000 on tuition.</p>
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You sure that’s algebra and not analysis?</p>
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<p>Better yet, require no one to declare a major upon admission. Rather than have such a structure liberal arts core, that leaves little room for exploration, only require students to take the basic pre-reqs the first year and let them fill in the rest with whatever classes they feel like taking.</p>
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<p>Ironically, most of the best European and Asian universities, many of which are heavily subsidized, do that. Of course, the US also has a strange system with regards to the professions. With the exception of engineering and accountancy, law and medicine require post-graduate study, whereas you can start medical and legal education at the undergrad level in most other places…</p>
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And then award a degree for… unfocused exploratory study? I think that would achieve the opposite of making students reflect on what they want to get out of their education. Why have a goal if you can take it one semester at a time without any immediate repercussions? Also, how would professional licensing work in the absence of any sort of standards?</p>