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What's the highest level of math that math majors take at college?

  1. Jul 16, 2014 #1
    For example, the highest level of math that high school senior takes in high school is AP Calculus BC. But what's the highest level of math that math majors take in college? How about for engineering majors in college?
  2. jcsd
  3. Jul 16, 2014 #2
    Mathematics in high school is linearly ordered, for example you need to take algebra before calculus, and calculus is (usually) the end of the road.

    Things are very different in college. Sure, many subjects have prerequisites, but you cannot neatly order the subjects anymore. Things like abstract algebra and differential geometry are pretty independent. You can take both at the same time, or you can take one much later than the other (or not at all). So in fact, there are highest levels of math is many directions, there is not just one level of math that is the highest. For example, set theory and forcing might be one "highest level class", but "algebraic geometry" might be another.

    Also note that after a while, you are expected to self-study subjects, they don't get taught anymore.
  4. Jul 16, 2014 #3
    I see what you mean. Thank you.
  5. Jul 16, 2014 #4
    As to the engineering part of your question: it depends. Obviously, the average engineering student isn't going to learn as much math as a math major. However, the amount of math that an engineering student learns is going to vary a lot depending on the school, the specific program (e.g. civil, mechanical, electrical), and the student's own interest in mathematics.

    Also, I should note that it's a little misleading to talk about which subject engineers and math majors learn. In my electrical engineering curriculum, I learned complex analysis, but I didn't dive nearly as deep into the theorems/proofs as a math major would. Loosely, engineers are interested in how they can use theorems to solve problems, while mathematicians are interested in discovering and proving new theorems.
    Last edited: Jul 16, 2014
  6. Jul 16, 2014 #5
    From what I have seen, an electrical engineering major (which usually requires more math than others) needs the same math as a physics major. Algebra, Trigonometry, Calculus, Differential Equations and Linear Algebra. Often another math class or two can be taken for interest or specialty like Partial Differential Equations, Discrete Mathematics, Statistics, etc.
  7. Jul 17, 2014 #6
    Thank you, guys.
  8. Jul 17, 2014 #7


    Staff: Mentor

    It's virtually unlimited.

    But in my math degree you could, if you were considered a good student, take some masters level courses as an undergraduate. The toughest at my school at that time was what was called Analysis B which was on the applications of Hilbert spaces.

    No one really wanted to do it but in my year me and two friends of mine turned up for it. Normally the lecturer discouraged students from taking it due to its difficulty but was happy with the three of us. BTW it was no where near as hard as its reputation and the areas covered were mostly what we three wanted which centred around applications to numerical analysis - but we did other stuff as well.

  9. Jul 17, 2014 #8


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    bhobba, how could your school justify holding a class for only three students registered? Does any university allow this for graduate level or other highly advanced courses?
  10. Jul 18, 2014 #9
    I see what you mean, bhobba. Thanks.
  11. Jul 18, 2014 #10
    I realize we're talking "highest" and not "most difficult," so this is all true.

    But I think the general consensus among undergraduates is that Analysis is the most difficult math class you will take as an undergraduate, best postponed as long as possible for "mathematical maturity" reasons.

    -Dave K
  12. Jul 18, 2014 #11
    Yes, that's true of course. Not at all uncommon for undergraduates to do this. Lots of people also just sit in/audit graduate classes. There are also classes that are split between grads and undergrads.

    Sounds like he meant himself and two other undergraduates in a graduate course, and there were likely other graduate students in the course.
  13. Jul 18, 2014 #12


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    Maybe I did misunderstand.
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