What kind of things should I do to prepare for medical school?

Why do they teach the kind of math in school that doesn't even prepare you for university math?

• People choose to major in pure math at university because they were good at math in school but the math in school in very different than that at university and sadly many then change their major because they just couldn't handle stuff like abstract algebra, analysis, etc. If you were good at physics in school, you won't have much problems with physics at university either because you're only learning the same thing, only that it's of a more advance level but that's not so with math... at university it'll like you're given a new kind of beast to handle. Even if you did very well at math in school, there's no guarantee that you'll succeed at math in university too. So now my question is why don't they teach math that's similar to what you'll see/encounter at university at school? Wouldn't that help many to not make the wrong decision of choosing to major in pure math? At least people will have the right idea of what to expect to learn at univeristy and only those that really are good at pure math will then be choosing to study it more deeply at university?

• Answer:

  This is an unfortunate aspect of the mathematics curriculum, but I don't see a convincing way around it. As others have said, the math that is commonly taught pre-university is useful and necessary for many disciplines, and so must be taught first. For most people then, the most advanced math class that can be taken by the end of high school is some calculus, which is still (especially in high schools) primarily computational. Now if someone gets through calculus, usually the next course to be taken is a proofs course, which introduces the student to the abstraction that you're talking about. This kind of course is often treated as a "weed-out" course for math majors. Here is the first time a student sees if he/she can do abstract or "pure" mathematics. Hopefully this course is taken early enough that if the student cannot manage, then the option of changing major is open. At many universities, you don't have to drop the math major entirely; rather, you can opt for an "applied" math major. These courses focus more on the computational side of things, and are therefore relatively similar to the pre-university coursework. Ideally a prospective math student in high school would be told something like this, and would know to have other options in mind. Perhaps they should also be asked to try to understand the proofs given of elementary calculus facts; these are also a good introduction to abstraction. A student who cannot understand the formal epsilon-delta definition of limit should be aware that these are the types of abstract concepts that will arise in pure mathematics. Of course, to be good at abstract math you need to have been good at common math as well. Someone who struggles with algebra will (and I've seen plenty of this) have even more troubles with calculus. Also, I don't know that I fully agree with you that other subjects are immune to this phenomenon. Every subject gets more detailed and difficult as a student progresses. I might agree that pure math is a bit of a high hurdle, but students change majors for many reasons. Okay, that's enough rambling, now I'll get back to your specific questions. Why not teach abstract math pre-university? Because, largely, none of it makes any sense without some basic knowledge first. I don't think anyone at my high school would have taken an abstract algebra course, or at least they wouldn't have stayed in it long. It would be nice to hint to students in high school calculus (or precalculus?) that the proofs are the important part for a pure math major. Let me also say that, if a student starts in university with pure math, then realizes that abstraction is not for him/her, then it was not a waste! The math courses that have been taken can be helpful for many other disciplines. I mention applied math above, but of course calculus, differential equations, and basic logic (among many other possible lessons) can be useful for physics, chemistry, etc.