<p>I'm a senior in HS, currently taking AP Calculus BC and AP Physics B, and while I don't struggle with these classes and have a passion for math, I'm worried by what I hear-- that the bridge from high school level math to college level is one that is extremely difficult to cross. Is this true? How much did you struggle with math classes in college?</p>
<p>Who told you this?</p>
<p>College math is much harder to me.</p>
<p>But I never took AP Math, so I don’t know about that. However I did better than a classmate who tested out of prereqs from AP Calculus.</p>
<p>It’s partially true, in the sense that basic analysis and algebra (groups, rings and fields, not symbolic manipulation) are proof-based courses, and not “computation/quantities” based like calculus and high school algebra. That can be a shock for many, though a few find it quite natural. The attrition rate in the first year of math is pretty high, because mathematics is not what many expect it to be for those who come unprepared. But if you have a passion for math I wouldn’t be too worried, except that your passion may be “challenged”, so to speak.</p>
<p>Pure math gets really abstract, and not everyone is quite prepared for just how weird and counter-intuitive things can get. However, once (if) you survive the shock, it’s usually not that bad, and then you have a wide variety of options, from the very pure to the very applied, and a strong theoretical base will help you conceptualize a lot of things abstractly and should give you good problem solving skills, as long as you keep in touch at least with the “real”, application side. I also recommend (in places where it’s not required still) for all math majors to take a few computer science courses (basic programming and algorithms).</p>
<p>How bad was it for myself? Well, my GPA dropped from the A/A+ range in high school to the B range in my first semester (with a C in Analysis I, that hurt, then again, I had 21% in the first midterm, though the prof said to the class, before handing them back “no, it’s not out of 25”), and I worked a lot more than in high school (really, back in high school, all I needed to do was to attend classes and pay attention to get A+, no studying necessary). My GPA slowly climbed back up over the years (I almost had a straight A semester in my last year), ending in between B+ and A- overall (slightly closer to the latter). I did go away from pure math (my original intent) more toward applied math and statistics, and ended up doing a PhD in stats (though in my bachelor, I had more applied and pure courses). I found the later courses much more interesting, and realized also some of those dry theoretical courses I had to go through at first would “pay off” later on.</p>
<p>No college program would allow you to take those classes without first being introduced to proofs; generally the topics covered in Algebra are briefly touched on in such a proof based class (with most of the prepatory groundwork for analysis having come from Calculus). </p>
<p>Realistically, Algebra should be the only difficult class to transition to, since its unlikely that you will have seen much of the material ahead of time (unless you take Linear Algebra and Number Theory first - which you totally should; LA in particular is a pre-req for algebra at my campus). Analysis is far easier than Algebra, and if you’ve done calculus and learned how to approach a proof - you’ve got all the tools you need.</p>
<p>Thanks everyone 
I think my first course I’m taking in college is going to be multivariate calculus, (hopefully at Berkeley). I’m prepared to work hard, so hopefully I shouldnt have too tough a time. Your replies were all very helpful!</p>
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<p>Well, I do come from a different system, but there was no formal proof-based course necessary for basic algebra and analysis. There were geometric proofs in the cegep linear algebra course (introduction to vectors, matrices and complex numbers) before university, but length segments on polygons are way less abstract than the epsilon-deltas of analysis and the groups and rings of algebra. My calculus courses were more theory based than the standard Stewart though. McGill does have a sink-or-swim attitude however, compared to many American universities.</p>
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<p>I don’t know why so many people find algebra tougher than analysis. To me it was the other way around (even though I had 3 courses of calculus before taking analysis). I fared way better in algebra, but in the end I had to take more analysis. It’s a shame, algebra was much more fun.</p>