<p>I am a high school senior currently. I have a 5 on the AP Calc BC exam and want to take this course in my freshman first semester. If anyone has experience with the course or has heard about it, could you please take a few seconds to answer some questions? </p>
<li><p>If I am thinking about majoring in applied math, should I go step by step and take the intro calc course? The reason I want to skip ahead is because I feel I know the BC material pretty well and would also like to leave room for higher courses in the future. </p></li>
<li><p>How does an ‘honor’ course differ from just a ‘regular’ multiv calc course? Is it more proof-based? Does it require prior knowledge of multiv calculus?</p></li>
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<p>Honors Multivariable Calc is more proof based than regular Calc and is intended for math majors. If you’ll be majoring in Applied math it’s definitely not a bad idea. </p>
<p>A lot of people will tell you not skip classes and take Calc I and II first but if you’re confident you know the material then skip them, otherwise take Honors Single Variable Calculus and then Honors Multivariable Caclulus</p>
<p>I took Honors Multivariable Calculus my first semester so I’ll share my experiences:</p>
<p>First, I would argue that 211 is not really proof-based. Sure, you might see some proofs in class of Green’s theorem or Gauss’ theorem or whatever, but for the most part, the homework problems are computational. The difference between 211 and 202 (the regular one) is mainly in the material covered and the depth. Since 202 is geared more toward non-math people, they will cover more applications of the partial derivative and multiple integral, whereas 211 doesn’t. However, 211 also goes into a bit more depth, and finishes the semester with a brief look at differential forms and manifolds, wedge products, exterior derivatives, and the generalized Stokes theorem. 202 does not look at this. Andrew Salch is teaching 211 next semester, just like this semester, and from what I’ve heard, he’s good.</p>
<p>If you’re not going to major in math, you have no reason to take Honors Single Variable Calculus. In fact, that course would probably frustrate you since everything is proof-based. I think you should skip straight into 211. I had a 5 on AB (not BC!), skipped right into 211, and got an A+ (had to get my grade “uncovered”). So it is very possible to do well.</p>
<p>Another option is 212, which is Honors Linear Algebra. This is very proof-based and very different from calculus. You may want to take this at another time.</p>
<p>The professor determines how grades are given out. Some professors (such as Professor Ha, who’s actually leaving) have pre-determined grade ranges posted on the course website before the year even begins. Your grade is determined by what range you fall in. In other words, completely based on your own ability and no one else’s. Could those ranges be adjusted? Maybe, but probably not.</p>
<p>Others will look at the class grades as a whole and then determine the cutoffs, or how far above average one must be. Some professors set average at B-,B,B+, or somewhere in between and then go from there. It completely depends on the professor. I’ve never had Salch so I have no idea how he grades. I took it with Qiao Zhang (one of the best professors I ever had, left last year though). I’m not really sure how he doled out grades.</p>
<p>So to answer your question in short, it depends on the professor.</p>
<p>I took Honors Multivariable with Professor Wilkin 2 years ago, and it seems like the class really depends on the professor you took it with. As far as I recall, our homework sets would be pretty much proof based with not that much computation. (Not as proof-heavy as Honors Linear Algebra, where I probably didn’t see more than a handful of numbers all semester, but still pretty proof heavy)</p>
If you have a 5 on Calc BC, I would definitely recommend skipping Calculus I and II.
Honor Multivariable doesn’t require any previous knowledge of multivariable calculus. It’s just a lot more in depth, and at least for me, was a lot more proof based, though I guess that depends on the professor. I took Honors Linear Algebra my freshman year (under covered grades) and decided to take Honors Multivariable my sophomore year. I would only recommend taking Honors multivariable if you really love pure math. If you’re more interested in applied math, engineering etc, then maybe the regular class might be more useful. If I had to choose again, I’m not sure I would take the honors variant. While I thought Honors Linear Algebra was actually useful in my upper level engineering classes, the more advanced material I learned in Honors Multivariable, while it was interesting, wasn’t really used in the future. Ultimately, if you love math, you’ll enjoy the class, but if you’re not so sure you do, then the regular version will teach all you need to know for future classes.</p>
<p>Thanks for the responses so far - very helpful and insightful.</p>
<p>I have done almost no proofs in my life. Would it be wise to jump into a proof-heavy course without experience? Would it be possible for me to learn how to do proofs as I learn the course?</p>
<p>This is multivariable calculus, not analysis or algebra. If Salch has you do any proofs, they will be limited to verifying identities or formulas. In other words, doing algebra. For example, you might be asked to verify some relationship between divergence and curl or use Gauss’ theorem to verify the flux through a spherical shell. In other words, it is doubtful you will be asked to “prove Theorem 3.11” or something like that (in fact, Colley’s book, the one used in 211, does a pretty good job in proving most of the theorems presented).</p>
<p>I would not call 211 a “proof-heavy” course. Honors Linear Algebra (212) is certainly proof-heavy. I thought 212 was harder than 211 so if you want to take 212 under the covered grades. that’s entirely reasonable.</p>
<p>The thing with proofs is that while it takes time to learn them, the fundamental idea is not difficult. Basically, you have a collection of theorems and definitions and your goal is to get from point A (the assumptions) to point B, (the result). The hard part is figuring out which roads to take to get there (not all roads lead to Rome!). The other difficult part is being rigorous, which tends to frustrate people new to proof-writing. People tend to state thing that seem obvious to them. Unfortunately, unless it is a truly trivial statement, everything needs justification.</p>
<p>My son is a senior in HS, had Calc BC last year and now has Multivariable Calc (typically 88-90 average). He hasn’t thought that much yet about registration for JHU classes (still mired in his HS work). </p>
<p>When he gets to JHU (mechanical engineering), I think he is leaning towards skipping Calc 1 but probably taking Calc II. He’s mentioned that he wants to have a good foundation from JHU. He may have the same view regarding taking AP credit with Physics where he had Mechanics (5) and E&M (likely 5). </p>
<p>Also I don’t know what is the best use of the ‘covered grades’ policy. I also read here on CC about someone getting an A+ grade uncovered, had never heard of that before… If a first semester freshman does well, they can decide to use a course for the GPA?. </p>
<p>About that “uncovered”, I just mean that I got to see it. Unfortunately, it doesn’t count toward my actual GPA.</p>
<p>As I’ve said before, I’m in favor of people using AP credit to skip ahead in math. But not in physics, even if they have 5’s on both exams. The calc classes will be difficult, even Calc I and II with a 5 on BC but I think these people will be bored in these classes and it’s better to get the more advanced math for the engineering courses. Physics is a lot harder and I think it’s really important to have a good physics foundation.</p>
<p>Just to give my two cents, if you are definitely leaning towards applied math, you will have to take discrete math at some point - this course introduces basic proof techniques like direct, induction, contradiction, etc. Not sure how much benefit this would have, since I took non-honors multivariable, but it might be helpful to gain a feel for proofs, if you took say Discrete Math with Honors Multivariable, in the fall.</p>
<p>I don’t think it’s supposed to…discrete is, well, discrete. Not continuous. Calc is all about continuity.</p>
<p>Anyway, here’s my question: is the math and/or applied math program particularly strong at JHU? Would you consider it one of the school’s strongest programs? Do students go to Hopkins specifically to major in math/applied math?</p>
<p>Math/applied math are not among Hopkins’ more well-known programs (ie BME, anything bio, physics, writing sems, music, blah blah blah). However, I really like the pure math department and every year, one or two people plan to go to grad school for math. The classes are small and with maybe one or two exceptions, the professors are all really good. I am happy with the department.</p>
<p>To address your comment about calc being all about continuity, you can actually do some neat things with discontinuities. For example, countable sets can’t form a continuum, and a function is Riemann integrable if and only if it is discontinuous on a set of measure 0. While continuity is a nice property to have (and you often need it), it’s fun to throw away continuity and see what happens!</p>
<p>Are you a math major? And, uh, speaking of being overshadowed heehee: would you say the math/applied math departments are seriously overshadowed by “BME, anything bio, physics, writing sems, music…?”</p>
<p>Yes, I am a math major. Stop using the word “overshadowed” as it is meaningless. There are actually more math/applied math majors than you would think because many people double-major. Yes, there are more BME’s than math majors, but when you take upper-level courses, you’ll find that there are more than a handful of math majors at the school.</p>
<p>Now, a question on the difficulty of the courses: in the upper-level courses (what’s considered upper-level, anyway?), do you ever feel lost? I’ve heard of math majors just staying up all night with no clue how to solve the problems. Do you feel this way often? What do you do?</p>
<p>As there are only 4 300-level courses (Differential Equations, Number Theory, Honors Differential Equations, Methods of Complex Analysis), I would consider 400 and above upper-level. I have taken 3 upper-level courses so far (Honors Analysis I and II, Topology), and I registered for two more (Algebra I, Real Variables [graduate course in analysis]).</p>
<p>I have never felt completely lost in a class. Hard? Certainly. Undoable? Definitely not. If you stick with the problems, you will eventually make progress (I won’t guarantee that you solve every problem correctly, most people don’t). However, no one just looks at a set and says “This will take me an hour, it’s that easy.” There will be times when a single problem will take you 2 hours or more, but I’ve never pulled an all-nighter trying to solve a problem. And of the three classes I’ve taken, topology was by far the hardest.</p>
Unfortunately, it doesn’t count toward my actual GPA.</p>