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realtalk-tj · 4 years

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Could you please explain in more detail what each of the math post-APs are and how easy/hard they are and how much work? Thanks!!

Response from Al:

This can be added on to, but I can describe how Multivariable Calculus is. First off, I want to say not anyone’s opinion should affect how difficult or easy a class would be for YOU. Ultimately, do the classes you’re interested in. Personally, I thought Calculus was cool as subject, so that’s why I pursued Multi. Multi. builds off of BC Calculus, Geometry, and even some of the linear algebra you learned from middle school (not to be confused with the Linear Algebra you can take at TJ), so as long as you have a good foundation in those subjects, I’m sure you’ll do well in Multi. Depending on your teacher, assessments may or may not be more challenging, and that’s why I strongly emphasize take the class only if you’re genuinely into it. Don’t take it because of peer pressure / because you want to stand out in colleges. I’ll let anyone add below.

Response from Flitwick:

Disclaimer: I feel like I’m not the most unbiased perspective on the difficulty of these math classes, and I have my own mathematical strong/weak points that will bleed into these descriptions. Take all of this with a grain of salt, and go to the curriculum fair for the classes you’re interested in! I’ve tried to make this not just what’s in the catalog/what you’ll hear at the curriculum fair, so hopefully, you can get a more complete view of what you’re in for.

Here’s my complete review of the post-AP math classes, and my experience while in the class/what I’ve heard from others who have taken the class. I’m not attaching a numerical scale for you to definitively rank these according to difficulty because that would be a drastic oversimplification of what the class is.

Multi: Your experience will vary based on the teacher, but you’ll experience the most natural continuation of calculus no matter who you get. In general, the material is mostly standardized (and you can find it online), but Osborne will do a bit more of a rigorous treatment and will present concepts in an order that “tells a more complete story,” so to speak.

The class feels a decent amount like BC at first, but the difficulty ramps up over time and you might have an even rougher time if you haven’t had a physics course yet when it comes to understanding some of the later parts of the course (vector fields and flux and all).

I’d say some of the things you learn can be seen as more procedural, i.e. you’ll get lots of problems in the style of “find/compute blah,” and it’s really easy to just memorize steps for specific kinds of problems. However, I would highly recommend that you don’t fall into this sort of mindset and understand what you’re doing, why you’re doing it, and how that’ll yield what you want to compute, etc.

Homework isn’t really checked, but you just gotta do it – practice makes better in this class.

Linear: This class is called “Matrix Algebra” in the catalog, but I find that title sort of misleading. Again, your experience will depend on who you get (see above for notes on that), but generally, expect a class that is much more focused on understanding intuitive concepts that you might have learned in Math 4/prior to this course, but that can be applied in a much broader context. You’ll start with a fairly simple question (i.e. what does it mean for a system of linear equations to have a solution?) and extend this question to ask/answer questions about linear transformations, vectors and the spaces in which they reside, and matrices.

A lot of the concepts/abstractions are probably easier to grasp for people who didn’t do as well in multi, and this I think is a perfectly natural thing! Linear concepts also lend themselves pretty well to visualization which is great for us visual learners too :)) The difficulty can come in understanding what terms mean/imply and what they don’t mean/imply, which turns into a lot of true/false at some points, and in the naturally large amount of arithmetic that just comes with dealing with matrices and stuff.

Same/similar notes on the homework situation as in Multi.

Concrete: Dr. White teaches this course, and it’s a great time! The course description in the catalog isn’t totally accurate - most of the focus of the first two main units are generally about counting things, and some of the stuff mentioned in the catalog (Catalan numbers, Stirling numbers) are presented as numbers that count stuff in different situations. The first unit focuses on a more constructive approach to counting, and it can be really hard to get used to that way of thinking - it’s sorta like math-competition problems, to a degree. The second unit does the same thing but from a more computational/analytic perspective. Towards the end, Mr. White will sort of cover whatever the class is interested in - we did a bit of group theory for counting at the end when I took it.

The workload is fairly light - a couple problem sets here and there to do, and a few tests, but nothing super regular. Classes are sometimes proofs, sometimes working on a problem in groups to get a feel for the style of thinking necessary for the class. if you’re responsible for taking notes for the class, you get a little bonus, but of course, it’s more work to learn/write in LaTeX. Assessments are more application, I guess - problems designed to show you’ve understood how to think in a combinatorial way.

Unfortunately, this course is not offered this year but hopefully it will be next year!

Prob Theory: Dr. White teaches this course this year, and the course’s focus is sort of in the name. The course covers probability and random variables, different kinds of distributions, sampling, expected value, decision theory, and some of the underlying math that forms the basis for statistics.

This course has much more structure, and they follow the textbook closely, supplemented by packets of problems. Like Concrete, lecture in class is more derivation/proof-based, and practice is done with the packets. Assessments are the same way as above. Personally, I feel this class is a bit more difficult/less intuitive compared to Concrete, but I haven’t taken it at the time of writing.

Edit (Spr. 2020) - It’s maybe a little more computational in terms of how it’s more difficult? There’s a lot of practice with a smaller set of concepts, but with a lot of applications.

AMT: Dr. Osborne teaches this course, and I think this course complements all the stuff you do math/physics-wise really well, even if you don’t take any of the above except multi. The class starts where BC ended (sequences + series), but it quickly transitions to using series to evaluate integrals. The second unit does a bit of the probability as well (and probability theory), but it’s quickly used as a gateway into thermodynamics, a physics topic not covered in any other class. The class ends with a very fast speed-run of the linear course (with one or two extra topics thrown in here and there).

The difficulty of this course comes from pace. The problem sets can get pretty long (with one every 1-2 weeks), but if you work at it and ask questions in class/through email whenever you get confused, you’ll be able to keep up with the material. The expressions you’ll have to work with might be intimidating sometimes, but Osborne presents a particular way of thinking that helps you get over that fear - which is nice! All assessments are take-home (with rules), and are written in the same style as problem sets and problems you do in class. The course can be a lot to handle, but if you stick with it, you’ll end up learning a lot that you might not have learned otherwise, all wrapped up in one semester.

Diffie: Dr. Osborne has historically taught this course, but this year’s been weird - Dr. J is teaching a section in the spring, while Dr. Osborne is teaching one in the fall. No idea if this trend will continue! Diffie is sort of what it says it is - it’s a class that focuses on solving differential equations with methods you can do by hand. Most of the class is “learning xx method to solve this kind of equation that comes up a lot,” and the things you have to solve get progressively more difficult/complex over the course of the semester, although the methods may vary in difficulty.

I think this is a pretty cool class, but like multi, the course can be sort of procedural. In particular, it can be challenging because it often invokes linear concepts to explain why a particular method works it does, but those lines of argument are often the most elegant. This class can also get pretty heavy on the computational side, which can be an issue.

Homework is mostly based in the textbook, and peter out in frequency as the semester progresses (although their length doesn’t really change/increases a little?). Overall, this is a “straightforward” course in the sense that there’s not as much nuance as some of these other classes, as the focus is generally on solving these problems/why they can be solved that way/when you can expect to find solutions, but that’s not to say it’s not hard.

Complex: I get really excited when talking about this class, but this is a very difficult one. Dr. Osborne has historically taught this course in the fall. This class is focused on how functions in the complex numbers work, and extending the notions of real-line calculus to them. In particular, as a result of this exploration, you’ll end up with a lot of surprising results that can be applied in a variety of ways, including the evaluation of integrals and sums in unconventional ways.

In some ways, this class can feel like multi/BC, but with a much higher focus on proofs and why things work the way they do because some of the biggest results you’ll get in the complex numbers will have no relation whatsoever to stuff in BC. Everything is built ground-up, and it can be really easy to be confused by the nuanced details. If you don’t remember anything about complex numbers, fear not! The class has an extra-long first unit for that very purpose, which is disproportionately long compared to the other units (especially the second, which takes twoish weeks, tops). Homework is mostly textbook-based, but there are a couple of worksheets in there (including the infamous Real Integral Sheet :o)

This course is up there for one of the most rewarding classes I’ve taken at TJ, but it’s a wild ride and you really have to know what things mean and where the nuances are cold.

#math #post-ap #complex #diffie #linear #multi #prob theory #concrete #amt

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