Honors Calculus versus Honors Analysis

Colleges and Universities A-Z University of Chicago ✅
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<p>First, quick background on my math education in high school. I took pre-calculus as a freshman, BC Calculus in sophomore year with a 5 on the AP, and this weird course that was basically a mish-mosh of linear algebra and multivariable calculus with a sampler of complex analysis (I have no idea what my teacher was thinking) at the end of the year. </p>

<p>Up until BC Calculus I had a decent handle on everything, but my math class junior year was honestly a bit over my head, especially because I found that I had a much harder time grasping linear algebra than multivariable calculus, and my teacher took a fairly rigorous approach of actually going through vector spaces, matrices, linear transformations and all that fun stuff before going into stuff like total derivatives and then making all the connections. </p>

<p>Grade wise, I did fine because our class had insane curves (I usually got from 30%-50% correct on most tests and quizzes and somehow pulled off an A- for the year because grading was entirely relative) but a lot of it was honestly regurgitation. I would blindly memorize formulas and proofs for theorems and hope for the best. It really bothered me that unlike in BC calculus, I didn't know what I was doing. I think some of this was due to me being lazy in junior year but a lot of was also due to my teacher, who was notorious for being impossible to understand. In fact, about half of my classmates in that class were in the exact same situation as I was - getting fine grades but not having a clue what was going on. </p>

<p>I figured I had enough of that, so I took AP Stats senior year, which, as everyone told me, was WAY easier than any calculus course I'd ever taken, but still, I really enjoy the class and I've probably found it the most useful class I've ever taken. The thing is, I still feel like the last time I was in a math class where I was really in control of what was going on was in sophmore year. </p>

<p>So then I get into UChicago and I'm not sure what to do about math. Since I have a 5 on the AP I could just take Honors Calc, which I hear is a rigorous course, but part of me wants to push myself and dig back into Apostol (my BC Calculus class primarily used Apostol volume 1 while the class I took last year primarily used volume 2) and see if I can really see what's going on. I guess my concern is whether or not I'll be able to handle Honors Analysis IF I get in (I realize that's a BIG assumption - repeat, I realize it's big, not trying to be cocky). Still, I'd like to be prepared to make a decision rather than be caught surprised during O-week on the minute chance that I do well on the placement exam. </p>

<p>On the other hand, since the calculus placement exam is all single variable anyway, it wouldn't be too hard to just try to review all the major theorems. Should I go crazy and try to review multivariable as well? How much does being placed into Honors Analysis help in terms of (1) pursuing a math major (right now I'm looking at doubling in Math spec. Econ and Econ) and (2) career placement (potentially finance)?</p>

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<p>Taken from another post of mine:</p>

<p>One thing that is very poorly elaborated upon before O-week is how much different Honors Calculus 16100 is from the AP Calculus classes you’ve taken in high school, which leaves some very solid math students, who’ve gotten 5s on both calc AP tests, thinking that they’re bound for Honors Analysis in their first quarter.</p>

<p>So, to clarify: Honors Calc is absolutely NOT a step down, or even on the same plane (ha ha) as Calc AB/BC.</p>

<p>As one who went through the 160s sequence having gotten 5s in both AP calc tests, I found Honors Calc 161-2-3 to be ferociously difficult at points. It exposes you to aspects of math that you might be completely unfamiliar (or only marginally familiar) with. The class is 98% proofs and features some very tricky problem sets and exams. And the proofs are certainly different from the kinds of proofs you’ve been exposed to previously. </p>

<p>The standard text book for the Calc 160s sequence is Calculus (3rd edition) by Michael Spivak (it’s a step up from Apistol). Any folks who fancy themselves potential math majors would do well to, at the very least, find a copy of this book and flip through it in the next 6 months. That said, the vast majority of math majors start by taking Calc 161. And, to give you an idea of how far you can go starting with that, I have a friend whose path through UChicago math was Calc 161-2-3, Analysis 203-4-5, and then whatever followed, and she’s now on a full ride at Cornell getting her PhD in mathematics.</p>

<p>That said, somewhere between 10 and 15 first year students place into Honors Analysis (MATH 20700) each year, which is pretty phenomenal, considering that I’m certain that there are more than 15 math geniuses per entering class. In fact, the majority of math majors never end up taking Honors Analysis in any year. It’s not an insult to anyone’s intelligence - it’s just that advanced/selective of a class (there’s only one section).</p>

<p>Also, I know “it’s just that advanced of a class” might sound enticing, but Honors Analysis is really not worth even wanting to take in your first year unless you honestly consider yourself to be in the top 1% of UChicago’s entering class in math. Unless you’re in that 1%, there’s a good chance that 207 would be a bit over your head, you’d get frustrated, end up being asked to drop down, or fail and then <em>have</em> to drop down.</p>

<p>That said, I assure you, if you’re meant to take Honors Analysis your first year, you’ll place into it. </p>

<p>Just so I’m not all gloom and doom however, if you want to have a good shot at placing out of 160s (expanding upon kitkatkatie’s advice), you’ll find the 160s textbook - the aforementioned Spivak’s Calculus, a portion of which is on googlebooks - learn it all, and do all the problem sets at the end of each chapter. You have to be comfortable with all that material as well, because the math placement test is timed, and they don’t just ask you to recite proofs on the free response section…</p>

<p>If you do all that and don’t place out of 160s, you’ll have given yourself a running head start - and the 160s sequence tends to be taught by the best and the brightest.</p>

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<p>A couple of grace notes to UChicagoGrad’s excellent post that I’ve picked up along the way:</p>

<ol>
<li><p>It’s not just a question of 160s vs. 207. There are essentially three placement options BETWEEN those two poles (in addition to the four placement options below 160s – math placement at Chicago is a real exercise in fit). There are the inquiry-based learning sections of 160s, that could very well be called a separate course. There is Math 199, which is the gateway course to a math major for people who didn’t take 160s. And there are inquiry-based learning sections of Analysis. Some people who place into 207 choose one of those options instead if they don’t want to devote themselves to one course to the extent required by 207 (some of those other math geniuses UChicagoGrad talks about).</p></li>
<li><p>Trust the math department! They really know what they are doing, placement-wise. They aren’t about holding anyone back artificially, either. I have heard many UChicago students talk about arguing themselves into lower-level math placements because they were intimidated by the course they placed into. I haven’t heard anyone who thought the course he or she placed into was too easy or too repetitive of things already learned.</p></li>
</ol>

<p>Also recognize that unless you have a really strong theoretical background – you know who you are! – you are probably better off taking 160s. That’s how the program is designed, and it’s designed that way for a whole bunch of reasons. The LAST thing you want is to trick someone into placing you into an inappropriate class – you will wind up dropping back, but only after untold agony, and there may be an ugly mark on your transcript as a result.</p>

<ol>
<li> I know that some second-year students are (or have been) allowed to take 207, too, after 160s(IBL) their first year. If you really want that overwhelming experience, you don’t necessarily have to get placed there before you start.</li>
</ol>

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<p>Parent of a second-year math major here…</p>

<p>S1 had the option of taking Honors Analysis last year and turned it down to take IBL Analysis instead. (There is only one section of IBL Analysis, BTW). It’s more focused on self-directed learning where the students derive everything rather than having it taught to them, and covered pretty much everything HA did. Most of his math major friends started in 160s and found it kicked their butts, especially the Lin Alg parts, which Chicago includes in its calc sequence rather than as a separate course. If you like the IBL approach, there are one or two IBL 160s sections each quarter, too. </p>

<p>S spent a lot of time last year helping friends and housemates with 160s. If you have not done a lot of proof work, you are better off in the 160s or attempting placement in 199, which is a course designed to prepare you for the proofs required in the regular analysis sequence. OTOH, if you take the 160s you are supremely prepared for the next analysis sequence and as JHS mentioned, one can go from 160s to HA as a second year. </p>

<p>The math department advisors are fantastic. They encouraged S to sit on a couple of different sections in the first week before he committed to get a feel for the approach, difficulty, etc. S1 also recommends Spivak > Apostol (yellow pigs represent!), but then again, my mom got him the Princeton Companion to Mathematics and I though his head would explode from joy. YMMV!</p>

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<p>Brief correction:</p>

<p>I just noticed that Spivak is on its 4th edition (2008), so that’s the version Calc 161 would probably be using.</p>

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<p>Yeah, upon deeper reflection I think I’ve really only nominally taken classes beyond single variable calculus, and in hindsight the cost of overextending myself was that I haven’t been in a math class where I really learned math since my sophomore year. </p>

<p>I think for now I’ll do my due diligence and do my best to review single variable calculus (thanks UChicagoGrad, I will order a used version of spivak tonight) and see where that takes me. I didn’t realize the math dept. would be so helpful in placements, so this is wonderful. Thank you all!</p>

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<p>I did math specializing in CS and econ at Chicago. I took 160s my first year, honors analysis my 2nd year. In high school, I did differential and integral calculus junior year, and no calculus my senior year, only ap stats.</p>

<p>A few thoughts:</p>

<ol>
<li><p>All math at Chicago is theory based. Learn how to do proofs, it will serve you well. I spent the first two weeks in 160s learning how to prove stuff with my TA.</p></li>
<li><p>You should take honors analysis if you believe you are ready. It’s an awesome course, and really will teach you a lot. I took it and enjoyed it quite a bit. You learn a ton of stuff that will crop up in other classes (e.g. complex analysis, PDEs, topology, functional analysis etc.). Even if you place into regular analysis, you can ask the instructors for honors analysis very nicely and they may let you try it out for the first few weeks. </p></li>
</ol>

<p>So my advice would be: see if you can register for honors analysis, and sit in for at least 2-2.5 weeks. After 2 weeks decide if you want to continue or if you are more comfortable transferring into 160s. IIRC, you can still transfer or drop classes upto the end of week 3.</p>

<p>I’d recommend 160s calculus over regular analysis though, and then take honors analysis the following year.</p>

<p>Also - don’t buy rudin for honors analysis. It’s a damn expensive book and a waste of money. Spend $10 and get Kolmogorov and Fomin and then pick up a few other nice cheap books (I probably bought 5 different books for honors analysis that cost ~$8/piece).</p>

<ol>
<li><p>If you are a math major at chicago, econ is easy. I never spent more than an evening on a problem set in econ (except for honors econometrics)…</p></li>
<li><p>Take econometrics early…ideally in your 2nd or 3rd year if you can. It helps for doing econ research.</p></li>
<li><p>The subject matter has a big influence on the class, but the professor is even more important. If you can take a class from Fefferman, I’d highly recommend it - I had him for two courses. Sally is also pretty good, although he proceeds at a slower and more methodical pace.</p></li>
</ol>

<p>Anyway, honors analysis was awesome, I highly recommend it. But I wouldn’t do specialization in econ and an econ degree, it’s sort of a waste. You’re better off taking classes in stats or maybe CS to give yourself more breadth.</p>

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<p>Honors Analysis is meant to be HARD like on par with Harvard’s legendary “Math 55” hard. The problem I have in with the OP’s post and higher level math is about the when he mentions memorization and regurgitation, that type of math doesn’t cut it in Olympiad-style papers and I’m fairly certain that Honors Analysis is filled with ex-USAMOers if not ex-MOPers…</p>

<p>In any event the math placement people are very good at what they do. Wherever you are placed that is most likely the best class for you. The one hitch is that if you are placed in regular anaylsis you may wish to take honors calculus such that you could take honors analysis in sophomore year.</p>

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<p>My S never got to USAMO (didn’t care for competition-type problems), but loved proofs. Chicago 160s and Analysis is ALL about proofs. It is an entirely different way of thinking about math, and if you can deal with the abstraction, that portends well for one’s future as a math major. </p>

<p>No calculators allowed – but there is nothing you’d need one for anyway.</p>